September 25, 2019 GammaFactory Proof-of-Principle Experiment LETTER OF INTENT GammaFactory StudyGroup Contact persons: M.W.Krasny,krasny@lpnhe.in2p3.fr,krasny@mail.cern.ch – GammaFactory team leader A. Martens, martens@lal.in2p3.fr – GammaFactoryPoP experiment spokesperson Y. Dutheil, yann.dutheil@cern.ch– GammaFactoryPoP study – CERN coordinator Glossary Some of the acronyms used in this letter are presented in the table below. Abbreviation Meaning AMO Atomic, Molecular and Optical physics AWAKE Advanced WAKEfeld Experiment BPM Beam Position Monitor BSM Beyond Standard Model CCD Charge-Coupled Device CKM Cabibbo–Kobayashi–Maskawa (matrix) CM Centre-of-Mass (frame) FEL Free-Electron Laser FP Fabry–Perot (interferometer) FPC Fabry–Perot Cavity GDR Giant Dipole Resonance GF Gamma Factory HEP High Energy Physics HiRadMat High Radiation to Materials HL-LHC High-Luminosity LHC IP Interaction Point IR Interaction Region LHC Large Hadron Collider at CERN LoI Letter of Intent LS2, LS3 Long Shutdown no. 2, 3 LSS Long Straight Section MD Machine Development NA North Area fx-target experiments at CERN: NA61/SHINE, NA62 and NA64 PBC Physics Beyond Colliders PIE Parasitic Ion/proton–Electron collider PoP Proof-of-Principle (experiment) PS Proton Synchrotron at CERN PSI Partially Stripped Ions R&D Research and Development RF Fadio Frequency RMS Root Mean Square SPS Super Proton Synchrotron at CERN SPSC SPS and PS Experiments Committee at CERN QED Quantum Electrodynamics TDR Technical Design Report .W Weinbergangle (mixing angle of electroweak interactions) YETS Year End Technical Stop Contents 1 Executivesummary ............................ 4 2 Introduction ............................... 6 3Key principles . . .. . .. .. . .. . .. . . . .. . .. . . . .. . . 8 3.1 Absorption and emission of photons by ultra-relativistic ions . . . . . . . . . . . . 8 3.2 Laser coolingof partially stripped ionbunches . . . . . . . . . . . . . . . . . 8 4 Physicsmotivation ............................ 10 4.1 Introductoryremarks .......................... 10 4.2 Atomicbeams ............................. 11 4.3 Gamma-raybeams ........................... 12 4.4 Secondarybeams............................ 14 4.5 Roadmapandstrategy .......................... 15 5 Challengesand accomplishments ...................... 15 5.1 Challenges.............................. 15 5.2 Accomplishmentstodate ......................... 16 6 ImplementationofPoP Experimentin SPS . . . . . . . . . . . . . . . . . . 18 6.1Overview............................... 18 6.1.1Keyexperimentalparameters ..................... 18 6.1.2 CompatibilitywithSPS operationmode . . . . . . . . . . . . . . . . . 18 6.1.3 Summaryofsubsystems....................... 19 6.1.4 Experimentalstagesand procedure . . . . . . . . . . . . . . . . . . . 21 6.2PartiallystrippedionbeamsinSPS ..................... 24 6.2.1 Ion StrippinginPStoSPSTransferLine. . . . . . . . . . . . . . . . . 25 6.2.2 Ion beam performance andbunch characteristics . . . . . . . . . . . . . . 25 6.2.3 Operational scenarios........................ 26 6.2.4 Locationfor InteractionRegion .................... 26 6.2.5 Beamcontrolanddiagnostics ..................... 29 6.2.6 Uncertainties, reproducibility, ripple and noise . . . . . . . . . . . . . . . 31 6.3 Opticalsystem............................. 32 6.3.1 Laser oscillatorandamplifer ..................... 32 6.3.2 Implementationoflasersystem .................... 33 6.3.3Fabry–Pérotcavitydesign ...................... 34 6.3.4 Laser-beam parameter optimisationatIP. . . . . . . . . . . . . . . . . 37 6.3.5 OpticalparametersatIP....................... 38 6.3.6 Integrationandfootprint....................... 39 6.3.7 Constraints on the synchronisation scheme . . . . . . . . . . . . . . . . 41 6.3.8 Radiationaspects ......................... 42 6.3.9 Required R&D and timescale for integration. . . . . . . . . . . . . . . . 43 6.4 DetectionofX-rayphotons ........................ 43 6.4.1 Simulations........................... 43 6.4.2 Photon detectors.......................... 47 6.5 Cooling............................... 50 7 Timeline,resourcesandorganisation. . . . . . . . . . . . . . . . . . . . . 51 7.1Timeline ............................... 51 7.1.1 Phase1: InitialStudies ....................... 51 7.1.2 Phase 2: SPS Proof-of-Principle Experiment . . . . . . . . . . . . . . . 51 7.1.3 Phase3: LHC Demonstrator Application. . . . . . . . . . . . . . . . . 54 7.2 Project resources ............................ 54 7.2.1 Budgetestimate.......................... 55 7.2.2 Manpowerestimate ........................ 56 7.3Organisationalaspectsandtasklist ..................... 56 7.3.1Taskbreakdown.......................... 57 8 Summary................................ 59 Appendices 60 1 GF community and expected participationin SPSPoP experiment . . . . . . . . 61 2 Photon absorption and emissionby ultra-relativistic partially stripped ions . . . . 63 2.1 Photonabsorptioncrosssection....................... 65 2.2 Estimateoftherequiredlaserenergy. . . . . . . . . . . . . . . . . . . . . 66 2.3 Saturationeffect ............................ 66 3 Simulationtools ............................. 68 3.1 GF-CMCC.............................. 68 3.2 GF-CAIN .............................. 68 3.3 GF-Python: Python-based simulation toolkit . . . . . . . . . . . . . . . . . . 69 3.4 Semi-analyticalapproach ......................... 70 1 Executive summary We propose an experiment to study collisions of a laser beam with ultra-relativistic atomic beam of Partially Stripped Ions (PSI), circulating in the SPS ring. It would be the frst collider experiment of photons from a laser beam with ultra-relativistic, .  1, atomic beams ever made. Over the years 2017 and 2018 the Gamma Factory (GF) study group, in the framework of the Physics Beyond Colliders (PBC) studies, demonstrated the capacity of the CERN accelerator complex to produce and store highly-charged atomic beams in its high-energy accelerator rings. The experiment proposed in this Letter of Intent (LoI) is the next natural step of the ongoing feasibility studies of the GF initiative for CERN [1–4]. It is a Proof-of-Principle (PoP) experiment designed to study the GF production schemeof X-raysatthe SPS.The outcomeof thisexperimentwould enableustoevaluatethe capacity of the GF scheme to produce unprecedented-intensity .-ray beams by a colliding laser beam with atomic beams stored in the LHC. The GF scheme is based on resonant excitation of the atoms with the laser beam tuned to the atomic transitions frequencies,followedby the processof spontaneous emissionof photons. The res­onant excitation of atomic levels of highly ionised atoms (ions) is possible due to the large energies of the ions generatinga Doppler frequencyboostofthe counter-propagating laser beam photonsbyafactor ofup to 2.. Spontaneously emitted photons produced in the direction of the ion beam, when seen in the laboratory frame,havetheir energy boostedbya furtherfactorof 2.. As a consequence the pro­cess of absorption and emission results in a frequencyboost of the incoming photon of up to 4.2 . In the GF scheme, the SPS (LHC) atomic beams play the role of passive photon frequency converters of eV-photons intokeV (MeV) X-rays(.-rays). For the concrete implementation of the GF scheme at the SPS we propose to collide a lithium­like lead, 208Pb79+, beam with 1034 nm photon beam generated by a pulsed laser, based on Yb-doped optical materials. The beam energy will be tuned to resonantly excite the 2s › 2p1/2 atomic transition1 of the 208Pb79+ atoms. Such a specifc choice of beam particles and a laser is purely technical. It minimises boththe necessaryworkandthe costoftheexperiment while remaining,asfarasthe tuning ofthe laserwavelengthtothe resonant atomic transitionis concerned, more challengingthanthe ultimate implementation of the GF .-ray production scheme at the LHC. Laser systems togetherwithFabry–Pérot(FP)opticalcavities, allowingto boostthepoweroflaser pulses,have alreadybeen implementedatDESYandKEK electronbeam storagerings[5,6]by teams including membersoftheGF group, withahighlevelof synergyfor manyofthe technical issues,likethe bunch-synchronisation scheme.Aspecifcityof hadron storageringsisthemuchhigherbeam rigidityin conjunction with the largerbunch lengths. Onthebasisofthe2018beam testswehavealreadydevelopedaschemeof producingandstoring the lithium-like lead beam in the SPS. Construction of a new Hz-frequency insertable stripper in the PS to SPS transfer line – planned already as a consolidation step of the CERN ion collision programme independentlyofthe present proposal –wouldallowusto operatethisbeam concurrentlywiththeproton or fully stripped lead beams by using a dedicated cycle, within the canonical SPS supercycle. The goals of the proposed experiment are: – Demonstrate integration and operation of a laser and a Fabry–Pérot cavity (FPC) in a hadron storage ring. – Benchmark simulations of atomic excitation rates. – Develop a collision scheme and implement the required operational tools that demonstrate agree­ment of spatial and temporal properties of the ion and laserbunches; match laser spectrum to the 1The atomic levels are described, throughout this document,byspecifying the orbital confguration of the outermost electron and the total angular momentum of the atom, J.For the nlJ level the outermost electron occupies the energylevel specifedby the principal quantum number n and has the orbital momentum l.For l = s, J-value representing the electron spin is omitted. atomicexcitation widthto demonstrate resonantexcitationofan adequate fractionoftheionbunch population; demonstrate reproducibility over manyaccelerator cycles. – Demonstrate laser and atomicbunches timing synchronisation. – Measure and characterise the photon fux from the spontaneous emission and unfold the spectrum of emitted X-rays. – Develop atomic and photon beams diagnostic methods. – Demonstrate laser cooling of relativistic beams and investigate different approaches. – Investigate feasibilityof atomicphysics measurementsin the ultra-relativistic regime. In addition to measurements related to the GF photon beam production scheme there are two particularly exciting perspectives, which may even infuence the ongoing and future CERN canonical research programme. Firstly, the resonant photon absorption and random emission naturally opens the path to a new technique of beam cooling. Methods of cooling of stationary atoms – exploiting internal degreesof freedomandtheDopplereffect–havebeen masteredoverthelastthree decadesbytheatomic physics community, and the elements of these cooling techniques could be implemented to the atomic beamsstoredintheSPSstoragering.Asuccessful demonstrationoftheDoppler beam-coolingofatomic beams at the SPS could open the possibility of injecting low-emittance beams of fully stripped isoscalar ions into the LHC. Such beams will be very important in the “precision measurement phase" of the LHC experimental programme. Secondly, the production of high-intensity photon beams may open a path to a muon collider based on electromagnetic production of low-emittance muon beams. It is estimated that three years will be needed for: the procurement and the “surface” tests of the vacuum chamber, the laser system, FPC and remote controls; the procurement of the photon-detector components; the construction of the new ion stripper and its installation in the PS–SPS beam transfer line; and for the installation of the vacuum chamber, the laser system, FPC and the photon-detection system in the Interaction Region (IR). The installations are foreseen to takea place during the 2021/22 and 2022/23 winterYear End Technical Stops (YETS). From the year 2022 onward, after the installation of the new stripper, the majority of the beam tests in SPS can take place inside a supercycle with other beams. Over the year 2022 it is planned to commission the photon detector and to fnalise the SPS beam characterisation. In 2023and2024,afterthe installationofthelaserandFPC,theplanistohaveaseriesofPoPrunstotalling about5weeksperyear,whichwouldbesplit betweentheexperiment commissioningwiththebeamand the measurements,andthe machinedevelopment(MD)periodsfor furtherexperimentdevelopment.The optimisation of particular aspects, like the photon-beam production effciency, or special measurements, like beam lifetime or beam blowup, might require a few dedicated runs with coastable beams. Beyond 2024, there will be an option for the laser system and photon detector upgrade over the long shutdown (LS3) period. The decision will be taken on the basis of the results of the 2023 and 2024 runs.Thegoalofsuchaphase2extensionwouldbetousetheGFPoPexperimentforthe atomicphysics research programme.If this optionis realised,theexperiment will remainintheSPSfortheLHCRun 4period scheduled from 2026 to 2029. The SPS PoP programme may therefore cover about a decade. The operational experience with the experiment, its results and their extrapolation to the LHC running conditions will be essential to assess the feasibility of an LHC-based photon beam production scheme. Theexisting PBC GammaFactory study group canbe considered asa proto-collaboration. Itis already signifcant in size and includes – in most of the PoP experiment domains – a requisite expertise. 2 Introduction The experimental studies of elementary particle collisions at the high energy frontier of the accelerator technologies have established, over the last century, the basic laws that govern our Universe at small distances. Each new generation of particle accelerators and particle colliders have delivered important discoveries. It is thus natural to continue the high-energy frontier path as the leading one in the High Energy Physics (HEP) research at CERN. The basic question which triggered the GF initiative is not whether this research path needs to be pursued – it certainly does –but if it is the most optimal onein the present phase of the HEP research in which: – a large number of theoretical model scenarios for Beyond the StandardModel (BSM) phenomena exist without pointing to the optimal energy and beam particles for the future particle collider to observe these phenomena, – the quantum feld theory framework providing the link between the results of precise measure­mentsof the quantum loop virtual phenomena andtheir (future) direct observation no longer pro­vides anysolid landmarks for predicted discoveries that are accessible for the present accelerator technologies or their incremental upgrades, – we do not have a mature, affordable technology to make a signifcant leap into high energy “terra incognita". The GammaFactory (GF) initiativeand its associated Proof-of-Principle (PoP)experiment, pre­sentedinthisLetterofIntent(LoI),targetanewand complementary researchpathwhichcanbepursued concurrently with the ongoing CERN research programme and in parallel to preparing a novel tech­nology for a cost-effcient return to the high-energy frontier research. Its primary goal is to extend the research scope of the existing world-unique CERN accelerator infrastructure. It is proposed at a cru­cial moment for CERN. The approval, fnancing and construction of CERN’s next high-energy frontier project will very likely be a lengthyprocess. It is also possible that the on-going LHC-based research program will reach earlier its discovery potential saturation. This generates an opportunity for novel research programmesin basicand applied science which could re-use CERN’sexistingfacilitiesinways and at levels that were not conceived when the machines were designed. The aim of the GF initiativeis to create newresearch tools, allowing to open new,cross-disciplinary research domains. This initiativewas presentedin[1] and subsequently endorsedby the CERN manage­ ment through the creation of the CERN GF study group, embedded within the Physics Beyond Colliders (PBC) studies framework. It proposes to produce, accelerate and store, for the frst time at high energy, atomic beams in the existing CERN accelerator complex. Excitation of their atomic degrees of freedom byphotonsfromalaserbeamis proposedtobeusedtoproducehigh intensityprimarybeamsofgamma rays and, in turn, secondary beams of polarised charged leptons, neutrinos, vector mesons, neutrons and radioactive ions. The GF goal is to establish a new, highly effcient scheme of converting the accelerator RF power,selectively,to these primary and secondary beams, making use of the large Lorentz relativistic factor. ofthe atomic beams which canbe storedinthe CERN storage rings.Ithasa potentialto achieve aleap,byseveral ordersof magnitude,in their intensity and/or brightness with respecttoexistingfa­cilities. The GF tools potentially available through the different primary and secondary beams will be applicabletoawiderangeofphysics communitiesand research programmes. The GF initiative enters a new research territory where new conceptual and technological chal­lenges have to be addressed to prove its technical feasibility. Its path from the initiative stage to the research project stageinvolves sixkeyR&D steps: 1. Demonstration of effcient production, acceleration and storage of atomic beams in the CERN accelerator complex. 2. Development of the requisite GF research programme simulation tools. 3. Successful execution of the GF PoP experiment in the SPS. 4. Building up the physics cases for the LHC-based GF research programme and attracting wide scientifc communities to use the GF tools in their respective research. 5. Extrapolation of the SPS PoP experiment results to the LHC case and realistic assessment of the performance fgures of the LHC-based GF programme. 6. Elaborationof theTechnical Design Report (TDR) for the LHC-basedGF research programme. The proposed six-step path to arrive at the feasibility proof of the GF concepts minimises both the infrastructure and hardware investments and interference with the ongoing CERN research programme. Alarge majority of the atomic-beam tests are planned to be executed and benchmarked at the SPS and subsequently extrapolated to the LHC running conditions. TheGFR&D programme startedin2017bycreatingtheGFstudygroupwithinthePBCframe­work. The GF study group, involving now 65 physicists and engineers representing 24 institutions in 10 countries, has already achieved the frst two of its milestones [7]. The next R&D step is the preparation and execution of the the GF PoP experiment at the CERN SPS to test the GF photon beam production scheme in collisions of relativistic atomic beams circulating in the SPS ring withlaser pulses. This LoI is our initial step towards achieving the third of the GF initiative milestones. Contrary to the frst two milestones, which were achieved within the PBC activities framework, by using the SPS and LHC Ma­chine Development periods for the requisite beam tests, reaching this milestone requires dedicated SPS running time and the incorporation of the laser system together with its associated FPC into the SPS accelerator ring. It thus requires a consideration and an approval process by the SPSC. The SPS PoP experiment plans to use the atomic beam of lithium-like lead, 208Pb79+, circulating in the SPS. The fully stripped lead beams are routinely accelerated in the CERN accelerators – it is only the electron stripping scheme in the PS-SPS transfer line which needs to be modifed. The optimal stripping scheme, to maximise the beam intensity of the 208Pb79+ beam, has already been developed and tested by the GF group together with the SPS operation team. The proposal is to place the laser system in an available location in the SPS tunnel in the LSS6 sector. We plan to use the 2s › 2p1/2 atomictransition, with the energy difference of 230.81 (5) eV, see section 6.1.1 andTable1for details. This transition can be excited with a 1034 nm pulsed laser by tuning the Lorentz .-factor of the stored SPS 208Pb79+ beam to the value of . . 96. The choices of the ion beam type and the atomic transition are tightly constrained by the present quality of the SPS vacuum system. The expected lifetime of such a beam in the SPS of about 100 seconds is comfortably larger than our estimated cooling time of such a beam of approximately 20 seconds. The 2s › 2p1/2 levell-transition width for the Li-like lead atoms, corresponding to the lifetime of the atomic excited state of 76.6 ps, is four orders of magnitude smaller than those for the n-level atomic transitions which are planned to be used to generate the GF photon beamsatthe LHC.Asa consequence,theSPSPoPexperiment will testthegamma-beam production scheme in a more challenging confguration than in the LHC case, providing an ideal testing ground for the LHC-based GF research programme. The SPS PoP experiment proposed in this LoI represents one of the six GF R&D steps which must be accomplished before the GF initiative becomes a CERN project. Its role, proposed set-up and goals for physics and accelerator technology can be best understood in the context of the overall scope of the GF initiative. Therefore, the discussion of the PoP experiment is preceded by presentations of the physics motivation driving the GF initiative, its R&D challenges and recent accomplishments. The concept and practical aspects of the PoP experiment (its integration into the SPS machine, the optical system, the secondary photon detection system, simulations of the collisions, the beam cooling and the detector response) are discussed in the implementation section of this document, with preliminary resources requirements and a tentative schedule. 3 Key principles The GF initiative proposes to use highly relativistic charged atomic beams and their resonant interactions with laser light. Atomicbeams,theprimaryGFbeams,are composedofionsfromwhichallbutafewelectrons have been strippedontheway betweenanionsourceandaringin whichtheyare stored, whichat CERN is the SPS or the LHC. In these synchrotrons, the beams can be stored at very high energies over a large rangeofthe Lorentzfactor: 30 <.< 3000,at highbunch intensities: 108 0)phase of the betatron oscillation is depicted on the left (a) (right (b)). The transverse cooling will occur in the case depicted on this fgure if more photons are emitted at x< 0 rather than at x> 0. (Adapted from [12].) 4 Physics motivation 4.1 Introductory remarks The physics motivation for the GF initiative is to open new research domains at CERN and to provide new type particle beams for the ongoing and future CERN research programme by using its existing ac­celerator infrastructurein unconventionalbutinnovativeway.TheGFgoalistoachieveasignifcantleap in their intensity, purity and energy range by using the high-energy atomic beams of partially stripped ions stored in the LHC rings. The GF is thus essentially the LHC-based research programme proposing a possible future exploitation scenario for this machine. It could be executed in parallel to the ongoing LHC research programme in a similar way as the already existing ion collision programme. Implementation of the GF at the LHC requires extensive R&D studies. Such studies, if conducted at the LHC, would require allocating a non-negligible fraction of its running time for the beam tests – unlikely to happen in the coming years. Since the dominant fraction of these implementation studies can bedoneattheSPSand subsequenlyextrapolatedtotheLHC running,we proposetheGFPoPexperiment tobedoneattheSPS.Thephysicsmotivationforthe SPS-basedexperimentisthus essentiallydrivenby the future LHC-based GF research programme. The future LHC-based GF research programme will exploit the following three broad categories of the GF beams: Atomic beams, Gamma-ray beams and Secondary beams. The atomic beams are the beams of partially stripped ions accelerated and stored in the LHC. Thegamma-ray beams can be pro­duced in the collisions of the atomic beams with the laser beams. The secondary beams can be produced in collisionsof the high-intensitygamma-ray beams with theexternal target(s). In Fig.3physics do­ mains which could proft from the availability of the GF beams are listed together with examples of the GF research highlights. The GF beams and the research highlights are discussed in the next section. Fig. 3: Physics domains and potential specifc research applications of the GF programme. 4.2 Atomic beams Beamsfor atomic, molecular and optical physics research High-energy beams of highly charged high-Z atoms, such ashydrogen-, helium-, or lithium-like lead, areof particular interest for the Atomic, Molecular and Optical (AMO)physics communitybuthave, so far,never been technologically accessible as tools for AMO research [13]. Their principal merits are the following: – strong electric feld binding the remaining electrons to the nucleus – larger by up to fve orders of magnitude with respect tohydrogen atoms – providing unprecedented sensitivity to QED-vacuum effects, – strong amplifcation of the weak-interaction effects – larger by up to nine orders of magnitude with respect tohydrogen atoms – allowing to study atomic and nuclear weak interactions with unprecedented precision, – straightforward interpretationofexperiments withhydrogen-likeor helium-likeatoms – simplicity and high-precision calculations are inaccessible for multi-electron atoms, – high-energy atomic transitions of highly charged ions, normally inaccessible with the existing lasers, can be excited owing to the Doppler effect – the large Lorentz .-factor of the ion beam compensates the ~ Z2 increase of the electron binding energies, – residual(orinjected)gas moleculesinthestorageringcouldbeusedtoexcitetheatoms,allowing for precise studies of their emission spectra. The AMO research highlights include: (1) studies of the basic laws of physics, (2) precise mea­surement of sin2 .W in the low-momentum-transfer regime, (3) measurements of the nuclear charge ra­dius and neutron skin depths in high-Z nuclei and (4) searches for dark matter particles using the AMO detection techniques which are complementary to those used in particle physics. The AMO research programme can be addressed already by the PoP experiment at the SPS. Isoscalar beamsfor precision electroweak physics at LHC Isoscalar nuclei such as Ca or O, containing the same number of protons and neutrons, are optimal for the LHC electroweak (EW) precision measurement programme. Thanks to their weak and strong isospin symmetry they allow to circumvent the dominant sources of uncertainties in the measurement of the EW parameters of the Standard Model [14–17]. The relationship between the W + , W - and Z bosons production spectra for isoscalar beams simplifes the use of the Z-boson as a precision ‘standard candle’ for the W -boson production processes [14]. As anexample, with isoscalar beams one could measure the W -bosonmassattheLHCwiththe precision betterthan 10 MeV [17]. However,their present production schemes result in luminosities which are much lower than can be achieved with protons, negating this advantage. For these relatively light ions, unlike Pb–Pb collisions, the nucleon–nucleon luminosity is not + limited by ee --pair production and electron capture or by electromagnetic dissociation, but by the beam emittanceandtheionbunch intensity.Areductionofthe beam emittance through cooling could allow for an increase of the nucleon–nucleon collision luminosity. The GF recipe to achieve this goal is to cool the partially-stripped atomic isoscalar beams in the SPS and, following the stripping of the remaining electrons in the transfer line between the SPS and the LHC, to collide the low emittance beams in the LHC. If the transverse beam emittance of the colliding LHC beams of Ca or O ions couldbe reducedbyafactorof 10, then the effective nucleon–nucleon luminosity in the Ca–Ca and O–O collision modeswould approach the nominal pp-collisions luminosity. ForCa–Ca collision mode, theaverage numberof beam-particle collisions perbunch crossing ., would always be smaller than 1 – even at the highest effective nucleon–nucleon luminosity. This represents another advantage of with respect to pp-collisions where it could reach the values of . = 100 at the highest pp-collision luminosity. Electron beamfor ep operation of LHC Thehydrogen-like or helium-like lead beams can be considered as the carriers of the effective electron beams circulating in the LHC rings. Collisions of such a beam with the counter propagating beam of protons can allow to observe both the proton–lead-nucleus and the electron–proton collisions in the LHC detectors. LHC could thus be operating as an effective parasitic electron–proton(ion) collider (PIE) [18]. The PIE ep collider could reach the centre-of-mass (CM) energy of 200 GeV and the luminosity of 1029 -2 cms-1, both inferior to the corresponding parameters of the HERA collider,but suffciently large to provide a precise, in situ, detector-dependent diagnostics of the emittance of partonic beams at the LHC, in the low Bjorken-x region, and a precise, percent-level, calibration of the luminosityof the proton– nucleus collisions at the LHC. Atomic beamsfor plasmawake-feld acceleration TheGF atomic beamshave been already usedbytheAWAKEexperimentto calibrateits electron spec­trometer withmonochromatic electrons attached to lead ions over their acceleration cycle and stripped offat the entry to the spectrometer [19]. Theyhave two other potential merits which can be evaluated and exploited in the future. The high-intensity atomic beams could be effcient drivers for hadron-beam­driven plasma wake-feld acceleration [20]. Beam cooling can reduce their emittance allowing for the increaseddensityofthedriverbeaminplasma, resultinginhigher accelerationrateofthe witnessbeam. In addition, atomic beams carry “ready-to-accelerate" electrons. These electronsexploited initially in the cooling process of the driver beam can be subsequently used – following their stripping – to form a precisely synchronised witnessbunch. Our preliminary studies show that the reduction of the beam emittance by at least an order of magnitude and cooling time below tens of seconds are feasible both for the SPS and LHC atomic beams. 4.3 Gamma-ray beams With the GF approach, the laser light excites a resonant atomic transition of a highly-charged relativistic ion resultingina spontaneously emitted photon.The frequencyboostisupto 4.2,so thata photon beam in a broad energy range reaching up to 400 MeV can be driven by the high-. CERN atomic beams. The resonant photon absorption cross sectionisuptoafactor 109 higher than for the inverse Compton photon scattering on point-likeelectrons and, asaconsequence, an atomic-beam-driven light source intensity can be higher than thatof electron-beam-driven onesbya largefactor. Gamma ray source The presently operating high-intensity Free Electron Laser (FEL) light sources produce photon beams up to the energies of . 25 keV. The GF photon beams could extend their energy range by four orders of magnitude with FEL-like beam intensities using the atomic beams stored in the LHC. While the FEL photon beams are optimal to study the atomic and molecular structure of matter, the GF beams would allow to resolve the structure of atomic nuclei. In addition, theyhave suffcient energies and intensities to produce secondary beams of matter particles. Low-intensity light sourcesin the MeV energy range have already been constructed and are still in operation in several countries. The highest fux which has been achieved sofar is 1010 photons per second. Alltheexistingfacilitiesrelyonthe processoftheinverse Compton scatteringofa laser beam on a highly relativistic electron beam. Since the cross section of the inverse Compton process is small, in the O(1 barn) range, in order to achieve the fux of 1010 photons per second, both the laser and energy recovery linac technologies have to be pushed to their technological limits. With short excited-state lifetimes, the GF photon-beam intensity is expected not to be limited by the laser-light intensitybutby theavailableRFpowerof the accelerator ringin which atomic beams are stored. For example, a fux of up to1017 photons emitted per second can, in principle, be reached for photon energies in the 10 MeV region already with the present 16 MV circumferential voltage of the LHCRF cavities. This photon fuxwouldbeafactorof 107 higher than that of the highest-intensity electron-beam-driven light source HI.S@Durham operating in the same energy regime. Such an intense photon fux, corresponding to up to 1024 photons per year, would sizeably in­creasethe sensitivityof searchesforveryweakly interactingdark matter particlesinthe “anthropologica” keV–MeV mass region, e.g. in a beam-dump, light-shining-through-the-wall type of experiment, using a broad-energy-band beam of the GF photons. Photon collision schemes Ahigh-intensityand high-brilliancephotonbeam producedbytheGFfacilitycanbeusedto conceive the frst realisation of two types of photon–photon colliders at CERN: – elastic photon scattering collider (below the threshold of producing matter particles), covering the range of CM energies of up to 100 keV, achievable in collisions of the GF photon beam with the laser beam stacked in a FPC, – matter particle producing collider covering the energy range of up to 800 MeV, achievable in collisions of the photon beam with its counter-propagating twin photon beam. Thefrstofthetwo colliderscanexplorethe domainof fundamentalQED measurements,suchas the elastic large-angle light-by-light scattering observed with a rate of up to . 1000 events per second. For comparison,onlytensofeventsofthistypeare detectedoveroneyearofthepresentLHCoperation. The second scheme, having suffcient energy to produce both opposite charge and colourless pairs of fermions (electron or muon) and opposite charge colour-carrying pairs of fermions (quarks) could explore colour-confnement phenomena at the colour-production threshold. Shouldanysignalof e.g.an axion-like particleora dark photonbe observedina shining-through­the-wallexperiment,oneoftheabovetwo colliderscouldbecomeaDarkMatter ProductionFactoryby maximising the resonant production rate of dark matter particles through a suitable narrow-band choice of photon energy. Finally, the photon beam could also collide with the LHC proton or ion beams. The CM energy range of the corresponding photon–proton and photon–nucleus colliders would be in the range of 4 - 60 GeV. 4.4 Secondary beams TheGF beamofgamma rays canbe usedto produce secondary beamsin collisions withanexternal target. Such a scheme represents a change of paradigm for the secondary beams production: from mining, in which the dominant fraction of the energy of the primary beams is wasted, to precision, or production-by-demand. The GF secondary beam production scheme is based on the peripheral, small-momentum-transfer electromagnetic collisions of its photon beam with atoms of the target material. As a consequence, a large fraction of the wall-plug power which needs to be delivered to the atomic beam storage ring for continuousproductionoftheprimaryphotonbeamcouldbe transmittedtoachosentypeofthesecondary beam. Such a scheme could reduce considerably the target heat load at a fxed intensity of the secondary beam,facilitating its design and circumventing the principal technological challenges whichlimit the intensities of the proton-beam-driven muon, neutrino and neutron beams. Polarised electron, positron and muon beams The high-intensityGF beamofgamma-rays couldbe converted intoa high-intensity beamof positrons and electrons. If the photon beam energy is tuned above the muon-pair production threshold, such a beam also contains a small admixture of µ + and µ -. Beams of different lepton favours could easily be separated using the time of fight method, since the produced electrons and positrons move with almost the speed of light while the GF muons are non-relativistic. Forthe resonant absorptionand subsequent spontaneous emissionofphotonsbyatomswithspin-0 nuclei which do not change their electrons-spin state, the initial polarisation of the laser beam is trans­ferred to the emitted photon beam. Circularly polarised photons, if converted to lepton-pairs in the electromagnetic feld of atoms (or nuclei), produce longitudinally polarised leptons. The target intensity of the GF source of polarised electrons/positrons is 1017 positrons per second, assuming the present CERN accelerator infrastructure and presently available laser technology. Such an intensity, if achieved, would be three orders of magnitude higher than that of the KEK positron source [21], and would largely satisfy the source requirements for the ILC and CLIC colliders, or for a future high-luminosity ep (eA)collider project based on an energy recovery linac. The target intensity of the GF beam of polarised muons is 1012 muons per second. If achieved, it would be four orders of magnitude higher than that of the .E4 beam [22]. Two schemes can be envisaged to reach such an intensity target. In the frst one, the energy of the photon beam is tuned to its maximal value and muon pairs are produced by photon conversions. For the LHC energies, this scheme requiresa signifcantleapinthe intensityand bandwidthofa dedicatedFEL sourceof ~ 100 nm photons and an upgrade of the circumferential voltage of the LHC RF system. Alternatively, positron bunches produced by a low-energy photon beam would have to be accelerated a the dedicated positron ringtothe energyexceedingthe muon-pair production thresholdin collisionswitha stationarytarget,i.e. 2 Ee ~ (2m µ)/(me) [23, 24]. For this scheme no LHC upgrade is necessary and the conventional laser technology is suffcient. The intensity of the muon beam in the abovetwoschemes will always be inferior to the proton-beam-driven muon sources. However, for both the above schemes the product of the muon source longitudinaland transverse emittanceswouldbe smallerbyat least four ordersof magnitude than that for the pion-decay-originated muons. The GF driven high-brilliance beams of polarised positrons and muonsmay thereforehelpto reactivate,inanewway,R&D programmeson:(1)theTeV-energy­scale muon collider, (2) the polarised lepton–hadron collider, (3) fxed-target Deep Inelastic Scattering (DIS)experiments and(4) the neutrinofactory. High-purity neutrino beams The low-emittance muon beams could be used to produce high-purity neutrino beams. Thanks to the ini­tial muon polarisation and the(V -A)-structure of the weak currents, muon-neutrino (muon-antineutrino) beams could be separated from the electron-antineutrino (electron-neutrino) admixture on the bases of their respective angular distributions. In addition, the neutrino and antineutrinobunches of each favour could be separated with nearly 100% effciencyusing their timing. The fuxes of the neutrino and an­tineutrino beams would be equal and theycould be predicted to a per-mille accuracy. The high-purity neutrino and antineutrino beams could be used e.g. for the precision measurements of the CP -violating phase in the neutrino CKM matrix. Neutron and radioactive ion beams TheenergyoftheGFphotonscouldbetunedtoexcitetheGiantDipole Resonance(GDR)orfssionres­onances of large-A nuclei, providing abundant sources of: (1) neutrons with the target intensity reaching 1015 neutrons per second (frst-generation neutrons), (2) radioactive and neutron-rich ions with the target intensity reaching 1014 isotopes per second. The above fuxes would approach those of other European projects under construction, suchasESS,FAIRandthe future EURISOLfacilities. Theadvantageofthe GF sources is their high effciency – almost 10% ofthe LHCRFpower canbe converted into thepower of the neutron and radioactive-ion beams. 4.5 Roadmap and strategy The phases of the GF studies and its milestones are discussed in details in Section 7.1. The implementa­ tionofthe LHC-basedGF research programmeis conditioned,ontheonehand,byasuccessfulexecution oftheSPSPoPexperimentandextrapolationofits resultstotheLHC conditionsand,ontheotherhand, by the schedule of the LHC operation. Our initial vision assumes a staged approach. In the frst stage, assuming a successful demonstration of the Doppler cooling capacity of the PSI beams by the PoP experiment, cooled ion beams would become available: for collisions at the LHC – decicatedto precisionEW measurementsandfortheAWAKEexperimentaslow-emittance plasma wake-feld driver beams. The GF helium(hydrogen)-like lead beam could also be injected to the LHC, following the LS3installation of the new beam collimators, for the operation of the LHC as an electron– proton collider. The second stage could start following the installation of the laser system in the LHC tunnel and would include production of the photon beams for dark matter searches, atomic physics programme and precision studies of non-linear QED. The production of the secondary beams could be realised in the third phase of the project. Realistically, it is unlikely that the second and the third stage of the GF research programme could start before the LS4 shutdown. This leaves a suffcient time for theexecutionoftheSPSPoPexperiment,extrapolationofits resultstotheLHC running,andforthe preparations for the LHC-based GF programme, respecting both the technical constraints identifed by the PoP experiment and the actual interests of the physics community. 5 Challenges and accomplishments 5.1 Challenges The existing CERN accelerator infrastructure has already demonstrated its capacity to produce, acceler­ateand storethefullyand partially strippedionsinits storagerings.Sofartheleadandxenonionshave been acceleratedand storedattheLHC,butanextensionoftheLHCion running programmeto include the oxygen, calcium or argon ions is already under discussion. The step to include the corresponding atomic beams of partially stripped ions requires only a minor conceptual and hardware investment with development of a new stripping scheme, and production and installation of new strippers in the beam transfer line(s).Severalfactorsmaylimitthe lifetimeofthe atomic beams:thevacuumquality, molecu­lar compositionsofthe residualgas, space-chargeeffects, intra-beam strippingand intra-beam scattering and the Stark effect. Laser systems together with FP optical cavities have already been implemented at DESY and KEK electronbeam storagerings[5,6]by teams including membersoftheGF group,withahighlevel of similarity for manyof the technical issues, like thebunch-synchronisation scheme.Aspecifc feature ofthehadronstorageringsisthemuchhigherbeamrigidityin conjunctionwiththelargerbunchlengths which complicates the design of the interaction region. The design needs to make the best compromise between matching the laser frequencybandwidth both to the width of the atomic excitation and to the momentum spread and angular dispersion of the ensemble of atomic particles. For the extreme case of the largest photon-beam energy and intensity, the maximal power of the GF photon beam may reach 0.1–1 MW. The exploitation of such a powerful photon beam produced in a superconducting storageringisanythingbutobvious,andits feasibility remainstobe demonstrated. The development of targets for the secondary beams will proft from the present development of the target designs and R&D on neutrino and neutron spallation sources. Using the photon instead of proton beams is, by far, more convenient – the targets will be thinner, with only a small fraction of energy wasted. An effcient separation scheme of the electron and positron beams from the muon beams will have to be developed. Another challenge is to develop, very often ab nihilo, the GF simulation software required to: (1) optimisethe strippingschemeof atoms,(2) describetheeffectofthevacuum qualityatvarious stagesof the acceleration of the atomic beams, (3) simulate the beam dynamics of the atomicbunches (betatron oscillations, intrabeam scattering, beam impedance, etc.), (4) simulate the collisions of the laser pulses withthe atomicbunches,(5)evaluatevarious beam-cooling scenariosand(6)studythe propertiesofthe primary and secondary beams. 5.2 Accomplishments to date The GF R&D programme started in 2017 and has already achieved the frst twoof its six milestones, with the successful SPS and LHC beam tests and the development of software tools for the beam tests and SPS experiment design. The achievements and lessons drawn are presented in the following sections. SPS and LHC beam tests in 2017 and 2018 In 2017 the 129Xe39+ atomic beam was accelerated, stored in the SPS and studied at different fat-top energies [25–27]. The lifetime was shown to be limited by electron stripping in collisions with residual gas. The analysisofthe measured lifetime constrainedthe molecular compositionofthe residualgasand allowedtheexpected lifetimesofthehydrogen-and helium-like lead beamstobe estimatedtoat least 100 seconds. With only 40 seconds needed to fll the SPS and to accelerate thebunches up to the LHC injection energy, this measurement-based prediction opened the possibility of injecting such beams to the LHC ring. In 2018, after the installation of a new aluminium stripper foil in the PS to SPS transfer line, both 208Pb81+ and 208Pb80+ beams were successfully injected to the SPS and accelerated to 270 GeV proton equivalent energy. The observed lifetimes of the 208Pb80+ and 208Pb81+ beams of, respectively, 350±50 and 600 ± 30 seconds agreed with our predictions based on the extrapolation from the 2017 129Xe39+ runs. The achieved intensities of the 208Pb81+ and 208Pb80+ beams were also in a good agreement with our expectations based on the calculations of the stripping effciencyfor the initial 208Pb54+ beam. Finally,and most importantly,the achievedbunch intensityofthe 208Pb81+ beam, of 8×109 unit electric charges,was comfortably higher thanthe minimum requiredfor monitoring suchbunchesintheSPSand the LHC. The 208Pb81+ beam was, later in 2018, injected into the LHC and ramped to a proton equivalent energy of 6.5 TeV [28]. The observed lifetime at top energy was ~ 40 hours, and with 6 bunches circulatingin the LHC the intensitywas7 × 109 unit charges perbunch. The principal outcome of the 2017 and 2018 GF test runs was the proof that the atomic beams can be formed, accelerated and stored in the existing CERN SPS and LHC rings. The majority of the operation aspects for such beams have been successfully tested. An important specifc achievement was to demonstrate thatbunches of 108 hydrogen-like lead atoms perbunch canbeeffciently produced and maintained at the LHC top energy with the lifetime and intensity fulflling the GF requirements. One of thepivotal conceptsoftheGF initiative – that relativistic atomic beams canbe produced, acceleratedand stored – has therefore already been experimentally proven. The tests also validated our initial software tools, which will be elaborated further to extrapolate the production effciencies of 208Pb81+ and 208Pb80+ to arbitrary species (characterised both by the nucleus charge and the number of attached electrons) and to predict their lifetimes in both the SPS and the LHC. Two outstanding issues were identifed in the 2017 and 2018 beam tests. Firstly, the lifetimes measuredintheSPSandthe inferredvacuum pressureand compositions indicate that, presently,onlythe high-Z atoms carrying electrons only on the K and L atomic shells can be effciently accelerated/stored in the SPS before being transferred to the LHC. Once injected into the LHC rings, where the residual gas pressureisafactor. 1000 lower than in the SPS rings, the beam lifetimes, even for low-Z atoms, satisfy witha large safetyfactor theGF requirements. The present poor SPSvacuum quality constraints the design of the SPS PoP experiment – both by reducing the type of atomic beams which can be used andbythe necessitytodevelopfast beam-cooling schemes, such thatthe cooling timeis signifcantly smaller than the beam lifetime. Secondly, the collimation effciencyfor the 208Pb81+ beam in LHC was, as expected, inferior to that for the fully stripped 208Pb82+ beam. The present LHC beam collimation system was not designed foratomicbeamsandisfarfrombeingoptimal,andmitigation strategiesareneededtoreducethemost critical losses. Initial simulations indicated that the likely reason for the poor collimation performance is the parastitic stripping action of the primary collimators. Simulations show that the TCLD collimator scheduled to be installed in LS2 can substantially reduce the losses, and preliminary calculations did not reveal anyshowstopper for reaching the nominal HL-LHC Pb intensity the 208Pb81+ ions. Alternative mitigation strategies, such as orbitbumps, will alsobeinvestigated. Development of software tools The GF programme to date has already required the development of new software tools to prepare the beam tests, to generalise their results to other beam species, to evaluate the intensity reach of the GF, to optimise the Interaction Point (IP) of the laser pulses and the atomicbunches, to study the internal dynamicsofthe atomicbunchesexposedto collisions withthe laser light,to optimisethe Doppler beam­cooling methods and to study the extraction and diagnostics of the GF primary and secondary beams. Existing software tools to study stripping of electrons in metallic foils and to study beam–gas col­lisions of highly charged ions [29] have been calibrated for their high-energy applications using striping effciencies and beam lifetimes measured at the SPS and at the LHC. Two parallel GF group projects are pursued to develop the requisite, new software tools for sim­ulation studies of the atomic beam dynamics: (1) based on a semi-analytical approach and (2) based on Monte Carlo techniques to study dynamics of individual atoms. The goal of these two projects is to sim­ulatethe timeevolutionofthe atomic-beambunch parametersexposedto collisions withthe laser beam – thebunch emittances, the energy spread and thebunch length – and to studyvarious beam-cooling scenarios. Several Monte Carlo generators are being developed independently within the GF group. They simulate the production of the photon beams in collisions of atomicbunches with the laser pulses. The major challenge for these developments is to incorporate, for the frst time, resonant atomic-physics processes into the frameworksdevelopedby the particlephysics community. 6 ImplementationofPoP Experimentin SPS 6.1 Overview The SPS PoP aims to demonstrate the feasibility of the most important aspects of the GF scheme. To provide a foundation for the main technological and accelerator concepts, an early choice was made to locate the experiment in the SPS tunnel on the circulating beam. The objectives of the experiment are: – Demonstrate integration and operation of a laser and a FPC in a hadron storage ring. – Benchmark simulations of atomic excitation rates. – Develop a collision scheme and implement the required operational tools that demonstrate agree­ment of spatial and temporal properties of the ion and laserbunches; match laser spectrum to the atomicexcitationwidthto demonstrate resonantexcitationofan adequate fractionoftheionbunch population; demonstrate reproducibility over manyaccelerator cycles. – Demonstrate laser pulse and PSIbunch timing synchronisation. – Measure and characterise the photon fux from the spontaneous emission and unfold the spectrum of emitted X-rays. – Develop atomic and photon beams diagnostic methods. – Demonstrate laser cooling of relativistic beams and investigate different approaches. – Investigate feasibility of relativistic atomic physics measurements. The proposed setup is based on an optical resonator, with the FPC constructed around the IP, with an optical length harmonicof the spacing betweenbunches. The laserwould pump this resonant cavity with a much higher frequencyof 40 MHz andmuchlowerpulse energyoftheorderofµJ, relying on a cavity Q-factor in the range of 10, 000 to provide the high photon fux needed at the interaction point. 6.1.1 Key experimental parameters With the available SPS magnetic rigidity, vacuum pressure and ion species, an extensive study of the available atomic transitions concluded that the PSI species should be the Li-like Pb (i.e. with a charge state of 79+), and that the transition to be excited by the photons should be the 2s › 2p1/2 transition. The most recent results on the calculated 2s › 2p transition energies for the Li-like Pb ion are collected in Table 1. The three latest calculations include the estimates of their uncertainty. The result of the measurement 2s › 2p3/2 transition energy is presented in the last line ofTable1 as an indication of the precision level of the corresponding calculations. Comparisons of the theoretical predictions and the experimental results for both the2s › 2p1/2 and 2s › 2p3/2 transitions areavailable only for the Li-like Xe.Four recent theoretical resultsare comparedwithexperimentaldata(lasttwolines)inTable2. 208Pb79+ We assume the 2s › 2p1/2 transition energy for the ion to be 230.81 (5) eV – the averagevalueof the calculation results presentedin Ref. [36] and Ref. [37] – and thelifetimeofexcited state .(2p1/2) to be 76.6 ps, from Ref. [36]. The full set of high-level parameters for the SPS PoP experiment used for simulations and the experiment design are summarisedinTable3. 6.1.2 Compatibility with SPS operation mode The GF PoP experiment can make use of a cycle within the normal SPS supercyle provided that the ion stripper foil can be moved in and out on a cycle-by-cycle basis (see Section 6.2.1) and also that any movable devices in the PoP experiment itself, like the X-ray detector, can be positioned outside the Table 1: Transition energies (eV) of the2s › 2p1/2 and 2s › 2p3/2 linesinthePb, Li-likeion.Todate thereis no measurement of the 2s › 2p1/2 energy. 2s › 2p1/2 2s › 2p3/2 year method reference 231.374 2642.297 1990 MCDF VP SE [30] 230.817 2641.980 1991 MCDF VP SE [31] 230.698 2641.989 1995 RCI QED NucPol [32] 231.16 2642.39 1996 3-rd order MBPT [33] 230.68 — 2010 RCI QED NucPol [34] 230.76(4) 2642.17(4) 2011 S-m. 2-l. NucPol [35] 230.823(47)(4) 2642.220(46)(4) 2018 RCI QED NucPol [36] 230.80(5) 2642.20(5) 2019 S-m. 2-l. NucPol [37] — 2642.26(10) 2008 EBIT (measured) [38] Table 2:Transition energies (eV) of the2s › 2p1/2 and 2s › 2p3/2 lines in the Xe, Li-like ion. 2s › 2p1/2 2s › 2p3/2 year method reference 119.84 119.82 119.83 119.82 — 119.820(8) 492.22 492.21 492.23 492.21 492.34(62) — 1993 1995 2010 2011 1992 2000 RCI QED NucPol RCI QED NucPol RCI QED NucPol S-matrix 2-loop NucPol Beam-foil (measured) Beam-foil (measured) [39] [32] [34] [35] [40] [41] aperture needed for all other beams (or left in safely for all beams). In addition, the prompt radiation environment produced by other beams must be acceptable for the laser and cavity electronics. Under these conditions a dedicated GF cycle could be used for the experiment with a fat-top length which could be up to ~ 10 s. For very specifc measurements that require long fat-top length a dedicated coasting beam cycle could be used (see Section 6.2.3). 6.1.3 Summary of subsystems Laser The seed laser for the FPC version is described in detail in Section 6.3.1. An Yb laser operating at the ffth sub-harmonic of the RF, approximately 40 MHz, and at a wavelength of 1034 nm is proposed, consistingofalowphasenoise oscillatorandtwo ampliferstagesdeliveringabout 50 W average power. Apulse stretcher and compressor together with tunable bandwidth flters are implemented to match the required spectral and temporal characteristics of the PSI beam. Resonant cavity The resonant cavity is described in detail in Section 6.3.3. The key features are a vertical crossing, with total cavity round-trip length L =7.5m (mirror spacing of 3.75 m), corresponding to a frequency of 40 MHz, with the length tunable to match the PSI revolution frequency. A two-mirror geometry is Table 3:SPS PoP experiment parameters. 208Pb79+ PSI beam m – ion mass 193.687 GeV/c2 E – mean energy 18.652 TeV . = E/mc2– mean Lorentz relativisticfactor 96.3 N – number ions perbunch 0.9 × 108 .E/E – RMS relative energy spread 2 × 10-4 n – normalised transverse emittance 1.5 mm mrad .x – RMS transverse size 1.047 mm .y – RMS transverse size 0.83 mm .z – RMSbunch length 6.3 cm Laser Infrared . – wavelength(~. – photon energy) 1034 nm(1.2 eV) ../. – RMS relative band spread 2 × 10-4 U – single pulse energy at IP 5 mJ .L –RMS transverse intensity distributionatIP(.L = wL/2) 0.65 mm .t – RMS pulse duration 2.8 ps .L – collision angle 2.6 deg Atomic transition of 208Pb79+ 2s › 2p1/2 ~.0 0 – resonance energy 230.81 eV .0 – mean lifetime of spontaneous emission 76.6 ps ~.max – maximum emitted photon energy 44.473 keV 1 proposed, with one motorised mirror. The mirrors will be placed inside the SPS vacuum, in a dedicated vessel which will contain the input and output windows. A crucial aspect for the integration of the laser cavity into the SPS is tokeep the impedance of the system low enough in order not to disturb the high-intensity proton beam runs. This will be accounted for at the design phase of the FPC and will be further validated with SPS experts and dedicated simulations to make sure that it complies with the SPS specifcations. In the current design of the FPC, an impedance shield is foreseen inside the vacuum vessel with two slots for the laser beam and RF contacts at the extremities. Photon detection The detection of the X-ray photons downstream of the interaction point will be performed with a ded­icated in-vacuum monitor. Since the excited-state lifetime has a decay length of ~ 2m, the fux and energy spectrum of the corresponding X-ray beam would depend on the distance from the IP to the po­sition of the detector. The number of X-ray photon produced is high and would allow different detector technologies to be considered, including scintillators coupled to photomultipliers or a CCD camera, or semiconductors, such as Silicon pixel detectors or diamond detectors. The instrument will need a rather large dynamic range, since the off-resonance X-ray fux will be up to several orders of magnitude lower than on resonance. Forthe initialexperiment,the baseline solutionistousea detectionsystemcomposedofa scintil­lating screen and a camera, see Section 6.4.2. This would provide a robust and simple solution that can be integrated into the accelerator beam line and its control system using technologies already available on the SPS. Synchronisation The laser and ionbunches require accurate and precise synchronisation. A new master RF oscillator at high frequency(for instance 400 MHz)can be used to lock both the laser and the SPS RF system. This system, similartotheoneusedfortheAWAKEexperiment,wouldprovide stableand reproducible synchronisation betweenthelaserpulseandtheionbunch.Avariablefnedelaywillberequiredtoallow the precise adjustment of the phasing between both beams. 6.1.4 Experimental stages and procedure The experimental procedure can be divided into two basic stages of “Resonance Finding” and “Opti­misation and Characterisation” to demonstrate the basic concept of resonant exciting highly relativistic atomic transitions and detecting the emitted photons, with two further stages of “Cooling” and “Atomic Physics” targeted at demonstrating the feasibility of specifc applications. Stage 1: Resonance fnding The natural resonance linewidth . is around 10-5 eV,which means that the rest-frame spread in resonant energiesinthe ensembleof ionsinthebunchis dominatedbythe Doppler broadening arising fromthe momentum spread. This is of the order of 0.05 eV for a RMS momentum spread .p/p of 2 × 10-4 . To maximise the fraction of the ions in resonance, a number of experimental parameters need to be tuned independently: – the relative timing between the laser pulse and the PSIbunch, referred to as the synchronisation; – thePSI beam energyto matchthe photon energyintheion reference frametothe central transition energy; – the spatial overlap between the ion and laser beams in the vertical and horizontal planes. The laser beam transverse size at the IP is .L =0.65 mm, comparable to the ion bunches of around .x =1.2 mm in the horizontal plane and .y =0.8 mm inthevertical one. The initial alignment of the PSI beam will make use of two BPMs located upstream and downstream of the laser cavity (see Secion6.2.5). TheseBPMswillbe fducialisedtothelasersystemto ensurearelative alignment between their electric centre and the design IP of .BPMs 0.1 mm. With a typical performance in the xy, fducial < measurement of a closed orbit these BPMs should measure the position of the PSI beam with an error .BPMs 0.1 mm. Therefore a conservative estimate of the total transverse initial misalignment xy, beam < between the laser and beam axis in the horizontal plane is .x< 0.2 mm. In the vertical plane the same initial misalignment of .y< 0.2 mm is considered. However, the laser axis crosses the ion beam axis with the design crossing angle of .L =2.6° in that plane which transformsavertical misalignment intoa longitudinal oneof .y › s< 4 mm. Depending on the model usedforthe interaction betweentheionbunchandthe laser, eitherof those quantitiesmaybe used. The controlof the temporaloverlap between the laser pulse and the ionbunchis critical andis further discussed in Section 6.3.7. This will be controlled by the SPS phasing or cogging system. The implementation couldbevery similartothe system alreadyin useforthe synchronisationoftheextracted bunch and laserof theAWAKEexperiment [42]. The proposed systemis discussedSection 6.2.5 and would ensure an initial timing offset .t< 0.5 ns. For the spectral overlap, the nominal RMS relative laser bandwidth of2 × 10-4 is identical to the RMS Doppler spread in theion beam of 2 × 10-4. The relative uncertainty in the calculated transition energy is around 2 × 10-4 or 46 meV in the ion reference frame. The central laser frequencywill be measured with a much better precision and can thus be neglected. The absolute relative SPS momentum stability is about 1 × 10-4, while the relative uncertainty on the absolute value is estimated at 3 × 10-4 [43,44]. It adds an absolute uncertainty on the energy of the photon in the ion reference frame of 69 meV. We also consider a misalignment of the laser cavity mirrors by0.25 mm causing a relative uncertainty on the interaction angle of 0.5% or .. =0.227 mrad and a shift in the energy of the photon in the ion reference frame of 1.2 meV.Overall,these combinetogiveatotal maximum(i.e.linearsum) uncertainty in the relative energy of 116 meV,or around±5 × 10-4 relative. Thereforea systematic scanoftheSPS PSI beam momentumin5stepsof 2 × 10-4 is assumed to be needed to bring the system into resonance and we can consider a relative energy offset of .E/E =2 × 10-4 . Thoseexpectedinitialoffsetsare summarisedinTable4.Overall,forthis initial resonancefnding, the spatial and timeoverlap between the PSIbunch and the laser pulseis ensuredby the laser cavity instrumentation and its accurate fducialisation. The matching of the PSI beam to the laser energy is accomplished by a small scan in beam momentum. Table 4:Initialoffsets between the ionbunch and the laser pulse. .x – Horizontal offset 0.2 mm .y –Vertical offset 0.2 mm .t –Timing offset 0.5 ns .E/E – Relative energy offset 2 × 10-4 In case excitation is not detected at this stage, for example because of a very large undetected systematic offset in the cavity BPM readings, twofallback scenarios could be implemented. The PSI beam could be diluted in every dimension in order to observe at least some photons. The SPS transverse damperandRF system canbe confguredto achievethe requiredblow-upinall6dimensions. Alterna­tively or in addition, systematic scans of the transverse beam position at the IP and energy of the PSI beam could be repeated until X-ray photons are detected. Stage 2: Optimisation and Characterisation Once an X-ray signal has been reliably detected, an optimisation routine can be deployed to maximise the signal, using the four parameters listedTable4and the X-ray detector signal as the observable. The advantagesofa numericalapproacharespeedand resiliencetoanysystematicdriftsorhiddendependen­cies. For instance, the relative timing is correlated to the vertical position of the IP. This optimisation is somewhatcomplicatedbythe naturaldecayofthePSI intensity,aneffectwhichwillneedtobefactored into the algorithm. An important part of the experiment will then consist in careful measurement of the dependencies of the observed signal on the parameters under control. For this PoP, the aim is to make measurements from which basic ‘physics’ parameters can be derived: reproducibility, stability, resonance width, res­onant frequency, cross section and excited-state lifetime. The possible observables are the X-ray fux and the X-ray energy spectrum, and the parameters that can be varied are the laser power, the laser–PSI phase, the laser–PSI offset in position and angle, the PSI relativistic .-factor (beam momentum), and the PSIbunch lengthand momentum spread. The responseoftheX-ray signaltothe controlledvariations in these parameters will be the basis for the determination of the physics parameters. Some time will be dedicated to measuring the reproducibility of the signal, both for the cycle-to­cycle stabilityandalsothe stabilityofthesignaldecaythroughthefll.Forthis,thetoolsalreadyinusein theSPSforthe analysisofthe harmonic contentoftheslowextractioncanbedeployed,againtakinginto accountthenaturalsignaldecay[45].Thiswillalsogive informationaboutthestabilityofthe resonance through the SPS fll, which will be affected by variations in the contributing machine parameters, like the momentum. Methods of untangling these variations from the signal reduction obtained through the PSI lifetime and emittance growth need to be developed, in order be able to properly measure the PSI lifetime. Calculations of the excitation cross section from the measurements will require absolute measure­ment of the fux, knowledge of the excited state lifetime, together with as precise as possible knowledge of the 6D PSI distribution, as well as the laser beam intensity distribution in space, time and energy at the IP. The measurement of the resonance width will be dominated by the Doppler broadening, and only the width of the ensemble (basically the momentum spread) can be characterised. The accuracyof the measurement of the resonant frequency(transition energy) will be determined by the momentum spread and distribution in the beam, as well as the knowledge of the SPS momentum and of the laser spectral distribution. Characterisation of the PSI beam size evolution through the fll in the different dimensions will be important. It may also be required to make systematic measurements of thebunch characteristics if thecycle-to-cyclevariationislarge,tofactoroutthe dependenceofthe measuredX-rayfuxonthose parameters. Stage 3: Cooling demonstration The feasibilityofcoolingwillbeinvestigatedoncethebasicsetupand optimisationis complete.Forthis, a precise relative alignment of the SPS momentum with the laser wavelength is needed to ensure that the optimum number of PSIs with positive momentum offset are excited, maximising the cooling rate (see Section 6.5). Achieving this precise alignment is likely to be somewhat delicate, and will rely on the previous measurements of stability and drift. If the machine is reproducible enough, the initial adjustment of the particle momentum would be enough. Otherwise, a precise scan of the momentum might be needed to fnd the resonance, maximising the X-ray fux to fx the optimum particle momentum. If this needs to be done for every cycle (for instance if the reproducibility is a sizeable fraction of the laser bandwidth) then an automatic tool will be needed. With a relative laser bandwidth of ~ 2 × 10-4 and the expected momentum reproducibility around an order of magnitude smaller, this should not be considered as an issue (see Section 6.2.6). Once optimised,the longitudinal cooling willbe observedasa reductioninbunch length,which could be detected in the SPS by the existing wall current monitor. The effects of the transverse cooling are more diffcult to observe as the reduction in emittance is expected to be slower. The transverse beam size monitor currently installed in the SPS, based on beamgas ionisation (BGI) [46], could be used for that purpose. Stage 4: Atomic Physics demonstration Thephase1photon detectorsetup discussedinSection6.4.2willallowustoenterthedomainofatomic physics measurements with ultra-relativistic atomic beams.Ameasurementofthe 2s › 2p1/2 transition energy will be the frst measurement of the “Lamb-like-shift" in high-Z Lithium-likeatomsbytheir direct excitation. Achievinganultimate measurement precisionof atomic transitionsin high-Z atoms belowthe 10-4 level,inphase2ofthePoPexperiment operation,wouldallowustostudythe relativistic,vacuum polarisation, electron–electron interaction and weak interaction effects with unprecedented precision. Initially,the measurement of the absolute SPS beam energy,using the present dedicated calibration techniques [43, 44], is expected to be accurate to 0.04% and will limit the precision of the absolute measurement of transition energies to that level. Otherfactors limiting the measurement precision that will have to be studied and taken into account are the RMS momentum spread in the beam of 0.02% and the imperfect knowledge of the detailed longitudinal distribution. Theymay limit the precision on the spectroscopicmeasurementataroundthesamelevel.Theimpactofthesefactorsareexpectedtobe largely reduced by Doppler cooling of the PSI beams. Other effects, like the PSI intensity decay and emittance growth, will also need to be studied and accounted for. The initial, phase 1, measurement of the excited-state lifetime with a single plane detector will be very crude. Its precise determination will require adding new detector planes at suitable spacing downstream and introducing the secondary photon collimation system allowing to separate early and late decaysofexcited atoms. This couldbe donein phase2of the PoPexperiment following the LS3 shutdown. In this phase, new techniques of absolute calibration of the SPS energy, based on dedicated SPS runs with low-Z PSI beams and/or with non-zero spin ions could also be employed to improve the precision of the atomic transition energies measurement below the 10-4 level. In the frst case, the SPS beam energy could be calibrated using calculated transition energies for low-Z atoms for which the relativistic, vacuum polarisation, electron–electron interaction and weak interaction effects can be neglected. In the second case, the measurement could be based on optical pumping of the nucleus po­larisation followedbythe measurementofthe nucleusspin precession. Finally, complementary methods developed for the calibration of the electron beam energy by Compton back-scattered laser photons at the VEPP-2000 electron-positron collider [47] could also be used. They were demonstrated to provide a 5 × 10-5 precision of the absolute energy calibration. Anotherexcitingphase2optionforthe atomicphysicsresearchwouldbetosearchforexotic excited states of the lithium-like lead atoms, in particular long-lived states which could be excited by beam-gas collisions. The photon detector system would have to be upgraded to measure single photons with high spacial and energy resolution. Finally,thephase2oftheexperimentmayinvolvea precise relative measurementofthediffer­encesinthe atomic energylevelsforthe fouravailable lead isotopes. These measurements couldprovide a precise insight into the internal structure of the nuclei. 6.2 Partially stripped ion beams in SPS The SPS presently operates at 450 GeV energy for the LHC proton injection and at 400 GeV for the Fixed-Target protons to the North Area (NA). In addition, ion species including fully-and partially­stripped 208Pbhavebeen acceleratedand transferredtotheNAandtheLHC.Forlongflls(coasts)where the fat-top length is greater than about 10 s, the proton energy is limited to 270 GeV (magnetic rigidity of 900 T m)by the maximum RMS power the network can supply for the SPS dipoles and quadrupoles. An important parameter for the Gamma Factory experiments is the average vacuum pressure, which determines the PSI lifetime – this is 1.2 × 10-8 mbar, since the SPS vacuum system is not baked out.Themain parametersoftheSPS accelerator pertainingtothePoPexperimentareshowninTable5. Table 5:SPS accelerator parameters. Circumference 6911.566 m (208Pb79+ .96) frev 43 373 Hz fRF (208Pb79+ .96) 200.384 MHz Transition. 22.7 Transverse horizontal tune 26.13 Transverse vertical tune 26.18 Maximum magnetic rigidity (cycled) 1498.2 Tm Maximum magnetic rigidity (coast) 900 Tm Average vacuum pressure 1.2 × 10-8 mBar Annual total operational time 5150 h Annual physics (FT) time 3200 h Annual dedicated machine development time 370 h Fig. 4: Transmission effciencysimulations usingBREIT for the production of 208Pb80+and 208Pb81+.Athinner foil of about 70 µm will be used for a 35% yield of 208Pb79+. The plot also shows the measured values during the SPS tests in 2018, black cross for 208Pb80+and red cross for 208Pb81+ . 6.2.1 Ion StrippinginPStoSPSTransferLine The minimum solution to deliver the beam of the 208Pb79+ ions to the SPS is based on the existing stripper infrastructure and on the present scheme for the fully stripped ion beam. The existing stripper station in the PS–SPS transfer line will have to be equipped with a new foil which can be retracted every supercycle for the other beam types. The foil material and thickness should maximisethe production rate of the 208Pb79+ ionsby stripping25 electronsof the initial 208Pb54+ ions delivered by the PS beam. One of the multiple goals of the beam tests with 208Pb81+ and 208Pb80+,discussed in Section 5.2, was to calibrate the BREIT simulation code [48]. This code was then used to defne the requisite stripper material and the stripper thickness. In Fig.4the measured stripping effciencies for the 208Pb81+ and 208Pb80+ beams with the initial beam of 208Pb54+ are shown. Three versions of the BREIT code, ad­justed to describe the measurements, were used to extrapolate these results to the case of the 208Pb79+ beam and to defne the optimal thickness of the Aluminium foil and its uncertainty. The maximum stripping effciency(208Pb79+ production fraction) which can be achieved is 35%. 6.2.2 Ionbeamperformanceandbunchcharacteristics For the proposed stripping scenario the characteristics of the atomic beam of the208Pb79+ ions can be unambiguously extrapolated from the typical beam conditions in the SPS during the canonical operation of the beam of the fully stripped lead ions. Table6 shows the relevant beam parametersexpected for the PoPexperiment. The longitudinal parameters are achieved witha totalRFgapvoltageof 7 MV. Lower voltages down to ~ 2 MV are possibleto achievealower momentum spread,attheexpenseofthelargerbunch length. Concerning the bunch pattern, two scenarios are possible and both were used in 2018 for the fully stripped lead beam [49]: –4bunches separatedby100 ns andupto9injections separatedby 150 ns, –3bunches separatedby75 ns and up to 12 injections separated by 150 ns. Thesetwoschemes seedifferent spacing betweenbunches.Asystem runningat leastat 40 MHz wouldbe capableof interacting witheverybunch. The ionsperbunchat injectionis derived fromthe LIU target [50] (seeTable 2.4 therein), scaledby the transmissioneffciencyof 208Pb79+ . Table 6:208Pb79+ bunch parametersintheSPS.Ionsperbunchat injectionis calculatedfromtheLIUtargetbunch intensityinSPS[50]forthefully strippedleadions, scaledbythe strippingeffciencyof 208Pb79+calculated using BREIT and shown in Fig. 4. Transverse normalised emittance 1.5 mm mrad Bunch length 213 ps Momentum spread 2 × 10-4 Expected lifetime 100 s Ions perbunch at injection 0.9 × 108 Maximum numberofbunchesin the ring 36 6.2.3 Operational scenarios The SPS is a cycling machine serving different users from cycle to cycle according to a programmable sequence which is called the supercycle. The proposed experiment will require a short cycle within the SPS supercycle to do most of the beam commissioning and measurements. In case acceleration up to different energies is needed, each fat-top energy will correspond to a different cycle. This operational scenario has been already demonstrated during the 2017 and 2018 beam tests. Only for specifc measurements orin the case the resonant fnding procedure that require tospend more than 10 s at fat-top, a dedicated coasting beam cycle could be used. The maximum acceptable RMS resistive power dissipated in the main dipole magnets for the SPS is 37.9 MW, while the total maximum power for the main dipoles and the main quadrupoles is 44 MW. This constraint may, for large momentum beams, limit the possible supercycle combinations, and also the allowed maximum fat-top length. This is illustrated in Fig. 5. The beam can be coasted for indefnite periods only if the momentum of the beam particles satisfes the condition: p . 270 ZGeV/c, which corresponds to the maximal value of . = 110 for 208Pb79+. For the 208Pb79+ beam having its momentum tuned to excite the 2s › 2p1/2 atomic transition . = 96.3. The fat-top length for such a beam is thus not constrained by the maximal value of the power dissipated in the SPS magnets. 6.2.4 Locationfor Interaction Region The SPS has six Long Straight Sections (LSS), each with four dipole-free half cells with about 30 m drift space.Attheextremitiesof eachLSSa dispersion suppression cellhas2missing dipolesattheendof the frst arc cell with a drift space of around 13 m. Much of the LSS space is taken up with the existing equipment (RF in LSS3, injection in LSS1, dump in LSS5, slow extraction in LSS2). The main criteria for the selection of suitable locations are: – nomajor changescanbemadetotheSPS lattice(main magnets,keyfunctional elements); – the installed equipment must be compatible with aperture required for the Fixed-Target and LHC beams; – the radiation environment should be as low as possible (prompt and residual); –a locationwithstrongbumper magnetsis preferredfor steeringbeamathigh energy. Fig. 5: The maximum possible SPS fat-top length as a function of beam momentum, respecting the power limits in the main magnets.For 208Pb79+ a momentum of 280 ZGeV/c corresponds toa . of 114, for whicha maximum fat-top length of around 200 s would be possible. Locations on the LSS were investigated frst, and the half-cell 621 has been selected in the drift left by the missing dipoles for the dispersion suppressor. The location is free of other devices and can make useofthestrongdipole(extractionbumper)magnetsusedto establishtheSPSextraction trajectory. Fig.6ashowsatopviewoftheregion withtheSPS tunnel,the TT60 lineforfastextractionof the SPS beam towards the LHC or HighRadMat and the TI18 side tunnel. This tunnel was used for transferring positronsfromtheSPStotheLEP,andisnowempty.Asitliesvery closetotheSPSringit is proposed to be used to house the laser electronics in order to shield it from radiation coming from the SPS(see Section6.3.8).In addition,theexisting penetrations betweentheSPSandtheside tunnelcould be used to transport the primary laser beam to the laser cavity – theycan be seen on the top left corner of Fig. 6b. Optical lattice parameters at IP The optics assumed for the GF PoP experiment is based on an integer tune of 26 (Q26) and is standard forthePbion beamsfortheLHCandtheNA.The optics parametersattheIP are listedTable7, together with the RMS beam sizes obtained with the beam parameters inTable 6. The beam size, divergence, dispersion and dispersion derivative are all important for the dynamics of the laser–PSI interaction. Layout and aperture constraints Figure7showstheevolutionofthe beam sizeand optical functions aroundthe proposedPoPexperiment location. To ensure that the PoP does not interfere with nominal SPS operation we consider the space around the reference beam axis that needs to bekept free of anyelement, the stay-clear region. In the horizontal plane this region is computed based on the maximum excursions of: – injected proton fxed target beam at 14 GeV and the 12 mm mrad normalised emittance plus the alignment error and tolerances; – slowly extracted separatrix with 400 GeV protons on the 1/3 resonance (asymmetric); – thebumped orextracted beam, although nota concernin the dispersion suppressor region. Intheverticalplaneonlythe injectedprotonfxedtargetat 14 GeV and the 8 mm mrad normalised (a) (b) Fig. 6: (a) The schematic view around the SPS half-cell 621 with the proton beam going from right to left and (b) panoramic picture taken from downstream the cell. The green-dashed box represents the location considered for the laser cavity and the red-dashed box the projected location of the optical room located in TI18 on the SPS wall. The optical room is represented with a flled greyrectangle on the schematic view (a). Some approximate lengths are also given. emittance is considered, with the alignment error and tolerances. The resulting stay-clear regions in each plane is shown as dotted lines in Fig. 7. The aperture of the SPS magnetic elements is sized to roughly follow the envelope of the largest beams accelerated and we can see that the stay-clear region is very close to the apertures of the elements on either sides of the dispersion suppressor. In details, the stay­clear region is 90 mm × 45 mm (for horizontal and vertical planes) at the entrance of the laser cavity and 108 mm × 38 mm at theexit. At the location considered for the X-ray detector(s = 6458 m)the stay-clear region is 118 mm × 34 mm. Table 7:Optical parameters at the IP in the half-cell 621. s Azimuthal position 6451 m .x = -1 .ßx/.s -1.549 2 ßx 55.32 m Dx 2.462 m DPx 0.0976 .y = -1 .ßy/.s 1.301 2 ßy 43.87 m Dy 0.0 m DPy 0.0 q .px = x.x +(.p/pDPx)2 3.66 × 10-5 q .py = y.y +(.p/pDPy)2 3.09 × 10-5 q .x = xßx +(.p/pDx)2 1.05 × 10-3 m q .y = yßy +(.p/pDx)2 8.27 × 10-4 m Fig. 7: Layout, optical functions and beam sizes with aperture limits around the interaction region. The IP is represented by a vertical green dotted line and the laser cavity by the green box. The vertical grey dotted line represents the location of the X-Ray detector. Note that the beam goes from left to right. 6.2.5 Beam control and diagnostics Transverse beam position and size Two Beam Position Monitors (BPM) will be installed upstream and downstream of the FPC in order to guaranteea good spatialoverlap between the ion and thelaser beams. The BPMs shouldbe mounted on the same girder as the laser cavity mirrors and should be pre-aligned with respect to those mirrors with a precision better than 100 µm using metrology technique in the laboratory. The BPM electronic read-out system will use a CERN standard system, called ‘DOROS’ [51], which has already demonstrated in the SPS a few microns resolution. The existing SPS orbit corrector system is expected to effectively cover the required range of beam motion at the IP to control the spatial overlap between the ion beam and the laser pulse. At the rigidity considered for the PoP experiment, the SPS lattice correctors have modest strength.Atypical rangetomovethe trajectoryofthe beamina3-bump confgurationis around 5 mm, signifcantly larger than what should be needed. In case it is needed, resonant bumps with multiple lattice correctors give access to a much larger range of beam movement. In the horizontal plane the strong dipole corrector MSPH.62199 located downstream of the FPC could also be used to move the ion beam. The transverse beam size can be increased if needed (for example to reduce the search space for the resonance fnding) by using the transverse damper for controlled emittance blow-up. This will be in anexpertmode,with supportfromtheRFexpertsforeachsetup.Toreachthemaximum possiblebeam size the blow-up takes several seconds and needs to start before the ramp. Wire scanners are generally used to measure the transverse beam size in the SPS. That will not be possible with the PSI beam as interaction with the wire would quickly strip electrons from the ions. However, beam-gas ionisation monitors [46] would provide a continuous measurement of the transverse beam size through the cycle. Energy control Control of the energy of the ion beam is critical to excite the PSI transition. However, in a synchrotron this can be achieved through the change of different machine parameters and with varying effects. We discuss here3 cases referred as constant frequency, constant optics and constant feld cases. Constant frequency constraints the beam revolution frequency to be fx by maintaining the RF frequency frf . Note that the revolution frequency frev =1/hfrf with h = 4620 the SPS harmonic number at fat-top and that the laser cavity frequencyis locked to the revolution frequency: h fcav = frev. (3) 5 We can now relate the SPS average bending feld relative variation in the SPS dB/B to the relative change in momentum dp/p: dB dfrev .2 - .t 2 dp = .2 + (4) t Bfrev .2 p with . the Lorentzfactorof the PSI beam and .t the SPS transition energy. As we fx the RF frequency we have dfrev =0 and the frst term on the righ-hand side vanishes. Considering dp/p = 10-3 the needed relative change in the feld is dB/B =0.945 × 10-3 . However, as the IP is in a dispersive region with Dx =2.462 m we also need to consider that a shiftinthebeam momentumwillalsochangethebeam trajectoryattheIPby dx = Dx×dp/p ' 2.5 mm in the case we consider. Although non-negligible, such a shift can be easily compensated by the SPS orbit control, discussed in Section 6.2.5. Constant optics constraintsthe beam trajectorybysynchronously changingtheRF frequencyand the dipole magnetic feld. Changes in the beam revolution frequency, momentum and average radius R are linked through: dfrev 1 dp dR = - , (5) frev .2 pR but, as we consider that the feld is synchronously changed to fx the trajectory, we have a fxed average radius and dR =0. Considering dp/p = 10-3,with the conditions of the PoPdfrev/frev =1.04 × 10-7 or dfrev =0.004 66 Hz. From Eq. (3) we can see that a change in revolution frequencyof the ion beam has to be followed by the optical laser cavity length: c L =5 (6) h × frev with c being the speed of light. Then, we can derive the relation between the cavity length and the revolution frequency variations: c 1 dL = -5 dfrev (7) hf2 rev and in our case we fnd that for dp/p = 10-3 , dL = -804 nm. Constant feld case fxes the magnetic feld of the SPS while the RF frequency is changed to change the beam momentum. The relevant differential relation is: dB dfrev .2 - .2 dp t = .2 + , (8) t Bfrev .2 p but as we fx dB =0 it simplifes to dfrev/frev = .dp/p with . =1/.2 - 1/.2 the momentum t compactionfactor. Considering a relative change in momentum of dp/p = 10-3 and with the PoP specifcations we fnd dfrev/frev = -1.83 × 10-6 or dfrev = -0.0795 Hz. But again, the most relevant quantity is the associated change in the cavity length dL = 13.7 µm. The case of constant frequency is favoured as any change in length of the cavity beyond sev­eral nanometres would cause a loss of its internal lock and take possibly minutes to recover from (see Section 6.3.3). Synchronisation and longitudinal beam diagnostics Thelasertimingsystemisfurther describedinSection6.3.7.Thecontrolofthetemporaloverlapbetween thelaserpulseandtheionbunchis criticalandwillbe primarily controlledbytheSPSRFphasingor coggingsystem.The implementationcouldbevery similartothesystemalreadyinuseforthesynchro­nisationoftheextractedbunchandlaseroftheAWAKEexperiment[42].In addition,an independentand local measurementof the temporaloverlap between the ionbunch and the laser pulse willbe performed close to the IP. It would rely on the simultaneous monitoring of the signals from the BPMs and from a laser diode usingfast digitisers. Taking into account all cable and optical delays,a robust and direct measurements of the two beam temporal overlap can be easily obtained with an error of .t< 0.5 ns. TheexistingSPSwall current monitorwouldprovideprecisebunchlength measurements.Calcu­lations forabunchof 1011 charges and 250 ps showed a very good accuracyof 2.5% [52]. The nominal initial conditionsoftheGFPSI beam arevery similaranditisexpected thatthe longitudinal cooling will can be observed using this device. Longitudinal tomographyis also beingdeveloped,but will probablyonlybeavailablefor recon­structing measurements, not on-line [53]. 6.2.6 Uncertainties, reproducibility, ripple and noise The standarddeviationofthe measuredcycletocycleorbitpositionfortheQ26opticsaroundthewhole machine is 200 µm in the horizontal plane and 50 µm in the vertical, measured always at maximum beta of about 109 m [54]. Usingthe optics parametersattheIPtheexpected standarddeviationofthe position of the ion beam is around 140 µm in the horizontal plane and 30 µm in the vertical plane. Those jitters are much smaller than the beam size and should therefore have only a small impact on the fraction of excited ions per crossing. From the measurements documented in [54] the beta beating is estimated to be 25% in the hori­zontal plane and 10% in the vertical plane. This translates into an uncertainty on the ion beam size of around 10% in the horizontal plane and 5% inthevertical plane. Such systematic shift from the nom­inal conditions considered here should only have a minor effect on the fraction of excited ions and are neglected here. The measured cycle-to-cycle stability of the beam momentum is 1.3 × 10-5, as measured in 2015 [55]. Larger shifts and longer term drifts, for instance when the supercycle composition is changed, is of the order of 2 × 10-4 . 6.3 Optical system Given the chosen ion species, the transition energy and the lifetime of the resonance are determined. The width of the transition of the ions in their rest frame .= ~/.0 . 9 × 10-6 eV, which corresponds to a spectral bandwidth of the laser, in the laboratory frame, of .. . 1/4...0 . It is determined by the requirement that the laser wavelength . matches the transition energy ~.0 . 2.hc/.. The choice of 0 the laser wavelength is driven by the availability of a high average power mode-locked laser system. It is thus decided to avoid frequencydoubled laser systems which would induce, de-facto, a loss of pulse energy. If a FPC is used for pulse energy enhancement at the interaction point, the choice of a green laserwould additionally induce increase lossesby absorptioninthe optical coatings,andin turn increase the issues relatedto high-power stackingin FPCs.Itis thus decidedto pursuethe studies witha laser wavelength in the infrared, and as a baseline we choose . . 1034 nm, though other wavelengths may be considered in the range of 1020 - 1070 nm. This choice corresponds toa Lorentzfactor . . 100 and thus .. . 10 MHz. The corresponding laser bandwidth is consequently of .. . .2../c . 35 am. However, the ion energy spread .E/E . 2 × 10-4 induces large broadening of the required laser spectrum .. . ..E/E . 0.2 nm, so that mostof the ions areexcitedby the laser pulse. In order to excite a large fraction of ions at each turn in the SPS ring, the laser-beam must deliver a few millijoules per interaction at least. Two strategies can be considered. Either (1) interaction with a singleionbunchata rateof about43kHz,or(2) interaction withallionbunchesat ratesof5MHzto 20MHz, correspondingtoabunchspacingof200to50ns.Bothoptionsare consideredinthis section. The design of the optical system is constrained by the transition energy of the chosen ions for the PoP experiment, the ion beam size and duration, and fnally by the requirement to integrate it in the SPS ring, considering both footprint and radiation levels. We frst review the constraints in terms of performances of the laser system and then discuss its integration in the SPS at the end of this section. 6.3.1 Laser oscillator and amplifer Assuming a single ion bunch interaction scenario, the laser system should deliver at least 5 mJ and 43 kHz, leading to an average power exceeding 200 Watts. Considering the installation in the SPS, with very restricted access, the laser driver can only be an industrial-proven laser system. Commercial laser systems delivering a few tens of Watts at a few tens of kHz repetition rates are available [56– 60]. Nowadays, in the picosecond regime, two technologies are considered mature: one based on an Ytterbium doped thin-disk amplifer and the second one based on a large mode area Ytterbium fber amplifer.Arobust alternativeisahybrid architecture combining both technologies, withthe fberforthe low-power front-end and the thin-disk amplifer for the fnal high-energy laser amplifer. As anexample, systems delivering between 2 and 15 mJ are sold by TRUMPF (DIRA series of scientifc systems) [61, 62]. ActiveFiber GmbH [63] or Amplitude Laser [64] sell the fber amplifer delivering up to a few 2 hundredsofWatts. The footprintof these laser systems does notexceed 2 m. However these state­of-the-art high-power laser systems are very expensive, in the > 1 MCHF range. TheTANGOR system from Amplitude Laser[65] basedonthehybrid approach could deliver eitherafew µJ at 40 MHz,which would be nicely suited to seed the FPC (see later) or also up to 500 µJ at 43 kHz. This is well below the initially targeted energy per pulse,but the fexibilityof this systemis interesting. The system allows tuning of the spectral bandwidth and thus the pulse duration [66], which maybe useful for optimisation of the interaction rate and understanding the validity of the simulations. Moreover, this system in the range of 0.5 MCHF, being able to be used in a single shot and in an optical cavity mode may be of interest in a situation where there is a need to mitigate the experimental risk related to the implementation of the FPC in the SPS tunnel. Despite these systems are all integrated products, their operation in the SPS environmentmustbeevaluated. Indeed,thepulseenergyand duration consideredhereprecludeanylong­distance beam-transport line. However, located in the side tunnel close to LSS621, constraints related to the radiation feld seem to be reduced. These systems are also expected to be relatively expensive compared to the proposal to use the FPC. In LSS621, the interaction point could be located in a long chamber tube with a folding mirror allowing to get a small crossing angle. The laser beam could be transported under a vacuum pipe and chambers from the side tunnel where the driver laser system could be installed. The spatial matchingofthe laser beamtothe transverseionbunch size canbe done withthe helpofimagingtelescopealongafewmeterslaserbeamtransportensuringastableand collimatedbeam in the interaction area. Instead, we propose to implement a system that can be operated with multiple bunches of PSIs and that will provide an excellent test-bench for the operation of such a system at a larger scale, for instance at the LHC. However, commercial laser systems that deliver several kilowatts at 40 MHz repetition ratesdo notexist. The useof an enhancement cavity, namely theFabry–Pérot cavity, is thus considered.Itis seededbyaloweraverage-power laserthatwouldbe lessexpensiveto produce and is commercially available, depending on the required performances. This option is considered as the baseline solution, since it is expected to allow a cost reduction of the overall system. The related optical systemmayalsobeeasiertotuneintermsofthepulse durationandspectrum.Itmustbeemphasisedthat a similar system has already been operated in accelerator environments for some time, see for instance Ref. [67]. A few milli-joules energy per pulse correspond to several tens of kilowatts of stored power in the optical resonator. The total power that can be stored in the cavity is constrained by the maximum fuence (energy per unit surface) that the intra-cavity mirrors can support and the thermally induced deformation of the mirror substrates due to residual absorption, at the level of a part per million, in the mirror coatings [68]. The former effect is limiting when the laser-beam sizes on the mirrors are relatively small. The latter induces presence of higher-order modes in the optical cavity that, in turn, induce losses and instabilities in the locking of the FPC [69]. Intra-cavity average power of 600 kW has been reached in optics laboratories [70]butinvolves the useof relativelylow-fnesse cavities and high-power(500 W) laser systems. This type of confguration is more expensive than the one considered for the GF PoP experiment which relies on maximising the fnesse of the optical cavity [67]. 6.3.2 Implementation of laser system The laser system seeding the FPC must deliver about 50 W at 40 MHz with a low phase noise and, ideally,withtheabilitytotunethespectrumand/orthepulsedurationbyusingFourier limitedpulsesor longitudinally chirped pulses. The laser design is relying on a chirped pulse amplifcation scheme and is consisting of fve main logical blocks, see Fig. 8. 1. The frst block consists of a pulse laser oscillator, which must be equipped with a translation stage in order to adjust its repetition frequency to that of the FPC, a coarse and slow tuning based on a Peltier,anda piezo-electricforfaster adaptionandlockofthe laser oscillatorontheFPC.The laser oscillator must have low phase noise to ensure an easy locking to the FPC. 2. The second element, the front-end module, consists of three parts. First a bandwidth management module that comprises two fber Bragg gratings thermally controlled that allow to low-pass and high-pass flter the laser spectrum that is too large to be amplifed (pulse duration is too short in the amplifer). The bandwidth of the selected spectrum will determine the minimal spectral bandwidth that will be achieved at the end of the amplifcation stage and thus the spectrum of the laser that will interact with ions. After the two flters, a Chirped Fibre Bragg Grating, also thermally controlled will allow to tune the stretching of the pulse according to the selected bandwidth and the level of residual stretching after re-compression in the fnal stage of the laser system, before injecting the FPC, see Fig. 9. The actual spectrum after these elements will be precisely measured by means ofa high-resolution spectrometer. Given that the groupinvolvedin the GammaFactory has no experience with such a tunable bandwidth system, this must be tested within a dedicated R&D prior fnalising the ordering of the fnal laser system. An electro-optic modulator (EOM) used for the locking procedure of the laser on the FPC by generating sidebands follows this bandwidth management module. Finally, a pre-amplifer is seeded to compensate for the losses in various elements inserted in this block to get an output power at the level of 100 mW. 3. A frst amplifer based on a Ytterbium doped single-mode fber allowing to reach up to 5 W is implemented after the front-end block. 4. Asecond large effective mode area fber amplifer reaching up to 50 Wwill then be used to reach the required power to seed the optical cavity. One alternative, as mentioned above, is to replace thelargemode areafberbyasolid-state Ytterbium:YAGamplifertoavoid non-lineareffectsand laser induced damage at the end of the fber core. 5. Finally, a block containing the compressor, with fxed parameters, certainly a Chirped Volume Bragg Grating will be implemented. An additional high-power spectral flter will allow to remove the blue-sideofthe spectrum that mustbe removedtoavoid heatingoftheion beamby interaction with the lower energy ions. Finally, the polarisation of the beam is brought to circular and a telescope will be implemented to match the beam size and divergence on the frst mirror of the FPC. Then, the beam will be stabilised by means of a dedicated set of steering mirrors and, if needed, stabilised up to fewµrad (RMS) pointing by means of active analogue feedback on the position and pointing of the laser beam. Aspectrometer may also be implemented in this module in order to check the spectrum before injection in the FPC. Given that the PoP is expected to be located in LSS621, the laser system will be installed in the side tunnel. Thus, the laser-beam will be transported up to the FPC over a few meters by means of a high-vacuum laser beam transport line. Some diagnostics could be integrated in the mechanical frame of the FPC, as discussed below. 6.3.3 Fabry–Pérot cavity design The fnesse of the FPC is determined by the optical round-trip length of the cavity and the line-width of the laser. Indeed, the FPC can be understood as a frequencyflter of the laser-beam spectrum. The line­width of a single peak in the laser-beam comb spectrum is diffcult to measure with a sub-kHz precision. We,however,knowfromthepastexperience2thatafewkHz line-widthbulk Ytterbiumlaser oscillator seedinga fbre amplifers deliveringseveral tensofWatts canbe routinely lockedtoa 25000 fnesse opticalcavityata repetition rateof 133 MHz.Itis thus reasonableto assume thata 10000 (5000) fnesse for operationsat40(20)MHz canbe implemented. The correspondinggainonthe laserpowerwould then depend on the regime in which the FPC is designed, as determined by the relation between the transmission of the coupling mirror and the product of the refectivity of the mirrors of the FPC. At this stageofthe designwe can assume,forthesakeof simplicity,thatwe canbuildacavity thatwould deliver again of 5000 (2500) at 40 (20) MHz. Assuming that 180 kW can be stored in the FPC, corresponding to 4.5 mJpulseenergyavailableintheFPC,itrequirestoprocurea seed-laserwithpowerofabout 50 W, assuming roughly 70% of coupling effciency. The choice of the repetition rate of the optical cavity is mostlydrivenby technical constraints. Thoroughlythe maximum fnesse,and thusthegain,is entirely determined, for a given laser oscillator line-width (i.e. phase noise), by the repetition frequency. Thus, reducingthe repetition frequency would reducethe numberof non-colliding roundtripsintheFPCbut would also reduce by the same amount the maximum available energy per photon pulse at constant seed-laser power, or would double the seed laser power at a given intra-cavity pulse energy. This would increase the cost of the seed-laser system and also the cost of the FPC that would, moreover, become more complicate to operate. We consider, in the following, that the repetition frequency of 40 MHz is the baseline option for the design. If the phase noise of the laser is found better than expected, the design could be upgraded to 20 MHz or, more simply, to a higher FPC fnesse at 40 MHz to increase the 2The R&D programme within the ThomX project [71]. Fig. 8: Schematic description of the laser system that is expected to be used to seed the FPC. See text for details. Fig. 9: On the left axis, anexampleof the transmission and refection curves obtainedby combining2fber Bragg gratings with a compensated dispersion and a chirped fber pulse stretcher. On the right axis the dispersion is givenas functionofthewavelength. These systemsare commerciallyavailableatTeraXion,forexample,withan integrated temperature electronic controller allowing to tune independently the blue and red edge of the flter, and the group delay dispersion. available energy for collisions, thoughkeepingita reasonablelevel, so that theeffectof thermal loading ofthe mirrors,dueto intra-cavity losses,iskeptata reasonablelevel. ThelengthoftheFPCmustbetunable,sothatits round-tripfrequencymatchesafrequencyequal toaninteger harmonicofthebunch repetitionrateandtherevolutionfrequency.Inordertoachievethis, at least one of the mirrors of the FPC must be motorised, either with a stepping motor or with a piezo-electric translation stage with a large travel range to allow to set-up the cavity at the right length. This adjustment is usually done only once for a very long period of time if the reference frequencyis stable enough. The choice of the actuator will depend on how frequent a tuning needs to be done, radiation harness of the components and their vacuum compatibility. An annular piezo-ceramics also equips the rear side of one the mirrors in order to electronically lock the FPC on the reference frequency. We are used to implement FUJICERAMICS [72] components which allow to tune the mechanical length of the cavityby 5 nm/V.Lowvoltagesof less than 12 Vare usually implementedin ordertokeepthe noiselow, but higher voltage up to about150 Vcan be appliedto extend the range. This higher-voltage option has to be experimentally investigated in order to ensure its viability. The corresponding maximum optical length tuning range of the cavity in the synchronisation loop of the FPC is thus of .L/L . 1.3 × 10-8 , which translates directlytoa frequencystabilityoftheRF referenceof .f40 . 0.5 Hz or equivalently 5 Hz at 400 MHz. Once the length of the cavity is fxed, the FPC geometry must be chosen. Since the atomic transi­tion is sensitive to the angular momentum of the interacting photons, the eigen-mode of the FPC is thus required to match that of the angular momentum of the atomic transition. Assuming that the ion beam is not specifcally prepared such that bound electrons take random spin projection along the beam direc­tion (a.k.a. nearly the laser beam direction), the interaction is not expected to depend on the laser-beam helicity. This constraint implies that non-planar 4-mirror cavities with high fnesse cannot be used for this purpose, since theyare exhibiting helicity dependent resonance frequencies [73] due to the presence of a topological phase. The simpler choices thus reduce to either two mirror or planar, 4-mirror optical cavities. The clear advantageof 4-mirror(2 spherical,2 planar)bow-tie optical cavitiesin the related contextof Compton back-scatteringgamma sourcesis their abilitytoprovide stable geometries witha small laser-beam size (a few to several tens of micrometers) at the interaction point, while providing independently the freedom to control the FPC optical length precisely. This ability is unnecessary in the caseoftheGFPoPexperiment, sincetheion beam sizeis relativelylarge (typically aboutafew millime­tres). Additionally, the main drawback of this solution is that it involves a 4-mirror optical cavity which must be aligned once in the accelerator tunnel. However, highly refective mirror coatings may be pol­lutedbydust,andtheir performancemightbe signifcantly reduced.Thisalignmentproceduremustthus be performed in a highly controlled and clean (typically ISO5 class) environment. This is challenging in the accelerator tunnel of the SPS and would impose to install a laminar airfow in the accelerator tunnel. The possibility of installing the whole system in a surface clean-room and transporting it pre-aligned is in principlea possibilitybut the 4-mirror geometry and the required alignment precision makeit diff­cult to preserve during installation in the tunnel. The 2-mirror geometry, however, greatly simplifes the mechanical integration of the system and, more importantly, allows suffciently precise pre-alignment procedures to be performed on the ground before a careful installation in the tunnel, where either the alignment could be quickly corrected by manual operation or remotely performed by integrating proper motorised mounts and dedicated diagnostics. Both options needs to be investigated in terms of the risks of pollution of the FPC and increase in complexity of the mechanical implementation and potential slight vacuum degradation related to increase of motorised stages under vacuum. Finally, the choice of the 2­mirror FPC naturally allows to minimise the crossing angle between the ion and laser beams, thus the interaction rate. It is thus chosen to implement the 2-mirror FPC for the GF PoP experiment at the SPS. The requirement on the stability of the cavity length is constrained by its fnesse. Actually, any small shiftofits length inducea shiftofthe frequency. The stabilityof this frequencymustbe withinthe linewidth when comparing it to the optical frequency, i.e. .L/. =..FPC/(c/.) < 1/F. It implies numerically that .L< 100 pm. 6.3.4 Laser-beam parameter optimisation at IP Using the semi-analytical approximation, a scan of the laser-beam parameters is performed, and shown in the Figs. 10–12. It has been found that it is ideal to have the RMS laser-beam size of about a 1mm or more. This willbeshowntobe incompatible withthe opticalcavity caseinthenext section.A more reasonable RMS beam size of about .L =0.65 mm can be implemented though. According to the 2­dimensional space optimisation given in Fig. 12, in this condition, the optimum RMS laser-beam pulse duration is about .t =2.8 ps. 6.3.5 Optical parameters at IP Among 2-mirror FP cavities the hemispherical or confocal geometries could be envisaged. From a practicalpointofview, especiallyforthe alignmentofthe system,the hemisphericalversion seem easier to implement. Given the length of the optical cavity, driven by its synchronisation to the ion beam, the only remaining parameter is the radius of curvature R of the spherical mirror in the hemispherical geometry. The 1/e2 transverse size of the laser beam intensity versus the position of the plane in the FPCisshowninFig. 13.Witha 10 m radius of curvature, the divergence at the middle of the FPC is less than 100 µrad. The size of the beam at the middle point of the optical cavity is given in Fig. 15 and the fuence on the entrance mirror as a function of R is given in Fig. 14. The 10 m radius of curvature is a baseline for the design of the FPC for the GF. This choice, however, needs some validation with some R&D studies. 0 R.Alarger value of R is preferred in order to mitigate the risk of damaging the fat mirror. 6.3.6 Integration andfootprint The mechanical designis constrainedbytheavailable spaceintheSPS beamlineand tunnelandthe lim­ited time for the installation and beam-offcommissioning. The opto-mechanical and beamline design is in particular drivenby the necessityofa non-disruptive integration, respecting the SPS beam impedance constraints. This particular aspect will be validated in close collaboration with the relevant CERN ex­perts. The system is also conceived in a way that it will be pre-aligned in a ”surface“ clean-room and quickly realigned in-situ, with the possibility forfast change or removalof the mirrors,if required. From ourexperience,acombinationof granite epoxy withlowthermalexpansion nickel-ironalloy gives a good support for high reliability and precision Compton interaction point. In the case of the PoP experiment,the beam sizes arelarge with respectto usualafew tensofµm beam size. Nevertheless, the optical cavity length of 3.75 m, the limited access and the unknown temperature variation during the machine operation constrain the interaction support stability to be in equivalent class of the Compton one, implying transverse (angular) RMS stability better than 10 µm (10 µrad)for the mirror support bases. The density of the granite epoxy is 2.3 kg/dm3 . The granite block support is lightweight, allowing insertion of the necessary diagnostics, electronics and power supplies in the aperture with a reinforced radiation protection. In a preliminary mechanical drawing design study, a simple view of the interaction point system is given in fgure Fig. 16. The integrated tools for handling of the 10 tons module are shown. Mechanical manual movers are not intended to be implemented at this stage since the PSI beam position will be tunable and monitored thanks to a pair of dedicated BPMs surrounding the FPC. At the location LSS621, it is intended to equip the side tunnel with a dedicated clean optical room withair control, which willbeakeyaspectforthe successoftheexperiment. Thiswould ensure not only that the required level of cleanliness for the laser is system is simply ensured, but also that theenvironmentis thermalized whichwould signifcantly mitigate temperaturevariationsinthe tunnel that induce performance changes of the laser system. The drawback of this location is that it requires beam transport in high vacuum from the side tunnel to the FPC entrance. This seems possible using the existing penetration in between the two tunnels. The high-vacuum laser beam transport line with moderately large aperture .50 mm high refectivity dielectric multi-layer mirrors could transport the laser beam in the FPC and the refected signal from the FPC in the side laser to get the signal in “low­radiation” environment for the PDH. The laser beam transport line could be fxed in the top-side of the SPS tunnel up to the level of the end of the section LSS621, then cross on the ceiling the walking path and turn down to the frst mirror ultra-high-vacuum chamber of the FPC. As the laser waist on the input plan mirror of the cavity is relatively small, the telescope for the fne tuning of the spatial coupling can be installed in the laser room in the side tunnel. 6.3.7 Constraints on the synchronisation scheme One of the main operational constraint on the laser system is that it must be run almost continuously over the period of data taking due to warm up drifts that are customary in laser oscillator and amplifers. To account for this constraint, it is foreseen to lock both the laser system (including the FPC) and the proton/ion beam revolution frequency on an external clock. This will allow to maintain the laser sys­tem synchronised while operating the proton/ion beam. This will also be a convenience for realising independent tests and commissioning. Once the system is at its working point, the internal stability of the laser oscillator frequency is easily ensured in the case of the LSS621 location by implementing a laser room in the side tunnel, since it is mainly infuenced by environmental drifts for a low-phase noise oscillator. Under these conditions, the choice of a state-of-the-art phase noise performance laser and a stable mechanicaldesignoftheopticalcavityandbeam transportwill ensurethatalockofthelaserpulse repetition rate on the FPC reference can be ensured without lock losses over long enough time periods (several ten minutes, maybe hours). From our past experience the main unknown here is related to ad­ditional noise broughtinbythe small,but still, laser-beam transport line.Lower frequencyfuctuations of the FPC length will be damped by adding an overall loop to lock the optical system, as a whole, on a stable external reference. This scheme is shown in Fig. 17. As demonstrated above, the piezo-ceramic dynamics constrains the frequencyreference to be sta­ble within .f40 . 0.5 Hz at 40 MHz or equivalently 5 Hz at 400 MHz. This is in order to avoid a loss of lock due to the need of moving a translation stage in the cavity. The loss of the lock would induce the need for scanning the absolute phase to retrieve the collisions. By using a synchro-loop in the SPS on fat-top would allow to avoid this inconvenience. It is thus foreseen to employ a generator synchronised withGPStimerstodeliverthestable referencetothelaser oscillator.Thelattercouldbeeitherlockedon the reference frequencyatthe 10th sub-harmonicofthe reference generator,expectedtohavea 400 MHz frequency,or directlyatthe reference frequency. This choice willbedrivenbyrequirementsonthe resid­ual phase noise of the laser oscillator locked onto the external reference. The phasing procedure of the ionbuncheswiththeexternal referencewillbe similartothatexperiencedwiththeAWAKEexperiment. The phasing of the laser will be ensured by the use of consistent frequency-dividers for the laser and theionbunchesandaphase shiftermaybealso implementedinthe laser locking schemeto increase fexibility. Radial-loop or fxed feld feedbacks couldin principlebe used,butwould induce largerfrequency drifts when, during the experiment, the ion beam energy will be slightly scanned in order to fnd the resonance and optimum energy. These frequencydrifts would be too large for the range of the piezo-electric actuator that is foreseen to be implemented in the optical cavity. It must be, however, noted that asfar as timing jitters between the laser pulse arrival time and the ion beam arrival time (as opposed to drifts) are concerned, the system is relatively immune to such effects due to the long ion beam duration. 6.3.8 Radiation aspects Given that the laser systems needs to be integrated in the high SPS radiation feld, specifc care needs to be taken in order to validate this aspect. However, this constraint is greatly relaxed thanks to the choiceofintegratingthe criticalpartsofthelasersysteminasidetunnelandnotintheSPStunnelitself, where the typical yearly dose in LSS6 close to the beam line is of the order of magnitude of a kGy [74]. Given the limited choice of laser systems that may be used to provide the requested performance, and that these systems are not used to be implemented in high radiation feld environments, the strategy that is followed relies on minimising the global dose delivered to the critical parts, namely the laser and the related electronics. The literature is indeed sparse on the topic of the radiation dose to laser oscillators and amplifers typical of that required for the PoP experiment [75–77], especially when considering the high fux of high-energy hadrons of the SPS radiation feld. These systems seem to typically survive radiation doses in the kGy range,but the tested environments are different to that of the SPS. In that respect,thechoiceof implementingthesysteminthe locationLSS621isoptimalsinceitprovidesaside tunnel where the radiation feld is naturally shielded. Apossible placement for the laser room of about 2m by 3m is represented by the greyrectangle on Figure 6a. If required, additional shielding materials could be installed around it by using the remaining space of about 1m between the optical room and the walloftheSPSand TI18. Accesstothe laserwouldbe done throughthe nearbySPS tunnelandthe laser system is thus meant to be fully remotely controlled. However, a detailed study of the actual radiation feld in the side tunnel of the SPS still needs to be done, to validate numerically this aspect. In the early stage of the project, before that the LSS621 location was considered, the FPC and laser system was supposed to be installed in the SPS tunnel at the location LSS616. Given the critical aspect of the radiation feld on the laser and some electronics parts that are judged either impossible or extremely diffcult to deport, some preliminary measurements of deposited doses at the LSS616 location were made in the last running weeks of 2018, from the September 18th to the end of the year. This allowed to confrm the (expected) risks related to radiation feld in the long straight sections of the SPS, 2 since the inferred rates of about 1.5 × 1010 (2.1 × 109)high-energy hadrons percm and 1.4 × 109 (3.8 × 109)thermal neutrons percm 2 at the height (foor) 1m on the side of the beam line. These fgures preclude long-term use and storage of the laser system in the SPS tunnel which render the PoP operation diffcult to consider and imposes specifc care of single-event effects. These measurements will allow to calibrate the FLUKA simulations of the radiation feld in the long straight section of the SPS up to the actual location envisioned for the PoP experiment. These will, in turn, allow to determine if further shielding is required and if additional requirements are expected on the commercial laser systems and associated electronics. 6.3.9 Required R&D and timescalefor integration. As already briefy mentioned, R&D is required to early validate a few technical choices, namely the bandwidth/pulse length management scheme with thermally controlled Bragg gratings. The optical pa­rameters and the design of the telescope to adapt the laser to the optical cavity may also be tested early. Indeed, LAL is already engaging procurement and R&D on these two aspects, in order to validate these choices by mid-2020 in the worst case. These validations at low power may be pushed to high power to further validate the choice of the provider for the mirrors and to probe thermally induced effects in the 2-mirror optical cavity with the chosen radius of curvature and geometry. Most of the hardware required for these is already available at LAL and will allow designing the laser system for the PoP experiment by mid-2020. Once a fnancial green light is obtained, one year of procurement time for the laser oscillator, additional optical parts and laser amplifer is expected. In the meantime, the mechanical design of the supporting frame for the optical cavity, the design of the laser-beam transport line and their vacuum systems with necessary safeties, the drawing of the specifcations for the optical room that is intended to be located in the side tunnel will be engaged. This task is expected to last about six months, but couldstartatthesametimeasthelasersystemdesign.The increaseddurationisexplainedby necessary increased interfaces with surrounding mechanical elements and boundary conditions imposedby theex­isting penetrationsinwallsthatmayneed some iterations.Followingthisdesignphase, procurementwill be launchedandisexpectedto last about9months. This implies thatall elementary parts areexpected to be ready 15 months after a fnancial approval of the project. Laboratory assembly and optimisation of the whole system and development of requested control command software will be performed in the next9months, witha special caregivento remote operationofthe whole system, including feedbacks, followed by installation in the SPS and side tunnels. 6.4 Detection of X-ray photons 6.4.1 Simulations Photon fuxes The features of the emitted photon beams simulated by means of the Monte Carlo programs GF-CAIN, GF-CMCC and GF-Python are reported in this section. The details of the above GF simulation tools are presented in Appendix 3. The parameters of the simulations of relevance for the PoP experiment are collected inTable 3. Fig. 18 compares the GF-CAIN, GF-CMCC and GF-Python results for the laser (photon) pulse en­ergy dependence of the ion excitation rate in a single ion-bunch–photon-bunch collision. This plot car­ries two important messages. Firstly, the results of three independent programs are in a good agreement. Secondly, almost all the ions areexcitedin eachbunch crossing3.Forexample,in the caseofa 5 mJ laser pulse, 20.55% of ions absorb and subsequently emit a photon: this corresponds to a total fux of 1.85 × 107 photons perbunch crossing. The GF-CAIN and GF-CMCC charactersiticsofthephotonfuxare presentedFigs.19.Asshownin the left-hand-side fgure,the majorityof photons coming from spontaneous emissionsofexcited ions are emitted in the direction of the ion beam. The angular distribution of emitted photons is peaked around 10 mrad. The most energetic photons are emitted at small angles. The maximum photon energy is 44.47 keV. AsquotedinTable3,the lifetimeoftheexcitedionsis 76.6 ps in the ion rest frame. The corre­sponding laboratory-frame distribution of the path-length of the excited ions (from the collision point to the photon emission point), obtained using the GF-CMCC simulation code is presented in Fig. 20. This plot shows the most important difference of the PoP experiment confguration, based on the Lamb-shift-like, l-level, atomic excitation and the future LHC implementation of the photon production scheme based on the n-level atomic excitation. The excited-state lifetime in the latter case will be shorter by up to four orders of magnitude and the photon source will be a point-like source, contrary to the former case which isspecifctothe SPS-basedexperiment,wherethephoton sourcewillbe distributedoveralarge distance. As presentedinFigs.21,thelong decay-path, specifctotheSPSPoPexperiment,givesrisetoalossof the correlation between the radial position of the photon impact point on the detector plane, perpendicu­lar to the beam axis, and the photon energy. The degree in which such a correlation is smeared out will allow us to measure the lifetime of the excited state in the SPS PoP experiment. In Fig. 22 we present theexpected energy spectraof photons interceptedbya ring-shaped fat detector, placedat z =7 m from IP, within the radial distances of 4 cm 0 is signifcantly larger than the energy loss for theions with .E< 0,andthisistrueforalarge fractionoftheionbeam. This is achieved by setting the relative frequencyspread in the laser pulse to be equal to the half of the relative energy spread in the ion beam .. 1 .E = . (9) . 2 E In this simulationwe assumethe GaussianFourier-limited laserpulses with .t.. =1. Then, the relative energy spread .E/E =2 × 10-4 corresponds to the laser pulse duration .t =5.5 ps. Fig. 26 shows that over the frst 20 seconds of beam–laserinteraction the peak current in the ion beam increasesbyafactorof threeduetothe longitudinal coolingofthe beam – this shouldbe visible in the longitudinal beam current profle monitor of the SPS. Simulating a longer cooling process produces even a higher peak current in the ion beam. How­ever, for the large peak current the collective effects will become important and still have to be included into the simulation. In this simulation the only clearly observable effect is in the longitudinal ion beam distribution. However, since at the laser–ion beam interaction point there is a signifcant value of the horizontal dis­persion function(Dx = +2.4 m), we can also use the effect of dispersive coupling (see Section 3.2) in order to transfer the cooling into the transverse plane. This can be achieved by simply shifting the horizontal position of the laser focal point by 1 mm (towards negative x, as explained in Fig. 2). Such simulations are performed in a similar Jupyter notebook [86]. The results are shown in Fig. 27. We can seethatthe small shiftofthe laserfocalpointby -1 mm reducesthe numberofexcited ions from 16.2% to 12.4%which,in turn, reducesthe rateofthe longitudinal cooling,but thereisa dramatic increasein the rate of the transverse cooling instead. Shifting the laser focal point into the positive direction in x will result in the blow-upinstead of the reduction of the horizontal emittance. Understanding and control of these cooling/heating effects are very important for the LHC-based GammaFactory, where the rates of the laser cooling are greatly increased compared to the SPS Proof-of-Principle experiment. 7 Timeline, resources and organisation 7.1 Timeline The timeline for the SPS proof-of-principle experiment has been developed within the timeline of the overall GammaFactory R&D studies andis presented belowin this context. Theoverall GammaFactory initiative R&D has been conceived and setupin three main phases: – Phase 1: Initial Study; – Phase 2: SPS Proof-of-Principle Experiment; – Phase 3: LHC Demonstrator Application. The scheduling for these phasesis constrainedby the already approved operation scheduleofthe CERN accelerators [87]. The GF R&D timeline planning is defned to minimise interference with the ongoing CERN research programme. 7.1.1 Phase 1: Initial Studies The frst phase of initial studies started in February 2017, with the creation of the GF study group embed­ded within the Physics Beyond Colliders (PBC) framework. It included the exploration of the different concepts, theoretical studies and simulations, and preparation and execution of dedicated SPS and LHC accelerator tests performed over the years 2017–2018. This phase is now approaching completion with the present LoI for the GF PoP SPS experiment. The timeline of this Initial Study phase, together with itskeyachievements and remaining milestones superimposed on the LHC and SPS operation roadmap, is summarised in Fig. 28. 7.1.2 Phase 2: SPS Proof-of-Principle Experiment The proposed second phase of the GF initiative is the SPS Proof-of-Principle experiment with the ob­jectives described in details above. This phase will demonstrate the feasibility of resonant laser atomic excitation of relativistic atoms, and is the essential precursor for future higher-energy GF developments. The phase will need to be approved as a Project to construct, install and operate the experiment. The identifed planning of this PoP phase includes: 1. Procurement and laboratory tests of the vacuum vessel, laser-system, FPC and remote controls; 2. Procurement and tests of the photon-detector components; 3. Construction and installation (or upgrade) of the TT2 stripper; 4. Installation of the room for the laser in the SPS tunnel; 5. LSS6 installationofthevacuumvessel,the laser system,theFPCandthe photon detection system; 6. Overall experiment commissioning: hardware commissioning, beam commissioning, resonance fnding, measurements, photon detection, etc. The overall timeline of the PoP phase of the GF studies in the period 2020–2024, together with its milestones, is presented in Fig. 29. The installation of the infrastructure and sub-systems are foreseen to take place during the 2021/22 and 2022/23 winterYear EndTechnical Stops (YETS). The laser room is one of the critical points in the planning, since this infrastructure needs to be completed before any of the laser sub-systems can be installed. For this reason, the present planning is conservative in that it assumes: (1) that no works are possible in LS2, (2) that the YETS 2021/2022 is fully dedicated to the laser room and other infrastructure, and (3) that the laser system can only be installed and commissioned in the YETS 2022/2023. If some preparatory works can still be accommodated at the end of LS2, then the more margin could be generated in the critical path activity of the laser room installation. In 2021 the beam tests in the SPS will use the existing stripper (in a dedicated mode) and will focus on establishing and characterising the SPS cycle and the beam, as well as investigating the energy calibration methods. In 2022, with the new stripper available, the beam tests in SPS can take place inside a supercy­cle with other beams. It is planned to commission the photon detector and to fnalise the SPS beam characterisation and energy matching, as well as measurement of the performance with the new stripper. In 2023 and 2024, after the installation of the laser and the FPC, the plan is to have a series of PoP runs totalling about5 weeks per year, whichwouldbe split between (mostly)experimental time for commissioning and measurements with the experiment proper, and MD for beam improvement and technical aspects, like BPM commissioning. It is expected that most of this time will be in parallel operation. This scenario assumes thattheTT2 stripperis confguredinthe 2021/2022 YETSto allowthe foiltobe insertedfortheioncycles,and thatin consequencethePoPexperiment will usetheSPSringin a parasiticmodewith minimal interferencewiththe canonicalSPS operation.Afew dedicatedperiodsof experiment or MD for stand-alone runs with the SPS Pb79+ beam in a coast mode may be required, e.g. to optimise the photon beam production effciencyor perform long lifetime or blowup measurements. Beyond 2024, there will be the opportunity to improve the experiment in LS3 on the basis of the results from Run 3, for example with the improved detector(s) or laser system, and it is expected that the experimentwillremainintheSPSfortheLHCRun4period scheduledfrom2026to2029. The SPS PoP programme therefore covers about a decade. The operational experience with the experiment, its results and their extrapolation to the LHC running conditions will be essential to assess the feasibility of an LHC-based photon-beam production scheme. In parallel to running the PoP experi­ment, we plan prepareover the years 2023 and 2024,aGFTechnical Design Report (TDR) for an LHC Demonstrator Application. 7.1.3 Phase 3: LHC Demonstrator Application TheSPSPoPexperimentwillgivekeyinputforthe thirdphase:a demonstrationofa GammaFactory Application in the LHC, with the much higher Lorentz-. boostfactor. The detailed technical scope, timeline and cost of the LHC Demonstrator Application phase of the studies arehypothetical, as long as the PoPexperiment and the specifc LHC applications are not fnalised.Apossibleand logicalapplicationwouldbeto usethe Li-like Pb79+ in the LHC and to excite either the 2s › 3p1/2 or 2s › 2p3/2 transitions. This scenario would represent a “minimal investment” option, cover large domain of photon beam energies from 15 to 87 MeV,use the well-studied Pb79+ beam already foreseen for the running period following LS3 and could also directly re-use the laser and FP systemoftheSPSPoPexperiment.TheLHCexperimentwouldallowtostudythenew technical aspects of .-photon extraction, ionisation from double-photon absorption and .-ray detectors. In addition, it would open the possibility of new Atomic Physics measurements (combined measurement of the spin 3/2 state (LHC) and 1/2 state (SPS), measurement of the neutron skin of the nuclei in dedicated runs using different lead isotopes), a possible light-shining-through-the-wall demo experiment and characterisation of the secondary beams of polarised positrons and neutrons. The timelineofthe design, constructionand installationofaneventual Phase3LHC Demonstrator will begin around 2025 and is expected to last around 4–5 years, depending on the scope. 7.2 Projectresources The initial study (Phase1)of theGF R&D programmewas accomplished withouta dedicatedbudget line, since there was no material expenditure and the required fnancial support for studies was very kindly found within the Physics Beyond Colliders envelope. Manpower was found within the CERN Physics Beyond Colliders community and from external institutes. The cost and manpower needs for the LHC Demonstrator Application (Phase3) will depend heav­ily on the specifcs of the application tools chosen, since this will determine the laser technology, the interaction region design, the beam extraction and .-ray transport design. The scope defnition and de­tailedcostingofthisPhase3willbeakeypartoftheTDRstage,whichwillbe fnalised,atthe earliest, before the end of the year 2024. TheSPSPoPexperiment requiresa modestbut tangiblelevelof fnancialand manpowerinvest­ment for the design, construction, installation and execution of the experiment. The fnancial estimates are relatively well defned, since the costs for the technical sub-systems are based on similar systems for which the costs have been well established. The manpower estimates have been made for each of the subsystems (activity) and intrinsically have more uncertainty. However, the totals obtained are fully coherent with the manpower costs of similar size projects at CERN, for developments of similar tech­nologies, in terms of the kCHF per FTE of effort. The fnalisation of these estimates with the responsible teams and the collaboration will be one of the frst activities of the project after approval. The manpower for the project will rely heavily on the collaborating institutes, as well as CERN. The present members of the GF study group and their institutes are listed in Appendix 1. 7.2.1 Budget estimate The estimated fnancial costand manpower needsforthe Phase2ofthe project –theSPSPoPexperiment – are outlined in the following sections. The cost estimates are based on the scope described above, with the new stripper foil and the dedicated laser system to be installed, together with the FPC, the X-ray detector and all the experiment infrastructure. The main cost drivers are: 1. The new stripper in the PS–SPS transfer line, with changes to the local vacuum layout, controls and cabling; 2. The laser system in the SPS tunnel, with the laser room, the transport beamline, the infrastructure and cabling; 3. ThevacuumvesselandtheFPCintheSPSring,togetherwithcontrols,cablingandchangestothe local vacuum layout; 4. The photon detection system and readout in the SPS ring, together with controls, cabling and changes to the local vacuum layout. The preliminary cost estimates for the different sub-systems and other required expenditures are summarisedinTable8. The costs associated withthe controls, infrastructureand services neededforthe ion stripper, the laser and the diagnostics (e.g. cabling, shielding) are included in the estimates, as well as some costs for the collaboration for the design study. Manpower (Doctoral students and Post-Doctoral Research Assistants) which needs fnancing from the projectbudgetis also specifedexplicitlyin this materialbudget table. Table 8:Preliminary material cost estimates for the GammaFactory SPS PoPexperiment. Item Cost [kCHF] 1 Stripping foil unit (design, assembly, tests, installation – in synergy 125 with a foreseen stripper upgrade) 2 FPC (optics, support, interface, vacuum system) 180 3 Laser system (oscillator, amplifer, electronics, controls, assembly, lab 800 tests, shipping, installation) 4 Laser clean room and UHV transport line (in SPS tunnel) 600 5 Photon detection system (design, detector, controls, vacuum chamber, 100 assembly, tests, installation) 6 Beam position monitor (detector, cabling, electronics ) 50 7 Infrastructure and services (cabling, supports, shielding) 80 8 Manpower (Doctoral Student/PDRA subsistence) 350 9 Collaboration support (travel, subsistence) 80 Total 2365 7.2.2 Manpower estimate The provisional estimates for manpower needed for the provision or integration of the different subsys­temsisgiveninTable9. The numbers are total integrated FTE.years, and aredivided into the CERN Staff or the GF collaboration. The CERN manpower will cover site-specifc aspects, such as controls integration, tests, synchronisation and also contribute to experimental commissioning and tests. It will be distributed between the CERN accelerator departments. The GF collaboration manpower is mainly for thebulk of the activities for the laser system, the FPC and the detector and will need to be provided by the collaborating institutes. Abreakdownof theexpected costs and manpower profles per yearis madeinTable 10. Table 9:Preliminary manpower estimates for the GammaFactory SPS PoPexperiment. Item Collaboration DOCT/PDRA CERN [FTE.y] [FTE.y] [FTE.y] Strippingfoil unit 0.21.0 FPC 2.51.00.5 Laser system 2.53.00.5 Laser beamline 1.00.1 Photon detection system 2.02.0 Infrastructure and services 0.52.5 Collaboration support 0.20.5 Commissioning, measurements, analysis 1.81.52.3 Total 10.75.59.4 Table 10:Preliminary resource profle for the GammaFactory SPS PoPexperiment. Year Cost [kCHF] Manpower [FTE] Collaboration DOCT/PDRA CERN 2020 510 1.5 0.5 0.9 2021 705 2.6 1.0 2.5 2022 680 2.2 1.2 2.0 2023 260 2.2 1.4 2.0 2024 210 2.2 1.4 2.0 Total 2365 10.7 5.5 9.4 7.3 Organisational aspects and task list The SPS Implementationof theGF PoPexperiment will requirea defnedWork Breakdown Structure (WBS) and responsibilities allocated to the CERN groups for the cases where equipment is to be installed in the accelerator or integrated into the SPS control system, and for other crucial machine activities. The responsibility will be on the side of the GF collaboration for provision of specifc subsystems, simulation efforts and other deliverables. ApreliminarylistoftasksthatwillformthebasisfortheWBSisshownbelow,wheretheexpected responsibility sharing between CERN and the GF collaboration is indicated. Each task will have a task leader, selected once the LoI is approved, the collaboration is consolidated and we move to the technical design phase of the project. One of the frst activities at the start of the project execution will therefore be to fnalise the technical organisation and to defne the responsibilities of CERN and of the GF collaboration, based on this task list. Aformal collaboration agreementwillbeneededforthe responsibility defnitionandtoagreethe milestones and deliverables. An important initial milestone will be the formulation and signature of a Memorandum of Understanding (MoU) to formalise the collaboration and the various contributions of the different partners, including CERN. This shouldbe done within6monthsof the project start. 7.3.1 Task breakdown Atomic Physics input The calculations of the atomic resonance energy levels, cross sections and lifetimes will come from the contributing GF collaborators. This topic will also include input and calculations for the design of the Atomic Physics measurements and contribution to the analysis of the measurement data. Simulation and data analysis The simulations of the laser-photon interactions will be largely carried out by the contributing GF col­laborators, while the accelerator physics simulations will be shared between CERN and the GF col­laboration. Other more specifc topics, like the beam stability and impedance effects of the installed components, will be carried out by CERN. The analysis of the experimental data and the comparison with the theoretical calculations will be a joint effort depending on the specifc topic. SPS PSI Beams CERN will be responsible for the preparation, provision and characterisation of the PSI beams. This also includes the description of the accelerator optics and beam distribution characteristics at the interaction region and the detector. Stripperfoil and stripper unit The contributing GF collaborators will be responsible for the simulations of the stipping effciencyand specifcation of the foil, while CERN will provide the foil and the stripper system together with its controls, and install it into the PS-to-SPS transfer line. SPS Beam Diagnostics The beam diagnostics will be needed for the characterisation of the PSI beam transverse and longitudinal distributions, as well as the read-out of the beam position and intensity. In addition, the information on the beam momentum centroid and distribution will be required. These aspects will be the responsibility of CERN, although the incorporation of the BPMs in the vacuum vessel around the FPC will need close collaboration. Laser–PSI beam synchronisation The synchronisation between the laser and PSI beams will be under the responsibility of CERN, using theexisting technology.Thekeyaspectofthe defnitionofthe interfaces needstobe closely coordinated between CERN and the laser and FPC experts. Laser system andFabry–Pérot cavity The design and procurement of the laser system and the FPC including the vacuum vessel will be the responsibility of the contributing GF collaborators, complete with the local controls and infrastructure. The detailsoftheinterfacestothevacuumsystem,thesupport structuresandtheintegrationofthesystem into the CERN control system will need to be a joint effort. Laser room and beamlines The laser room with controlled environment and the beamlines to transport the laser beam to the FPC will be the responsibility of the contributing GF collaborators to provide, while the design, detailed integration and installation into the SPS tunnel will be performed in close synergy with CERN. Physical Integration in SPS tunnel CERNwillperformtheverifcationofthephysicalintegrationofthevarious systemsintotheSPS tunnel, with updates of databases, layouts and optics fles. Anydetailed drawings for this integration will be provided by the collaboration as part of the design. Integration into CERN control system Control of laser timing, power and other parameters will need to be included in the CERN control system, together with the acquisition of the laser and FPCparameters, and data from the photon detector. The data acqusition and control hardware will be a part of the detector and laser/FP systems procured by the collaboration, while the middleware layer and high-level software (including APIs, GUIs, logging) will be provided by CERN. Photon detection system The design, construction and installation of the X-ray photon detection system will be the responsibility of CERN. It is assumed that the existing technical solutions will be reused. The GF collaboration will support this with simulations and specifcations needed for the system defnition. SPS vaccum The responsibility for the SPS vacuum in terms of changes local to the FPC and detector, as well as in­formation needed for calculations of the PSI lifetimes, will be the responsibility of CERN. Specifcations for the pumping and instrumentation will be needed from the contributing GF collaborators for the FPC vacuum vessel. Radiation and beam loss simulations and effects The provision of radiation feld estimates including simulations of the effectiveness of shielding will be from CERN, on the basis of existing information on beam losses and expected distributions with the PSI beams. Radiation tests on specifc critical electronics and optical components will need to be jointly organised with CERN and the contributing GF collaborators. Impedance The impedanceofthe proposeddevicestobe installedontheSPSring will needtobe formallyvalidated byCERN,onthe basisofthe detailed design (geometriesandmaterials)providedbythe contributingGF collaborators.CERNwillneedtogiveaninputatthedesigntimetomakesuretheimpedance constraints are respected. Shutdown scheduling and planning The planning of the inspection and installation works in the CERN shutdowns will be managed by CERN with the input of the contributing GF collaborators on the duration and conditions of the various interventions. Radiation protection and safety Radiation protection and safety willbe organisedby CERN as partof the project safety fle. Infrastructure Infrastructure such as cables, cooling, ethernet or optical fbresin SPS LSS6 (for the laser, the FPC and the detector) and in TT2 (for the stripper) will be the responsibility of CERN, although the specifcation will need to be provided by the contributing GF collaborators for the laser and the FPC. 8 Summary We propose an SPS experiment to study a novel accelerator-based production scheme of high-intensity photon beams in an energy range inaccessible for present FEL technology. Our goal is to test this scheme at the SPS prior to its possible future implementation at the LHC.We plan to collide an atomic beam of lithium-like lead, 208Pb79+, circulating in the SPS, with a laser beam. The laser beam power will be enhanced in an optical resonator incorporated into the SPS ring, and the laser beam wavelength tuned with respect to the atomic beam momentum to maximise the rate of the resonant, 2s › 2p1/2, 208Pb79+ atomic transitions of the ions. In addition to the basic feasibility, one of the goals of the proposed experiment is to demonstrate that atomic beams can be effciently cooled, both longitudinally and transversely, at ultra-relativistic energies. The ultimateaimofthe GammaFactory initiativeisto createandtoexploitnewtypeofparticle beams characterised by a signifcant leap in their intensity, purity, energy range, and plug-power eff­ciency. The primary beam of .-rays is proposed to be generated by storing atomic beams of partially strippedionsintheLHCring(s)andbyexcitingtheiratomicdegreesof freedombylaserbeams.Thesec­ondary beams of polarised charged leptons, neutrinos, neutrons and radioactive ions would be produced in collisions of the high-intensity .-ray beams with external target(s). These primary and secondary beams,if producedby the GammaFactory, could open new perspectives for the High EnergyPhysics community and new cross-disciplinary research domains at CERN by re-using its existing accelerator infrastructurein unconventionalbut innovativeway. The GammaFactory Proof-of-Principleexperiment in the SPSis an important and necessary R&D step fora future GammaFactory research programme, and a realistic evaluation of the achievable photon beam intensities is the primary target of the proposed experiment. The GammaFactory R&D studieshave already made real progress andhave attracted the interest of manyresearch groups from aroundtheworld, representingdiversephysics communities. The demon­stration of effcient production, acceleration and storage of atomic beams in the CERN accelerator com­plex has been already achieved during the past two years, and the design of the SPS Proof-of-Principle experiment has been defned. If the proposed SPS experiment is approved, it will provide, at a modest cost and a negligible interference with the ongoing CERN research programme, the necessary input data for the quantitativeevaluationof the GammaFactory research potential. Appendices 1 GF community and expected participationin SPSPoP experiment The GF initiative is of general interest for the following scientifc communities: – the accelerator physics community; – the particlephysics community; – the laserphysics community; – the atomic, molecular and opticalphysics community; – the nuclearphysics community; – the appliedphysics community. TheGF study groupwas formally createdin February 2017 and nowincludes scientists repre­senting all the above communities. The group is, at present, composed of 65 researchers affliated to 24 institutes from 10 countries, and it is steadily expanding. Its present members are listed below. The composition of the group actively involved in the SPS PoP experiment will evolve from this community, with emphasis on the laser, accelerator and atomicphysics communities for the realisation andexecution oftheexperiment.Itwillbeopentonewresearch groupsandindividualswillingtojointheGF initiative, or just to participate in its PoP experiment. In particular, as the concepts for the LHC demonstration ex­perimentdevelop withthe progressintheSPS,itisexpected thatthe group willexpandinthe appropriate specifc directions. Membersof GammaFactory StudyGroup A. Abramov1, S.E. Alden1,R. AlemanyFernandez2,P.S. Antsiferov3, A.Apyan4, H. Bartosik2 , E.G. Bessonov5, N. Biancacci2, J. Bieron´6, A. Bogacz7, A. Bosco1, R. Bruce2, D. Budker8,9,10 , K. Cassou11, F. Castelli12, I. Chaikovska11, C. Curatolo13, P. Czodrowski2, A. Derevianko14 , K. Dupraz11,Y. Dutheil2, K. Dzierÿ¸ga6,V. Fedosseev2, N. Fuster Martinez2, S.M. Gibson1 ze, B. Goddard2, A. Gorzawski15,2, S. Hirlander2, J.M. Jowett2, R. Kersevan2, M. Kowalska2 , M.W. Krasny16,2,F. Kroeger17,D.Kuchler2,M. Lamont2,T. Lefevre2,D. Manglunki2,B. Marsh2 , A. Martens11,J. Molson2,D. Nutarelli11,L.J. Nevay1,A. Petrenko18,2,V. Petrillo12,W. P aczek6 , S. Redaelli2,Y. Peinaud11,S. Pustelny6,S. Rochester19,M. Sapinski20,M. Schaumann2,R. Scrivens2 , L. Serafni12,V.P. Shevelko5,T. Stoehlker17,A. Surzhykov21,I.Tolstikhina5,F.Velotti2,G.Weber17 , Y.K.Wu22,C.Yin-Vallgren2,M. Zanetti23,13,F. Zimmermann2,M.S. Zolotorev24 andF. Zomer11 1 Royal Holloway University of London Egham, Surrey, TW20 0EX, United Kingdom 2 CERN, Geneva, Switzerland 3 Instituteof Spectroscopy, Russian Academyof Sciences,Troitsk, MoscowRegion, Russia 4 A.I. Alikhanyan National Science Laboratory,Yerevan, Armenia 5 P.N. Lebedev Physical Institute, Russian Academy of Sciences, Moscow, Russia 6 Marian Smoluchowski Instituteof Physics,Jagiellonian University,Krak,Poland 7 Center for Advanced Studiesof Accelerators,Jefferson Lab, USA 8 Helmholtz Institute,Johannes GutenbergUniversity, Mainz, Germany 9 Department of Physics, University of California, Berkeley, USA 10 Nuclear Science Division, E.O. Lawrence National Laboratory, Berkeley, USA 11 LAL, Univ.Paris-Sud, CNRS/IN2P3, UniversitéParis-Saclay,Orsay,France 12 Department of Physics, INFN–Milan and University of Milan, Milan, Italy 13 INFN–Padua,Padua, Italy 14 University of Nevada, Reno, Nevada 89557, USA 15 University of Malta, Malta 16 LPNHE, UniversityParis Sorbonne, CNRS–IN2P3,Paris,France 17 HIJena, IOQ FSUJena and GSI Darmstadt, Germany 18 Budker Institute of Nuclear Physics, Novosibirsk, Russia 19 Rochester Scientifc, LLC, El Cerrito, CA 94530, USA 20 GSI, Helmholtzzentrum f Schwerionenforschung, 64291 Darmstadt, Germany 21 Braunschweig UniversityofTechnology and Physikalisch-Technische Bundesanstalt, Germany 22 FEL Laboratory, Duke University, Durham, USA 23 UniversityofPadua,Padua, Italy 24 Center for Beam Physics, LBNL, Berkeley, USA 2 Photon absorption and emissionby ultra-relativistic partially stripped ions The interaction of a photon with an ultra-relativistic partially stripped ion propagating in the opposite di­rectionisthekeyphenomenonexploitedbytheGFPoPexperimentto produce high-energygamma-rays. Duetoa relativistic Doppler shift,theionexperiencesinits rest framethe photonof much higher energy which,if resonant withits atomic-levels transition,is ableexciteit. Theexcitedioneventually decays intoits ground state emittinga photon. Duetothe ultra-relativistic motionoftheion,the secondary photon energy is increased with respect to the primary photon. This process is shown in Fig. 30. For ultra-relativistic ions, the scheme enables conversion of infra-red, visible or near-ultraviolet photonsintoX-rayorgamma-ray photons. Moreover,italsoprovides controloverthe secondary-photon frequencyby adjusting the ion energy. To consider the process quantitatively, we utilise 4-vectors(E/c, p) for the Lorentz transforma­tion. The ion 4-momentum is given by (.mc, .mv) and the photon 4-momentum is (~./c, ~k). If the z-axis is aligned with the direction of the ion motion, then the Lorentz transformation can be written as . . . . . . . 00 -ß. E/c E0/c 0 ... ... = ... ... ... ... 0 10 0 0 01 0 p px py (10) x , 0 p y 0 -ß. 00 . p pz z p =1/factor andß = v/c with v being the speed of the particle and c being the speed of light. where prime quantities are given in the ion rest frame (Fig. 31). Here, . 1 - ß2 is the Lorentz reduced Planck constant, kx = -k sin ., ky =0, kz = -k cos . and k = ./c (Fig. 31), one can rewrite Eq. (10) into . . . . . . 1 . 00 -ß. 1 ... - sin .0 0 ... .0 = ... 0 10 0 0 01 0 ... ... - sin . 0 ... ., (11) - cos .0 -ß. 00 . - cos . and hencethe relation betweenthephoton frequencyinthetwo framesisgivenby  .2  .0 = (1+ ß cos .).. . 1+ ß - ß .. . 2... 2 (12) Eq. (12) shows that the frequencyof the photon in the ion frame is 2.-times larger than in the laboratory frame, and hence it can excite transitions inaccessible to the light. An important issue seems to be a spread of the angle .., as ions would experience photons of different frequencies. However, from the Lorentz transformation .0 sin .0 = . sin ., (13) one can show that ..0 . .. 2. (14) and the spread is signifcantly suppressed. In particular, a spread on the order of .. . 1 mrad corre­sponds to an ion-frame frequencyspread of only ~ 10-6. This shows that the angular misalignment is not a serious problem. At the same time a much more signifcant contribution comes from the energy spread in the ion beam (typically . 10-4). Because of this spread, in order to excite a large fraction of the ions in the beam the relative frequencyspread of the laser pulse should be comparable to the relative energy spread in the ion beam. After a fnite time, an excited ion returns to the ground state emitting a secondary photon. This process is depicted in Fig. 32 in both the laboratory and ion rest frames. At this level, it can be assumed that the emission of the photon in the ion rest frame is isotropic. This is, however, strongly modifed when transferring the system into the laboratory frame. Let us consider now the process where the secondary photon is emitted in the same plane as the 0 absorbed photon (the xz 0-plane) at a random angle .10 . In such a case, the wave-vector components are givenby k0 = k0 sin .1 0 and k0 = k0 cos .1 0 and theinverse Lorentztransformationgives us the relation 1x 1z between the emitted-photon parameters in the two frames . . . . . . 1 . 00 ß. 1 ... sin .1 0 ... .1 = ... 010 0 001 0 ... ... sin .0 1 0 cos .0 1 ... .0 . (15) cos .1 ß. 00 . Hence, the secondary-photon frequencyis given by .1 = .(1 + ß cos .10 ).0 . 2.2(1 + ß cos .10 ).. (16) The laboratory-frame emission angle .1 can be also calculated using the inverse Lorentz transformation sin .1 0 .1 sin .1 = .0 sin .0 . sin .1 = , (17) 1 .(1 + ß cos .0 ) 1 yielding a typical of emission spread ..1 ~ 1/.. Asmall fraction of photons is emitted with.1 ~ 1 and in this case to separate the forward and backward emissions it is important to know cos .1: ß + cos .1 0 .1 cos .1 = .0.(ß + cos .10 ) . cos .1 = . (18) 1+ ß cos .1 0 The typical transverse kick obtainedbytheionduetothe photon emissionisvery small compared to the typical angular spread inthe ion beam. Therefore, the main effect of the photon emission on the ion motion is the small loss of the ion total momentum. 2.1 Photon absorption cross section The cross section of the ion excitation by a photon with the frequency .0 isgivenby [88,89] . =2.2 cref12g(.0 - .00 ), (19) where re is classical electron radius, f12 is the oscillator strength, .0 is the resonance frequencyof the 0 ion transition, g(.0 - .00 ) is the Lorentzian g(.0 - .00 )= 1 · . , (20) 2. (.0 - .0 )2 +.2/4 0 where . is the resonance width defned by the lifetime of the excited ion .0: 1 .= . (21) . 0 Also .02 .=2re0 f12 g1 , (22) cg2 where g1,g2 are thedegeneracyfactorsof the ground state and theexcited state. Therefore, .(.0 - .00 )= .0 , (23) 1+4.02(.0 - .0 )2 0 where .02 0 g2 .0 = . (24) 2.g1 .0 0 =2.c/.0 0 is the transition wavelength. 2.2 Estimate of the required laser energy Wecan estimatetheenergyofthelaserpulserequiredtoexcite signifcant fractionofionsinthebunch. If the laser wavelength perfectly matches the ion level we would need one photon per every .0 cross section, i.e. 2 w L N~.0 ~ , (25) .0 where wL is the laser beam transverse size (assumed to match the size of the ion beam). However, since the energy spread .E/E intheionbunchislarger thanthe widthofthe resonancewe need N~.0 photons for all possible frequencies, i.e.  .E . w2 .E L N~. ~ N~.0 ~ .0. 0 . (26) E.0 .0 E And the energy of the laser pulse should be 2 w L .E U ~ ~..0.0 . (27) .0 E Thisexpressionisan orderof magnitude estimateneglecting geometricfactorsofoverlap betweenthe laser and the ionbunch. 2.3 Saturation effect The number of excitation events for every ion (or probability of its excitation) can be found as dN~. Nexc = ., —(28) dS where . —is the excitation cross section averaged over the laser frequencydistribution and, as we have already seen, . — .0. In our model here, we assume that if Nexc  1, then Nexc is the probability of the ion excitation. ForNexc ~ 0.1 we should take into account the saturation effects. This can be done by solving the rate equation dP2 = m2P1 - m2BP2, (29) dt where P2,P1 are the probabilities of the ion to be in the excited and non-excited state, respectively (P1 + P2 =1). The rate of excitation events m2P1 is proportional to the population of the lower level P1, the photon density and the absorption cross section, while m2BP2 is the rate of stimulated emission events(B = g1/g2). Before the ion enters into the laser pulse: P1 =1 and P2 =0. To solve the rate equation we need to separate the variables: dP2 = m2dt. (30) 1 - (1 + B)P2 m2 depends on time during the passage of the ion through the laser pulse,but we already know the answer in the case of small P2 = Nexc  1, hence Z dN~. m2(t)dt =—(31) .. dS t Therefore the result of integration  R hi 1 - exp -(1 + B) m2(t)dt 1 - exp -(1 + B)dN~. . — dS Nexc = P2 == . (32) t 1+ B 1+ B dN~. dN~. As one can see, if . —is small it equals Nexc, while for large . —the result is limited by dS dS 1/(1 + B). 3 Simulation tools New simulation codes had been developed within the GammaFactory study group to implement the theory of collisions ofbunched ultra-relativistic atomic beams with laser pulses. The simulation results presentedinthisLoIhavebeen obtainedusingthese independentframeworks.Ashortdescriptionofthe codes is presented below. 3.1 GF-CMCC CMCC isaFortranevent generator dedicatedto simulationsof asymmetric electron–photon or proton– photon collisions [90]. The code has been adapted to simulate PSI–laser-photon interaction and it has been named GF-CMCC [3, 78]. The interaction is simulated in a static way, without propagation of the beams through each other(no time steps).Giventheion massandthe state-degeneracyfactors g1,g2,the beam is sampled according to the Gaussian distributions of position and momentum. The program loops over the macro-particles in which the beam is clustered in order to reduce the computational time. For every macro-particle the energy of the interacting photon is sampled around a mean value corresponding to the mean value of the desired resonance, and the resonant absorption cross section is calculated. In orderto defnethe total numberof PSIsexcited thanksto absorptionof photons fromthelaser, the program uses a Monte Carlo rejection method. The spatial, energy and density distributions of the laser and the interaction angle are taken into account. The ion de-excitation occurs at a distance from the interaction point depending on the mean lifetime of the spontaneous emission. The emitted photon is generated in the centre-of-mass frame and then Lorentz boosted in the laboratory frame. We are considering an isotropic photon emission in the PSI rest frame. Adepletionofthenumberof spontaneous emittedphotonscanbecausedbystimulated emissionof low energy photons occurringiftheexcitedion absorbsa second photon fromthe laser beam. Stimulated emission is more probable when the laser density is higher and the spontaneous emission decay time is longer. Disregarding stimulated emission, the code provides also a calculation of the total number of emitted photons based on the luminosity formula. 3.2 GF-CAIN GF-CAIN [91] is a stand-alone Monte Carlo event generator for collisions of PSIbunches with laser­ photon pulses including processes of resonant atomic photon absorption and subsequent spontaneous as well as stimulated photon emissions. It is based on the program CAIN for simulations of beam–beam interactionsinvolvinghigh energy electrons, positronsand photonsdevelopedbyK.Yokoyaetal.[92] at KEK-Tsukuba, Japan, and dedicated to the ILC project. In the current version of GF-CAIN two species of PSI are included: 12S1/2 › 2p 1. Thehydrogen-like lead ion 208Pb81+ with the transition: 1s 12P1/2 as an example for the LHC-based GF. 12S1/2 › 1s 22p 2. The lithium-like lead ion 208Pb79+ with the transition: 1s 22s 12P1/2 for simula­tions of the GF PoP experiment at the SPS. In the Monte Carlo simulations of GF-CAIN, frst thePSIbunch and the laser-photon pulse are placed at some distance from each other in the time moment t0 – usually the time t =0 corresponds tothe momentwhenthe centresofthePSIbunchandthelaserpulseoverlap. Then,the simulationof the collision between the PSI-bunch and the photon-pulse is performed in time steps .t according to the scattering probability ~~~~ P (~r, p, p, ß · k|) np(~k,t)c.t, ~k,t;.t)= .tot(~k) (1 - ~k/|~r, (33) ~~ where ~r, p~and ß are the PSI position, momentum and relativistic velocity, respectively, k – the photon ~~ wave-vector, np(~k,t) – the local photon density of the laser beam, and .tot(~k) is the total cross r, p, section for a single PSI–photon scattering, i.e. photon absorption by PSI corresponding to its transition to an excited atomic state. The time interval .t is adjusted such that P . 1. The Monte Carlo event generation is done in two stages: ~ 1. According to the probability P (~r, p, ~k,t) a scattering event is sampled using the von Neumann rejection method. 2. When scattering event occurs, an emitted photon is generated, i.e. its energy and emission angles are generated in the PSI rest frame according to the differential cross section, and then an event is Lorentz-transformed to the laboratory (LAB) frame. The above is repeated for each PSI macroparticle, and then generation moves to the next time moment, i.e. t +.t, .... The simulation is fnished when the fnal time moment t1 is reached. The generated event is represented by three lists of fnal-state macroparticles, i.e. the emitted photons, the excited and de-excited ions, together with their space-time coordinates, four-momenta and weights. This data can be written to a disk-fle or transmitted to an appropriate data-analysis program. In GF-CAIN the stimulated emission is implemented in the following way. First, the spontaneous­emission time-delay is generated from the exponential distribution with the mean value corresponding to the lifetime of the excited state. If the PSI is in the excited state, the stimulated emission is generated according to the probability P 0(~r, p~)= g1 P (~r, ~p), (34) g2 where P (~r, p~) is given in Eq. (33) and g1,2 are the state-degeneracyfactors. This is done with the use of the von Neumann rejection method, and when the event is accepted the ion returns to the unexcited (ground) state while the two photons are discarded. The unexcited ion can be excited again via the laser­photon absorption according to Eq. (33), and so on. The excited ions can emit photons not only during the timeof the collision between the PSI-bunch and the laser-pulse,but also afterwards when theytravel in the beam pipe. In GF-CAIN this is done with the help of special ‘drift’ routines which can propagate all fnal-state particles forward to an arbitrary time moment or z-axis coordinate, de-exciting the excited ions on the way via the spontaneous photon emission according to their lifetimes. 3.3 GF-Python: Python-based simulation toolkit In ordertodothe frst simulationsofthe GammaFactoryPSI beam dynamics,several Python scriptsand Jupyter notebooks were written and combined into a single comprehensive notebook addressing the PSI beam excitation with the laser pulse, photon emissions and turn-by-turn PSI beam dynamics. The code with detailed description is available on-line [85] (the theoretical part is described in Appendix 2). ThemainPython notebook describestheprocessof longitudinalcoolingintheSPS[85].Thisisa Monte Carlo code which performs turn-by-turn simulation of PSI beam dynamics including interactions with the laser beam, namely the excitation of ions and emission of photons, resulting in the recoil effect which is reducing the total momentum of the ion. No collective effects are taken into account here. Also, there are several variants of this notebook, addressing different aspects of the proposed experiment: distributions of emitted photons [93, 94], transverse cooling [86], optimisation of laser pa­ rameters [79]. The comparison of the ion excitation rates calculated by GF-Python, GF-CAIN and GF-CMCC is shown in Fig. 18. 3.4 Semi-analytical approach Inordertoperformquick optimisationofthelaserbeam parameters,a semi-analyticalapproachhasbeen developed. The PSI beam 3D direct space is randomly sampled. The momentum-space correlations are neglected. The laser-beamis assumedtobeFourierlimited withafat spectrum. The related sine-cardinal temporal distribution is approximated with a Gaussian distribution to allow analytical calculations. This approximation induces a loss of about 3.3% of the laser beam pulse energy in the tails that are not described by the Gaussian approximation. The interaction probability for each ion averaged over the spectrum is  = pmax 1 - exp(-(1 + B) Leie) , (35) pi ./pmax 1+ B where  ~.00 . ..E pmax =0.5 erf . (36) hc(1 + ß cos .L) . ..E 2 which accounts for thefact that onlya fractionof the upper partof the ions spectrum match the laser bandwidth .. (assumed fat) and for the saturation effect. The choice to only match the upper part of the ion spectrum is justifed in Section 6.5 where the cooling of the ion beam is discussed. Averaging the single probabilities pi over the Monte-Carlo samples provides the fraction of ions that is expected e to interact in average. In these expressions the parameters Li and . edenote the spatial and the spectral overlaps of the laser and ion beams, respectively. These two quantities correspond to the luminosity and the cross section in absence of saturation effects. The spatialoverlap termforagivenion identifedbyitsposition (xi,yi,zi) in the ion beam frame ZZZZ Lei =2nLc cos 2(.L/2) dx dy dz dtnlaser(xL,yL,zL - ct) .(3)(x - xi,y - yi,z - ßct - zi), (37) reduces to  2 nL x(zi tan(.L/2) + yi)2 i e Li = qexp -- , (38) 2.2 2.2 (1 + tan2(.L/2).2 /.2 ) 2..2 1+ .2 /.2 tan2(.L/2) LLzL LzL where nL is the number of photons in a laser pulse, .z = c.t is the longitudinal laser-beam size. The choice of the vertical crossing plane allows to minimise the crossing angle between the two beams and, in turn, maximises the overall interaction probability. 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