The ALICE Experiment to be installed at the Large Hadron Collider (LHC) will initially look at Pb82+-Pb82+ collisions. In a later stage, collisions of lighter ions are also foreseen. For lead ions, fast electron cooling will be used in the accumulation process at low energy to reach the beam brightness necessary for the experiment. For lighter ions, electron cooling becomes less efficient as the ratio Q2/A decreases (Q and A are respectively charge state and mass number of the ion). For this reason, a study has been made of the possibility to use the maturing technology of laser-cooling of fast ion beams to reach the desired emittances for lighter ions. The main problems encountered are the availability of useful ion species, the availability of corresponding laser systems, and the efficiency with which the transverse emittance can be reduced by the laser-cooling mechanism (which works mainly in the longitudinal plane)

Madsen, N

Nielsen, J S

Nielsen, JS

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Laser-cooling for light ion accumulation

EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCHORGANISATION EUROPEENNE POUR LA RECHERCHE NUCLEAIRECERN - PS DIVISIONCERN/PS 2000-029 (AE)LASER-COOLING FOR LIGHT ION ACCUMULATIONN. Madsen and J.S. NielsenAbstractThe ALICE experiment to be installed at the Large Hadron Collider (LHC) will initially look at Pb 82+ - Pb82+ colli-sions. In a later stage, collisions of lighter ions are also foreseen. For lead ions, fast electron cooling will be used in theaccumulation process at low energy to reach the beam brightness necessary for the experiment. For lighter ions, electroncooling becomes less efficient as the ratio Q2/A decreases (Q and A are respectively charge state and mass number ofthe ion). For this reason, a study has been made of the possibility to use the maturing technology of laser-cooling of fastion beams to reach the desired emittances for lighter ions. The main problems encountered are the availability of usefulion species, the availability of corresponding laser systems, and the efficiency with which the transverse emittance can bereduced by the laser-cooling mechanism (which works mainly in the longitudinal plane).7th European Particle Accelerator Conference, 26th - 30th June 2000,Vienna, AustriaGeneva, SwitzerlandJuly 13, 2000LASER-COOLING FOR LIGHT ION ACCUMULATIONN. Madsen, CERN, Geneva, SwitzerlandJ. S. Nielsen, ISA, Aarhus University, DenmarkAbstractThe ALICE experiment to be installed at the Large HadronCollider (LHC) will initially look at Pb82+ - Pb82+ col-lisions. In a later stage, collisions of lighter ions are alsoforeseen. For lead ions, fast electron cooling will be used inthe accumulation process at low energy to reach the beambrightness necessary for the experiment. For lighter ions,electron cooling becomes less efficient as the ratio Q2/Adecreases (Q and A are respectively charge state and massnumber of the ion). For this reason, a study has been madeof the possibility to use the maturing technology of laser-cooling of fast ion beams to reach the desired emittancesfor lighter ions. The main problems encountered are theavailability of useful ion species, the availability of corre-sponding laser systems, and the efficiency with which thetransverse emittance can be reduced by the laser-coolingmechanism (which works mainly in the longitudinal plane).1 INTRODUCTIONFor the ALICE experiment at the LHC a scheme for ac-cumulation of Pb54+ ions in the Low Energy Ion Ring(LEIR)1 has been proposed [1, 2]. The purpose of thescheme is to provide lead ion beams of high luminosityfor the experiment. The scheme, tests of which have beenpublished [3], has two goals. First of all it is an accumu-lation scheme, since present ion sources cannot deliver thedesired ion currents, and secondly it is an emittance reduc-tion scheme to reduce the emittances to the nominal valuesof 1.5 π mm mrad (1 sigma) normalized emittance in theLHC.However, it would be possible to increase the luminosityin the experiment if lighter ions with lower charges couldbe delivered. For this, and also for particle physics rea-sons, schemes for accumulating lighter ions are being in-vestigated.In this article the possibility of using laser-cooling foraccumulation is being investigated [4].2 ACCUMULATING WITHELECTRON-COOLINGThe scheme for accumulating lead ions is discussed in Ref.[3]. However, some aspects are similar to those for lighterions, and will be briefly discussed here.The accumulation of Pb54+ ions is done by a mixedhorizontal/longitudinal multi-turn injection. The linac pro-duces ions at 4.2 MeV/amu. The lead ion production is1LEIR is the former Low Energy Antiproton Ring (LEAR).optimized for Pb28+ production, and the ions are strippedat 4.2 MeV/amu to charge state 54+. One batch of ap-proximately 108 ions is injected every 0.4 s in about 200µs(about 30 effective turns in the machine). Electron coolingis used to cool the particles to the stack momentum. Rightafter the injection, the beam has a horizontal emittance (2σ)of about 50 π mm mrad, a vertical emittance of 10 π mmmrad and a relatively uniform ∆p/p of ±3×10−3.For the accumulation of light ions in LEIR, the schemeto be used for lead ions cannot be used directly. Table 1summarizes values for some of the ions considered for ac-cumulation in LEIR.Table 1: Parameters of various ions in LEIR [1]. In thetop part of the table Q¯ is the most abundant charge stateafter stripping at 4.2 MeV/amu. In the bottom part Q is theproposed charge states for accumulation. The transverseelectron cooling time (e-folding of emittance) τec is ob-tained by scaling the experimental results with Pb54+ withQ2/A. The intrabeam scattering (IBS) growth rate τibs isthe longitudinal growth rate, calculated with the programINTRABTC [5]. ∆Qˆv is the maximum tune shift calcu-lated in the worst case in the scheme, which is right aftercooling and rebunching in LEIR [1].Ion Q¯ NLEIR Q¯2/A τec τibs ∆Qˆv20882 Pb 54 1.2×109 14 0.2s 2.2s 0.0844020Ca 17 3.2×1010 7.2 0.4s 0.3s 1.2168 O 8 1.2×1011 4 0.7 s 0.3s 2.4Ion Q NLEIR Q2/A τec τibs ∆Qˆv4020Ca 10 3.2×1010 2.5 1.1s 2.4s 0.404020Ca 8 3.2×1010 1.6 1.7s 5.8s 0.26168 O 4 1.2×1011 1 2.8 s 3.8s 0.6168 O 2 1.2×1011 0.25 11s 57s 0.15From Table 1, it can be concluded that the main prob-lem with the lighter ions is the tune shift, as the longitu-dinal intrabeam scattering (IBS) growth times in all casesare small compared to longitudinal electron cooling times(10s of milliseconds). To deliver increased luminosity it isnecessary to accumulate the extra particles desired in a rea-sonable time, such that the integrated luminosity is actuallyincreased. Furthermore, as reducing Q2/A slows electroncooling, and reducing the number of particles per injectionincreases the accumulation time, it would be desirable tofind an alternative scheme. As laser-cooling is suited torelatively low charge states it might be suitable for exactlythis purpose.3 THE LASER FORCELaser-cooling is based on the fact that photons carry mo-mentum. When an ion absorbs a photon, the ions mo-mentum is thus changed by an amount equivalent to themomentum of the photon. If the ion then decays sponta-neously, a photon is emitted. The spatial distribution ofspontaneously emitted photons is symmetric; thus, if a con-dition can be achieved where an ion is continuously excitedby photons coming from one direction, and then decaysspontaneously, a net average force in the direction of theincoming photons is exerted on the ion. As the force isbased on resonance with the transition, it is velocity depen-dent due to the Doppler shift. The Doppler shift cause thevelocity range of the force to be short (typically∼ 20 m/s).Table 2 lists some lighter ions with suitable transitionsfor laser-cooling. There are at least 11 ion species whichhave been cooled to date, all of them singly charged. Table2 lists the three which have been cooled in a storage ring.Table 2: Parameters of light ion species which may belaser-cooled. Only Li+, Be+ and Mg+ have been cooledin a storage ring. A laser intensity of 12.7 W/cm2 hasbeen assumed. λair is the wavelength of the transition,τup the lifetime of the upper level, F reslas is the maximumlaser-force and Is is the saturation intensity [6].Species λair τup Is F reslas[nm] [ns] [mW/cm2] [MeV/c/s]6,73 Li+ 548.5 43.9 8.61 25.794Be+ 313.0 8.70 234 2242412Mg+ 279.6 3.8 751 5514020Ca+ 396.8 7.1 141 218115 B2+ 206.6 5.24 1.3×103 517In the lead ion accumulation scheme, the initial momen-tum spread was ±3×10−3, which, with a relativistic β of9.43% corresponds to a Doppler shift of order± 400 GHz.4 LASERSContinuous wave (CW) lasers for generating visible orultra-violet light come in many varieties. The parametersof interest for accumulation of particles are the laser powerwhich gives the available force, the frequency tunability,and the system stability, which for LEIR purposes shouldbe measured in days.With such stability requirements, the main interestwould be in ion-lasers or solid state (diode) lasers. As ion-lasers are based on specific transitions in the laser medium,these are fixed frequency lasers. Diode lasers can be tuned10’s of GHz (and at times more), but deliver frequenciesin the red to infra red region, which means that frequencydoubling will be necessary. The matching conditions forfrequency doubling cause the available online tuning rangeto be of order 20 GHz or less (i.e. the tuning range whichwill be feasible to carry out in the short time during ac-cumulation) [7]. Even if dye laser systems would be con-sidered, the online tuning range would only increase in thebest of circumstances to about 50 GHz.In terms of wavelength and power, it is not practical toobtain CW laser light below 200 nm, as light below thislimit is absorbed heavily by air. In the range 200 nm -400 nm power up to about 0.5 W will be possible at spe-cific wavelengths, decreasing as the desired wavelength ap-proaches 200 nm. Above 400 nm, several watts are possi-ble, again depending very much on the desired wavelength,as well as the financial investment.If laser-cooling is desired, it will be necessary to studythe specific case at hand, as it is not possible to obtain thepower levels mentioned above at all wavelengths. Beingable to tune the energy of the particles to a given Dopplershift is therefore highly desirable.5 LASER COOLINGIt was noted above that the momentum spread of the multi-turn injected beam corresponded to a Doppler shift of hun-dreds of GHz. This is much larger than the online tuningrange of existing laser systems. Therefore, only coolingwith a fixed frequency laser will be considered.∆v∆tLasera)∆vF||b)Stable PointIndAcFigure 1: See text for explanation. a) Longitudinal PhaseSpace during bunched beam laser-cooling. b) Cooling witha single fixed laser and an induction accelerator.Two methods have been demonstrated which accomplishlaser-cooling in a storage ring with a fixed frequency laser(Figure 1). The first is to do laser-cooling of a bunchedbeam, where the periodic synchrotron oscillations of theparticles may cause them all to experience the laser force,and thus with correct tuning of the laser, the synchrotronoscillations can be damped [8]. The second is to use aninduction accelerator to accelerate the ion beam into reso-nance with the laser. As the laser force is very large it willcounteract this force for ions which are within resonancerange, and thus a stable point in velocity around whichthe ions are cooled longitudinally is achieved [9]. The RFmethod has the advantage that once cooled, the beam canin principle be kept cooled for ever [8]. The RF can fur-thermore be used to accelerate the particles into resonancewith the laser, and thus improve the longitudinal coolingtime for large ∆p/p.For efficient and fast accumulation in LEIR it is neces-sary also to be able to stack in the transverse degrees offreedom. Transverse laser-cooling is accomplished indi-rectly, either through IBS or dispersive coupling [10, 11].IBS is not efficient for accumulation, as the initial injectedbeam is not very dense and therefore the IBS rates will below. However, in the final state after cooling, intra beamscattering may well be an important factor [11].Transverse laser-cooling through dispersion has beendemonstrated [10]. When an ion scatters a laser photon,its momentum and thus the closed orbit about which it os-cillates are changed. If this happens in a dispersive sectionof the storage ring, the amplitude of the betatron oscilla-tion is changed, and by suitable arrangement of the laserposition, cooling can be accomplished [12]. By introduc-ing coupling of the vertical and horizontal motion in thering, cooling can be accomplished in both dimensions.Table 3 shows the horizontal cooling times from a simu-lation of bunched beam laser-cooling of a single particle ina dispersive section of LEIR. For the calculation B2+ hasbeen used as this is the most promising species for LEIR(many of the ions available for laser-cooling have too highrigidity to be stored in LEIR). The laser position relative tothe beam center∆xlas and the frequency offset∆flas havebeen optimized in each case.Table 3: Horizontal emittance cooling times (e-folding)from a simulation of bunched beam laser-cooling of a sin-gle particle of 11B2+ at 4.2 MeV/amu in LEIR. A counter-propagating laser of 200 mW power with a size of 0.5 mm(sigma) and a wavelength of 227.1 nm was used. The lat-tice used is Machine 97-2 from Ref. [3], where βh = 2.2 mand D = 9.5 m in the cooling sections, and Qh = 1.59. TheRF is set to the second harmonic and the voltage to 6.5 kV.Single Part. Emit. [mm mrad]∆p/p 2.1 π 10 π 50 π ∆flas2×10−5 0.01s 0.09s 0.5s -0.2 GHz2×10−4 0.4s 0.6s 3.0s -17 GHz2×10−3 2.2s 3.3s 7.3s -200 GHz∆xlas -1 mm -4 mm - 10 mmThe cooling times given in Table 3 for the large emit-tances and momentum spreads are the initial cooling times;in most cases the cooling would stop after a time, as theparticle moves out of the range of the laser force (both infrequency and physical overlap). Therefore it will be nec-essary to move the laser both in frequency and position.Changing the position of the laser can be accomplishedwith a simple piezzo-based mirror system. However, asdiscussed before, the laser frequency cannot be changedby the large amounts necessary. At least two solutions arepossible to remedy this. One is to refrain from momentumstacking. This would however increase accumulation time.Another option is to accelerate the ion beam into resonancewith the laser and thereby cool it longitudinally. Accelera-tion can be done either with an induction accelerator [9] orusing RF acceleration. In any case, Table 3 shows that thecooling times for the full beam are an order of magnitudelonger than the requirements (about 0.2 - 0.5s). Thus unlesssignificantly more laser-power can be supplied it will not bepractical to use laser-cooling for accumulation in LEIR.6 CONCLUSIONSA preliminary study of the feasibility of using laser-coolingfor accumulation of light ions in LEIR has been described.The study shows that the main hurdles in using laser-cooling in a storage ring are the velocity range of the laser-force, combined with the relatively feeble laser intensitiesavailable at the wavelengths necessary. These hurdles canto some extent be overcome by using RF or induction ac-celeration and a dedicated storage ring lattice. A simulationof laser-cooling in LEIR shows that the accumulation timecompared to present day electron-cooling is about an orderof magnitude longer. Thus in the case of LEIR, the optiondoes not look promising for the moment.However, the study also indicates that if some effort isput into a storage ring with a lattice specially optimizedfor laser-cooling, and if, furthermore, external acceleration(RF or induction) is used to reduce the initial momentumspread, or only transverse filling is used, and if enoughlaser power could be obtained, then laser-cooling would bepossible. The purpose of doing this rather than electron-cooling, is that once comparatively small emittances havebeen reached, laser-cooling is orders of magnitude strongerthan electron cooling, and has been demonstrated to sustainrather large tune shifts [11]. Thus if high luminosity beamsare needed, laser-cooling may be a candidate, perhaps incombination with electron-cooling initially.7 REFERENCES[1] P. Lefe`vre and D. Mo¨hl, CERN/PS 93-62 (DI) (1993)[2] ALICE - Technical Proposal, CERN/LHCC 95-71[3] J. Bosser et al., CERN/PS 99-033 (DI), (1999)[4] S. Schro¨der et al., Phys. Rev. Lett. 64, 2901 (1990), and J.S.Hangst et al., Phys. Rev. Lett. 67, 1238 (1991).[5] R. Giannini and D. Mo¨hl, CERN/PS/AR 96-19 (1996)[6] N. Madsen, Ph.D. Thesis, Institute of Physics and Astron-omy, University of Aarhus, Denmark (1998)[7] J. S. Nielsen, Opt. Lett. 20, 840 (1995)[8] J.S. Hangst et al., Phys. Rev. Lett. 74, 4432 (1995)[9] Ch. Ellert et al., Nucl. Inst. & Meth. A 314, 399 (1992)[10] I. Lauer et al., Phys. Rev. Lett. 81, 2052 (1998)[11] N. Madsen et al., Phys. Rev. Lett. 83, 4301 (1999)[12] A. Wolf, Second Workshop on Diagnostics of Laser-CooledBeams, Sandbjerg, Denmark (1991)

Laser-Cooling for Light Ion Accumulation

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