1. Intensity Limits and Beam Performances in the High-Energy Storage Ring
HESR-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 Acceleration of 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/c
Production rate
2·107/s (7·1010/h) antiprotons
9/15/05
A. Lehrach, HESR, Coulomb ’05

3. A. Lehrach, HESR, Coulomb ’05
HESR Layout
One half of the arc super-period
Momentum range 1.5 – 15 GeV/c
6-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 = 12.18
γtr = 6.5i
9/15/05
A. Lehrach, HESR, Coulomb ’05

4. Experimental Requirements
PANDA (Strong Interaction Studies with Antiprotons):
Momentum range: 1.5 to 15 GeV/c
“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
Peak luminosity
2·1031 cm-2s-1
2·1032 cm-2s-1
Beam emittance
1-2 mm mrad
Momentum resolution
p/prms = 10-5
p/prms = 10-4
Beam Cooling
Electron Cooling
Stochastic Cooling
9/15/05
A. Lehrach, HESR, Coulomb ’05

5. Electron Cooler HV section HESR Electron Cooler
Feasibility study of magnetized electron cooling for the HESR 9/2003
(Budker Institute, Novosibirsk, RUS)
HV section
electrostatic accelerator
MV, up to 2 A
charged by H- beam
Cooling section
sc solenoid
length 30 m
magnetic field T
straightness 10-5
beam diameter mm
Bending section
electrostatic up to 21 KV/cm
bending radius 4 m
HESR Electron Cooler
High voltage
(8 MV) tank
12 m
Acceleration column
Charger: H- Cyclotron
HESR
beam
Cooling section
Solenoid
8 m
30 m
9/15/05
A. Lehrach, HESR, Coulomb ’05

6. Electron Cooling Force
Fit to Parkhomchuk formula
CELSIUS measurement
Dec. 2004
Measurements at CELSIUS seem to
predict an accuracy of the longitudinal
Parkhomchuk force within a factor of 2
Parkhomchuk model
(*particle frame):
Effective Coulomb log:
Coolig rate:
Longitudinal force (momentum spread ):
9/15/05
A. Lehrach, HESR, Coulomb ’05

7. Pellet target (WASA@CELSIUS)
Formation
of frozen
hydrogen
pellets
H2 (=0.08 g/cm3)
60000 pellets/s
 Beam spot
d=30 m
<n> = 5x1015 cm-2
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
9/15/05
A. Lehrach, HESR, Coulomb ’05

8. A. Lehrach, HESR, Coulomb ’05
Beam Heating
Transverse emittance growth in the target:
βx,y small, D=D‘=0, θrms: Mean Coulomb scattering angle
Longitudinal emittance growth in the target:
βs=h|η|/Qs (bunched beams), δrms: Mean relative momentum deviation
Multiple IBS:
(Soerensen or ‘plasma’ model)
Diffusion constant:
9/15/05
A. Lehrach, HESR, Coulomb ’05

9. Equilibrium for Core Particles (rms analytic model)
Results compare very well
with BetaCool simulations
With equilibrium emittance
With fixed emittance
1011 particles
1011 particles
1010 particles
1010 particles
Electron Cooler:
L = 30 m
Ie = 0.2 A
veff = 2·104 m/s
c = 100 m
Target:
Pellet Stream
dt = 4·1015 cm-2
t = 1 m
O. Boine-Frankenheim et al.
9/15/05
A. Lehrach, HESR, Coulomb ’05

10. INTAS Project “Advanced Beam Dynamics for Storage Rings”
FZ Jülich, GSI Darmstadt, JINR Dubna, Univ. Kiev, ITEP Moscow, TSL Uppsala
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
9/15/05
A. Lehrach, HESR, Coulomb ’05

11. A. Lehrach, HESR, Coulomb ’05
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. A. Lehrach, HESR, Coulomb ’05
Hadronic Interaction
Loss rate:
PDG
nt = 4·1015 cm-2
frev = 443, 519, 521 kHz
σppbar = 100, 57, 51 mbarn
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
9/15/05
A. Lehrach, HESR, Coulomb ’05

13. Single Coulomb Scattering
Loss rate:
εt = 1 mm mrad
nt = 4·1015 cm-2, Hydrogen
frev = 443, 519, 521 kHz
Rutherford Cross Section
1.5 GeV/c
9 GeV/c
15 GeV/c
Relative 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
9/15/05
A. Lehrach, HESR, Coulomb ’05

14. Energy Loss Straggling
Single collision energy loss probability ( energy loss):
Maximum energy transfer:
Scaling quantity (~ mean energy loss):
9/15/05
A. Lehrach, HESR, Coulomb ’05

15. Energy Loss Straggling
Loss probability per turn
Loss rate:
δeff= -εeff/(β20E0)=10-3
frev = 443, 519, 521 kHz
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
9/15/05
A. Lehrach, HESR, Coulomb ’05

16. Single IBS: Touschek Loss Rate
Single IBS changes the scattered particle momentum sufficiently
that it excides the momentum acceptance of the accelerator
Loss rate:
δeff=10-3
1/T0 = frev = 443, 519, 521 kHz
Touschek (IBS) lifetime increases with larger emittance
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
2·10-7
4·10-8
1/e Beam life time / h
6.9
1390
7000
9/15/05
A. Lehrach, HESR, Coulomb ’05

17. Relative Beam Loss Rate / s-1 A. Lehrach, HESR, Coulomb ’05
Beam Life Time
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
L0: initial luminosity
τ: beam lifetime
texp: experimental time
tprep: beam preparation time
np: number of particle
nt: target desnity
frev revolution frequency
9/15/05
A. Lehrach, HESR, Coulomb ’05

18. A. Lehrach, HESR, Coulomb ’05
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. A. Lehrach, HESR, Coulomb ’05
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 ramp
Tune and Chromaticity control
Beam preparation: Squeeze
Orbit Control for beam-target overlap
Physics: Beam-Target Interaction, IBS, beam losses
9/15/05
A. Lehrach, HESR, Coulomb ’05

21. Effect of Electron Beam
Tune shift:
at lowest momentum
ξ: neutralization factor
Electron heating .
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
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).
9/15/05
A. Lehrach, HESR, Coulomb ’05

22. A. Lehrach, HESR, Coulomb ’05
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
9/15/05
A. Lehrach, HESR, Coulomb ’05