9/15/05 A. Lehrach, HESR, Coulomb ’05 1
Intensity Limits and Intensity Limits and Beam Performances in the Beam Performances in the HHigh-igh-EEnergy nergy SStorage torage RRingingHESR-Consortium: FZJ, GSI, TSL, and Univ. of Bonn and Dortmund
HESR Layout Beam Equilibrium Beam Losses and Luminosity Other Intensity Limiting Effects Summary & Outlook
9/15/05 A. Lehrach, HESR, Coulomb ’05 2
Accumulation and Accelerationof Antiprotons at FAIR
Antiproton production
Linac: 50 MeV H-
SIS18: 5·1012 protons / cycle SIS100: 2-2.5·1013 protons / cycle
26 GeV protons bunch compressed to 50nsec
Production target: antiprotons 3% momentum spread
CR: bunch rotation and stochastic cooling at 3.8 GeV/c
RESR: accumulation at 3.8 GeV/cProduction rate
p2·107/s (7·1010/h) antiprotons
9/15/05 A. Lehrach, HESR, Coulomb ’05 3
HESR Layout
One half of the arc super-periodMomentum range 1.5 – 15 GeV/c6-fold symmetry arcs with a length of 155 m each.Mirror symmetric FODO structure designed as pseudo second order achromat with dispersion suppression.Two straight sections of 132 m length each. Ring circumference 574 m.
Qx = 12.16 Qy = 12.18γtr = 6.5i
9/15/05 A. Lehrach, HESR, Coulomb ’05 4
“High Resolution Mode” “High Luminosity Mode”
Momentum range Up to 9 GeV/c Full momentum range
Number of antiprotons 1010 1011
Target thickness 4·1015 cm-2 4·1015 cm-2
Peak luminosity 2·1031 cm-2s-1 2·1032 cm-2s-1
Beam emittance 1-2 mm mrad 1-2 mm mrad
Momentum resolution p/prms = 10-5 p/prms = 10-4
Beam Cooling Electron Cooling Stochastic Cooling
Experimental RequirementsPANDA (Strong Interaction Studies with Antiprotons):
Momentum range: 1.5 to 15 GeV/c
9/15/05 A. Lehrach, HESR, Coulomb ’05 5
12 m
Charger: H- Cyclotron
30 m
Solenoid
High voltage (8 MV) tank
HESRbeam
Feasibility study of magnetized electron cooling for the HESR 9/2003
(Budker Institute, Novosibirsk, RUS)
HESR Electron Cooler
Electron Cooler
Cooling section
HV section electrostatic accelerator 0.45 - 8 MV, up to 2 A charged by H- beam Cooling section sc solenoid length 30 m magnetic field 0.2 - 0.5 T straightness 10-5
beam diameter 6 - 10 mm Bending section electrostatic up to 21 KV/cm bending radius 4 m
Acceleration column
8 m
9/15/05 A. Lehrach, HESR, Coulomb ’05 6
Electron Cooling ForceParkhomchuk model (*particle frame):
Effective Coulomb log:
Coolig rate:
Longitudinal force (momentum spread ):
Fit to Parkhomchuk formula
CELSIUS measurement Dec. 2004
veff* 104 m/s
Measurements at CELSIUS seem topredict an accuracy of the longitudinal Parkhomchuk force within a factor of 2
2/32*2*
***
))()(()(
effC vv
vKLvF
10ln max
bbLC
3*
3
20
21
0 )(4
eff
eceep
vc
ALcnrrZ
2/322
31
0|| )(
eff
effeF
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Pellet target (WASA@CELSIUS)
Formation of frozen hydrogen pellets
H2 (=0.08 g/cm3)60000 pellets/s
<n> = 5x1015 cm-2
d=30 m
1 mm
HESR: Target will be switched on after injection and cooling/IBS equilibrium Transverse heating is required to ensure 1 mm spot size on the target
Beam spot
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Beam HeatingTransverse emittance growth in the target:βx,y small, D=D‘=0, θrms: Mean Coulomb scattering angle
radrmsrevrmsyx
yx
xx
cpMeVf
dtd 2
22,
, 1.14,21
Longitudinal emittance growth in the target:βs=h|η|/Qs (bunched beams), δrms: Mean relative momentum deviation
revrmsss f
dtd 2
21
Multiple IBS: (Soerensen or ‘plasma’ model)
Diffusion constant:
CLcrn ciiIBS2/13
030
2
|| 4
22/3||1
|| ~
IBSIBS
2/3||
||
IBSIBSD
2/5||
21
||
221
~
IBS
x
xIBS
x
xIBS DD
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Equilibrium for Core Particles(rms analytic model)
Results compare very well with BetaCool simulations
With equilibrium emittance With fixed emittance
O. Boine-Frankenheim et al.
Electron Cooler:L = 30 mIe = 0.2 Aveff = 2·104 m/sc = 100 m
Target:Pellet Streamdt = 4·1015 cm-2
t = 1 m
1010 particles1010 particles
1011 particles
1011 particles
9/15/05 A. Lehrach, HESR, Coulomb ’05 10
INTAS Project “Advanced Beam Dynamics for Storage Rings”
Kinetic simulation of cooling dynamics Benchmarking of different models for IBS, cooling
forces and beam-target interaction Analytical and numerical studies of instability
thresholds in the presence of cooling and space charge Impedance library Kinetic simulation studies of accumulation schemes
FZ Jülich, GSI Darmstadt, JINR Dubna, Univ. Kiev, ITEP Moscow, TSL Uppsala
9/15/05 A. Lehrach, HESR, Coulomb ’05 11
Beam Loss Mechanisms
Hadronic Interaction
Single Target Scattering out of the acceptance
Energy straggling out of the acceptance
Single IBS Scattering (Touschek loss rate)
9/15/05 A. Lehrach, HESR, Coulomb ’05 12
Hadronic Interaction
totalpptrev
tHloss nf )( 1
1.5 GeV/c 9 GeV/c 15 GeV/c
Relative loss rate / s-1 1.7·10-4 1.2·10-4 1.1·10-4
1/e lifetime 1.6 h 2.3 h 2.5 h
nt = 4·1015 cm-2
frev = 443, 519, 521 kHzσppbar = 100, 57, 51 mbarn
Loss rate: PDG
9/15/05 A. Lehrach, HESR, Coulomb ’05 13
Single Coulomb Scattering
t
teff
eff
titrev
tCloss
nrZZf i
,
4)( 22
040
2221
,
1.5 GeV/c 9 GeV/c 15 GeV/cRelative Beam Loss Rate / s-1 1.8·10-4 7.3·10-6 2.1·10-6
1/e lifetime / h 1.5 h 38.1 h 132.3 h
εt = 1 mm mradnt = 4·1015 cm-2, Hydrogenfrev = 443, 519, 521 kHz
Rutherford Cross Section
Loss rate:
9/15/05 A. Lehrach, HESR, Coulomb ’05 14
Energy Loss Straggling
][4.153 20
2
keVxAZZ
t
t
20
20
20
max )/(/212
pepe
e
mmmmm
max
202 1)(
w
Single collision energy loss probability ( energy loss):
Maximum energy transfer:
Scaling quantity (~ mean energy loss):
020 E
9/15/05 A. Lehrach, HESR, Coulomb ’05 15
Energy Loss Straggling
1.5 GeV/c 9 GeV/c 15 GeV/c
Relative Beam Loss Rate / s-1 3.5·10-4 4.1·10-5 2.8·10-5
1/e Beam life time / h 0.79 6.8 9.9
δeff= -εeff/(β20E0)=10-3
frev = 443, 519, 521 kHz
Loss probability per turn
effeffrevrev
tSloss fdwf
eff
max
max
20
max
1||, ln11)()(
max
Loss rate:
9/15/05 A. Lehrach, HESR, Coulomb ’05 16
Single IBS: Touschek Loss Rate
Relative Beam Loss Rate / s-1 1.5 GeV/c 9 GeV/c 15 GeV/c
0.01mm mrad 4·10-2 2·10-4 4·10-5
1mm mrad 4·10-5 2·10-7 4·10-8
1/e Beam life time / h 6.9 1390 7000
Loss rate:
Touschek (IBS) lifetime increases with larger emittance
2||
0
1 1)(effC
IBStIBSloss L
DT
Single IBS changes the scattered particle momentum sufficiently that it excides the momentum acceptance of the accelerator
δeff=10-3
1/T0 = frev = 443, 519, 521 kHz
9/15/05 A. Lehrach, HESR, Coulomb ’05 17
Beam Life Time
tIBSloss
tSloss
tClossHloss
tTotalloss )()()()()( 11111
1.5GeV/c 9 GeV/c 15 GeV/c
Relative Beam Loss Rate / s-1 7.4·10-4 1.7·10-4 1.4·10-4
1/e Beam life time / s ~ 1400 ~ 6000 ~ 7200
11100 10 to10, prevtp nfnnL
L0: initial luminosityτ: beam lifetimetexp: experimental timetprep: beam preparation timenp: number of particlent: target desnityfrev revolution frequency
prepexp
t
tteLL
]1[exp
0
9/15/05 A. Lehrach, HESR, Coulomb ’05 18
HESR Nominal Cycle
9/15/05 A. Lehrach, HESR, Coulomb ’05 19
Average Luminosity for HL
for different pbar production rates!
9/15/05 A. Lehrach, HESR, Coulomb ’05 20
Effects on the Beam
Injection: Losses due to injection oscillation and RF capture
Pre-Cooling: Cooled and hot beams merge
Ramp: Snapback Non-linear part of the rampTune and Chromaticity control
Beam preparation: SqueezeOrbit Control for beam-target overlap
Physics: Beam-Target Interaction, IBS, beam losses
9/15/05 A. Lehrach, HESR, Coulomb ’05 21
Theoretical “forecast”:N.S.Dikansky, V.V.Parkhomchuk, D.V.Pestrikov, Instability of Bunched Proton Beam interacting with ion “footprint”, Rus. Journ. Of Tech. Physics, v.46 (1976) 2551.
P. Zenkevich, A. Dolinskii and I. Hofmann, Dipole instability of a circulating beam due to the ion cloud in an electron cooling system, NIM A 532 (October 2004).
Effect of Electron Beam
Coherent Dipole Instabilities: In the presence of the electron beam in the cooling section, both longitudinal and transverse instability could take place for the circulating beam due to ion clouds
Tune shift:
2332
0
*
12
ecrrI
Q cpee
01.0 eQ
.
AIe 1
ξ: neutralization factor at lowest momentum
Electron heating
9/15/05 A. Lehrach, HESR, Coulomb ’05 22
Summary & Outlook
Beam equilibrium is dominated by IBS
heat the beam transversely
Major beam losses are induces by beam-target interaction
sufficient pbar production rate needed at low momenta
Beam effects and losses during cycle
Effect of the electron beam on the circulating beam