Intra- beam Sca-ering Effects in the Extra Low ENergy An;proton ring (ELENA)

Transcription

1 Intra- beam Sca-ering Effects in the Extra Low ENergy An;proton ring (ELENA) Javier Resta-Lopez, James Hunt, Carsten Welsch, Cockcroft Institute, The University of Liverpool IPAC 2015 Richmond, Virginia, USA

2 Outline Context ELENA overview EmiAance diludon and lifedme limidng processes Rest gas IBS Beam evoludon Summary and Future plans 2

3 Context An;proton Decelerator (AD) at CERN The AD provides low- energy andprotons (5.3 MeV kinedc energy) for different experiments dedicated to the producdon of andhydrogen and measurement of its properdes 2.7 GeV (2.7 GeV 5.3 MeV) 99.9% of the andprotons produced by the AD are lost due to the experiments' use of degrader foils needed to further decelerate them from the AD ejecdon energy (5.3 MeV) down to around 5 kev, the energy needed for trapping 3

4 Context An;proton Decelerator (AD) and ELENA at CERN ELENA will bring a 10 to 100- fold increase in the experiments efficiency, as well as the possibility to accommodate an extra experimental area to invesdgate gravitadon with andhydrogen (GBAR) 2.7 GeV Basic ELENA beam parameters (2.7 GeV 5.3 MeV) Energy range 5.3 MeV 100 kev Momentum range 100 MeV/c 13.7 MeV/c Intensity ~ 10 7 pbar Transverse acceptance 75 µm Parameters at ejection: Number of bunches 4 Δp/p (rms) ~ 0.05% Bunch length (rms) 0.33 m ε x, ε y (rms) ~ 1 π mm mrad GBAR ELENA 4

5 Schema;c layout Extrac;on towards exis;ng experiments ELENA overview Injec;on with magne;c septum ( 300 mrad) and kicker (84 mrad) High sensidvity magnedc pick- up for SchoAky diagnosdc (for intensity) and LLRF Wideband RF cavides C = 30.4 m e- cooler Bending magnets (π/3 kick angle) Scraper for destrucdve emiaance measurements CompensaDon solenoids Extrac;on towards new experimental area The e- cooler must be able to produce a cold and reladvely intense electron beam: k B T? < 0.1 ev, k B T k < ev n e m 3 Details in ELENA TDR, CERN (April 2014) 5

6 ELENA overview Op;cs Good tunability in the range 2 < Q x < 2.5 and 1 < Q y < 1.5 Q x 2.3, Q y 1.3 max β x 12 m max β y 6 m max D x 1.7 m <β x,y > 3 m <D x > 1.2 m At e- cooler posidon: β x 2 m β y 2 m D x 1.5 m MADX model based on the specificadons of the ELENA TDR 6

7 ELENA overview ELENA cycle deceleration coasdng beam deceleration bunching and extraction cooling during bunching prior to ejection (~ s) We have mainly focused on beam dynamics studies during the 1 st and 2 nd e- cooling plateaus 7

8 Emi-ance dilu;on and life;me limi;ng processes Hea;ng processes: InteracDon with the rest gas: Nuclear scaaering Single Coulomb scaaering MulDple Coulomb ScaAering (MCS) pardcle loss if high scaaering angle The ELENA vacuum pipe will be coated with Non- evaporable GeAer (NEG) films Expected residual gas composidon: 95% H 2, 2% CO, 2% CO 2, 1% CH 4 Nominal vacuum pressure for ELENA: P=3x10-12 Torr This pressure is a very safe limit in terms of both low MCS effect and very low rate of large angle sca-ering Intra- Beam Sca-ering (IBS): MulDple small- angle Coulomb scaaerings of charged pardcles within the accelerator beam itself. Exchange of energy between the transverse and longitudinal degrees of freedom 8

9 BETACOOL: BETACOOL simula;ons [A. Sidorin et al., NIM A 558 (2006), 325] CalculaDon of the evoludon of beam distribudons under the acdon of cooling forces (in this case electron cooling) + different scaaering effects Benchmarked against experimental data in different rings, e.g. Experimental studies of IBS in RHIC and comparison with BETACOOL simuladons 20 [µm] emittance Horizontal Ver;cal time [A. V. Fedotov et al., Proc. of HB2006, WEBY03, Tsukuba, Japan, 2006] [s] 9

10 BETACOOL simula;ons Simula;on condi;ons: MulDparDcle simuladons based on a Monte- Carlo method (model beam algorithm) 1000 modelled pardcles CoasDng andproton beam (at cooling plateaus) and bunched beam (before extracdon) Electron cooling considering a cylindrical uniform electron beam distribudon Cooling process + Rest gas + IBS (MarDni model) Cooling fricdon force computed using the Parkhomchuk s model (magnedsed electron distribudons) 10

11 x ( mm mrad) Beam evolu;on 1 st cooling plateau, p=35 MeV/c, coas;ng beam Electron cooling process in presence of rest gas and IBS Parameter evolu;on: Simulated 10 random seeds for the evoludon of a distribudon of 1000 modelled pardcles x (rms) t (s) y ( mm mrad) y (rms) t (s) p/p [%] p/p(rms) t (s) Step in cycle ε x, ε y [π mm mrad] (rms) Δp/p [%] (rms) Start 1 st cooling (35 MeV/c) 8.0, Ager 8 s cooling (35 MeV/c) 1.1, ConservaDve inidal values 11

12 Beam evolu;on 1 st cooling plateau, p=35 MeV/c, coas;ng beam Electron cooling process in presence of rest gas and IBS Beam profile evolu;on: Intensity [%] t=0 s t=2 s t=4 s t=6 s t=8 s Intensity [%] t=0 s t=2 s t=4 s t=6 s t=8 s Intensity [%] t=0 s t=2 s t=4 s t=6 s t=8 s x [ x ] y [ y ] p/p [ p ] During the cooling process, the beam distribudon quickly deviates from a Gaussian profile and a very dense core appears Core overcooling. UnderesDmaDng IBS effect in the core? 12

13 Beam evolu;on 1st cooling plateau, p=35 MeV/c, coas;ng beam Core- tail development: Fig0.1%. Figters during ring mthe seeds.the erent times mes beam stri- distriand a very very Figure 4: Distribution of an ensemble of 1000 modelled Figure 4:represents Distribution of anspread ensemble of 1000 The parabola the momentum of the electrons due to modelled space charge antiprotons in the cooler s (A)atand antiprotons in the cooler at t = at0 t s =(A)0 and t =at8t s= 8 s For large inidal beam size, pardcles in the tails experience weaker fricdon forces than in the core à for first cooling plateau. The parabola represents (B) for (B) the firstthe cooling plateau. The parabola represents development of core- tail pardcle distribudons the momentum of the electrons to space the momentum spread spread of the electrons due to due space chargecharge Javier Resta Lopez, IPAC 2015 charge. The straight blue line represents the dispersion line13

14 Beam evolu;on Core- tail development: Standard models of IBS, such as the MarDni model, are based on the growth of the rms beam parameters of a Gaussian distribudon. These models underesdmate the IBS effect for non- Gaussian distribudons. Further invesdgadon: Apply an IBS core- tail model (bi- Gaussian distribudon): IBS induced kicks based on diffusion coefficients which are different for pardcles inside and outside of the core Apply a IBS Local model: can calculate correctly IBS for arbitrary distribudons, but it takes a lot of computadon Dme [A. V. Fedotov, IBS for Ion DistribuDon Under Electron cooling Proc. PAC2005] 14

15 Beam evolu;on 1 st cooling plateau, p=35 MeV/c, coas;ng beam Core- tail development: IBS Mar;ni model vs core- tail model: Beam distribudons axer 8 s cooling 10 with IBS Martini model with IBS core-tail model 10 with IBS Martini model with IBS core-tail model Intensity [%] Intensity [%] x [ x ] p/p [ p ] The cooling of the core is smoother if an IBS core- tail model (bi- Gaussian) is applied and, probably, it describes more accurately the actual process 15

16 Beam evolu;on 2 nd cooling plateau, p=13.7 MeV/c, coas;ng beam x ( mm mrad) Electron cooling process in presence of rest gas and IBS Parameter evolu;on: Simulated 10 random seeds for the evoludon of a distribudon of 1000 modelled pardcles x (rms) t (s) y ( mm mrad) y (rms) t (s) p/p [%] p/p(rms) t (s) Step in cycle ε x, ε y [π mm mrad] (rms) Δp/p [%] (rms) Start 2 nd cooling (13.7 MeV/c) * 2.8, Ager 2 s cooling (13.7 MeV/c) 0.52, * Taking into account the adiabadc emiaance increase by a factor 2.55 because of the deceleradon from 35 MeV/c to 13.7 MeV/c 16

17 Beam evolu;on 2 nd cooling plateau, p=13.7 MeV/c, coas;ng beam Electron cooling process in presence of rest gas and IBS Beam profile evolu;on: Intensity [%] t=0 s t=0.5 s t=1 s t=1.5 s t=2 s Intensity [%] t=0 s t=0.5 s t=1 s t=1.5 s t=2 s Intensity [%] t=0 s t=0.5 s t=1 s t=1.5 s t=2 s x [ x ] y [ y ] p/p [ p ] In this case, the cooling is more homogeneous for both core and tails, and axer 2 s cooling the beam reaches the equilibrium 17

18 Beam evolu;on Before extrac;on, p=13.7 MeV/c, bunched beam Electron cooling process in presence of rest gas and IBS Parameter evolu;on: Simulated 10 random seeds for the evoludon of a distribudon of 1000 modelled pardcles x (rms) y (rms) p/p(rms) With cooling: Step in cycle ε x, ε y [π mm mrad] (rms) Δp/p [%] (rms) Start cooling (13.7 MeV/c) * 0.78, Ager 0.3 s cooling (13.7 MeV/c) 0.9, * StarDng values assuming Debunching/bunching with 50% blow- up 18

19 Summary and Future plans For a beaer understanding of the long term beam dynamics in the ELENA ring, we have started a detailed invesdgadon into the different cooling and headng processes which determine the beam lifedme and quality of the andproton beam Here we have put special emphasis on the study of the cooling process in presence of IBS Next steps: Comparison of equilibrium parameters using different models of IBS SimulaDons including e- cooler imperfecdons For simplicity we have assumed inidal Gaussian beam profiles. However, in pracdce, the distribudon of the beam injected from the AD could have a significant non- Gaussian shape. This characterisdc will be taken into account in future studies. IdenDfy potendal aspects of the machine that could be opdmised ELENA will be an ideal test- bench to compare experiments and simuladons of e- cooling at very low energies 19

20 Special thanks to: Christian Carli, Alexander Smirnov, and all the ELENA team at CERN Thank you 20

21 Intrabeam sca-ering IBS theory extensively described in the literature, see e.g. A. Piwinski, Proc. of the 9 th InternaDonal Conference on High Energy Accelerators, 1974, p. 405: smooth lazce approximadon J. Bjorken, S. MDngwa (B- M), Part. Accel. 13 (1983) 115: using the scaaering matrix formalism; valid for strong focusing machines; approximadons valid for ultrareladvisdc beams only M. MarDni, CERN PS/84-9 (AA) 1984: (extended Piwinski s model) valid for strong focusing machines. M. Conte, M. MarDni, Part. Accel. 17 (1985) 1: B- M theory adapted to include non- ultrareladvisdc correcdons and several approximadons for pracdcal purposes in some regimes of applicability (Wei, Parzen, Bane, Rao and Katayama, ), as well as refinements of the standard theories above, 21

22 Reservoir 22

23 Context The An;proton Decelerator (AD) at CERN provides low- energy andprotons (5.3 MeV kinedc energy) for different experiments dedicated to the producdon of andhydrogen and measurement of its properdes In today s set- up, about 99.9% of the andprotons produced by the AD are lost due to the experiments' use of degrader foils needed to further decelerate them from the AD ejecdon energy (5.3 MeV) down to around 5 kev, the energy needed for trapping From N. Madsen, AnDproton catching for andhydrogen experiments, ELENA Beam Physics and Performance CommiAee (19 July 2012): Energy straggling increases energy spread such that only few andprotons can be captured 23

24 Context Current setup: pbar 2.7 GeV AD DeceleraDon, stoch., e- cooling Degrader foil 5.3 MeV 5 kev TRAP The soludon: A small magnet ring that will fit inside the present AD hall ELENA: 30 m circumference decelerator to slow the 5.3 MeV andprotons from the AD to an energy of just 100 kev. 5.3 MeV ELENA DeceleraDon, e- cooling ~ 10-4 efficiency 99.99% lost 100 kev 5 kev TRAP SDll foil to decelerate to a few kev, but much reduced thickness ELENA will bring a 10 to 100- fold increase in the experiments efficiency, as well as the possibility to accommodate an extra experimental area to invesdgate gravitadon with andhydrogen (GBAR) 24

25 ELENA overview ELENA parameters For a coasdng beam Parameter 1 st plateau 2 nd plateau Beam momentum 35 MeV/c 13.7 MeV/c IniDal Δp/p 0.1% 0.05% IniDal 1σ emiaance 8 π mm mrad 2.8 π mm mrad Beam intensity 2.5x x10 7 Average beta funcdon β T 3 m 3 m Average dispersion D x 1.2 m 1.2 m ELENA acceptance A T 75 μm 75 μm Vacuum pressure 3x10-12 Torr 3x10-12 Torr Gas density n (at room T) 9.6x10 10 m x10 10 m

26 Electron cooler ELENA e- cooler system parameters for the simula;ons From ELENA TDR, CERN (2014): Parameter Value Momentum [MeV/c] Velocity factor β=v/c Electron beam energy [ev] Electron current [ma] 5-2 Electron beam density [m - 3 ] 1.38x x10 12 B gun [G] 1000 B drix [G] 100 Expansion factor 10 Cathode radius [mm] 8 Electron beam radius [mm] 25 Twiss parameters [m] β x =2.103, β y =2.186, D x =1.498 Flange- to- flange length [mm] 1930 Drix solenoid length [mm] 1000 EffecDve length (good field region) [mm] 700 Electron beam transverse, longitudinal temperature [ev] 0.01,

27 Electron cooling Fric;on force: The corresponding fric;on force vs ion velocity: Longitudinal Transverse / v i / 1/v 2 i F peak (for T tr =0.01 ev and T long = ev)= ev/m, at v i =6000 m/s F peak (for T tr =0.01 ev and T long =0.001 ev)= ev/m, at v i =11000 m/s F peak (for T tr =0.01 ev and T long = ev)= ev/m, at v i =6000 m/s F peak (for T tr =0.01 ev and T long =0.001 ev)= ev/m, at v i =11000 m/s 27

28 Intrabeam sca-ering IBS hea;ng rates 1 x, 1 y, 1 p / r 2 pc 32 p 3 4 x y p = ( N/C N b /(2 p s ) for coasting beams for bunched beams IBS becomes stronger when the phase space volume of the beam is reduced by cooling, thus limidng the achievable final emiaances 28

29 Beam dynamics 1 st cooling plateau, p=35 MeV/c, coas;ng beam Electron cooling process in presence of rest gas and IBS IBS growth rates Cooling rates Axer 8s cooling, equilibrium is not yet reached (1/τ y ) IBS changes sign from negadve (damping or cooling) to posidve (headng) at t 13 s 29

30 Beam dynamics 2 nd cooling plateau, p=13.7 MeV/c, coas;ng beam Electron cooling process in presence of rest gas and IBS IBS growth rates Cooling rates Equilibrium pracdcally reached axer 2 s cooling (1/τ y ) IBS changes sign from negadve (damping or cooling) to posidve (headng) at t 1 s 30

31 Beam dynamics Electron cooling process in presence of rest gas and IBS Invariant distribu;ons 1 st cooling plateau, p=35 MeV/c Δp/p ε y ε x Unphysical result? Standard models of IBS, such as the MarDni model, are based on the growth of the rms beam parameters of a Gaussian distribudon. These models underesdmate the IBS effect for beam distribudons far from Gaussian. Further invesdgadon to prevent overcooling: Core emiaances (68%) ~ 10-8, 10-9 π m rad 95% emiaances ~ 10-5 π m rad Very dense core Long tails highly populated Apply core- tail models Apply a Local model: it takes a lot of computadon Dme! 31

32 Space charge Space charge limit N for a stored andproton beam with ΔQ=- 0.1 Incoherent tune shig due to space charge effects: For a Gaussian distributed round beam: Q sc r p N B 1 f where B f is a bunching factor: B f = hii Î ( 1 if coasting beam p 2 z h if bunched beam C Here we have taken the rms emittance (pbar per bunch) N Bunched beam =8.0 mm mrad =2.5 mm mrad =1.0 mm mrad =0.5 mm mrad h=4, B f =0.107 σ z =0.3 m 13.7 MeV/c Beam momentum p [MeV/c] h is the harmonic number 4 bunches, assuming ε x,y 0.5 π mm mrad N total 1x