1. Calculation of Beam Equilibrium and Luminosities for ENC@FAIR
28-30 May | Andreas Lehrach

2. Accelerator Working Group
K. Aulenbacher, D. Barber, O. Boldt, R. Heine, W. Hillert, A.Jankowiak, A. Lehrach, Chr. Montag, P. Schnizer, T. Weis

3. Content Introduction HESR Experimental Requirements Beam Simulation
HESR Layout
Beam Simulation
Beam equilibria and luminosities for protons and deuterons
Summary
List of Major Task

4. HESR Experimental Requirements
PANDA (Strong Interaction Studies with Antiprotons):
Momentum range: 1.5 to 15 GeV/c (Antiprotons)
Effective target thickness (pellets): ·1015 cm-2
Beam radius on target (rms): mm
Momentum range
Number of antiprotons
Peak luminosity
Rel. momentum spread (rms)
High Luminosity
(HL)
1.5 – 15 GeV/c
1011
2·1032 cm-2s-1
1·10-4
High Resolution
(HR)
1.5 – 8.9 GeV/c
1010
2·1031 cm-2s-1
≤ 4·10-5
Electron and stochastic cooling
Thick internal (pellet) targets
Cavities for acceleration and barrier bucket (h=1 … 20) 4

5. HESR Layout Straight sections: cooler and target section
Momentum range: 1.5 – 15 GeV/c
Straight sections: cooler and target section
Ring circumference: 574 m
Stochastic Cooling 5

6. The Svedberg Laboratory Uppsala University
HESR Electron Cooler
Momentum range (Antiprotons): 1.5 – 8.9 GeV/c
Electron energy: 0.45 – 4.5 MeV
Electron current: A
Electron radius: 5 mm
Temperature of electron beam (t,l): 1eV, 0.5 meV
Magnetic field (cooling section): 0.2 T
Field qualtiy (rms): Br/B < 10-5 rad
Length of cooling section: Leff = 24 m
Point out interaction section, electrons, antiprotons, solenoids, (normal conducting) (Magnetic spectrometer energy calibration)
Cooling force needs to be stronger than at Fermilab to counteract the internal target
The Svedberg Laboratory Uppsala University
Cooling Section

7. Electron Cooling Force
Parkhomchuk model
(*particle frame):
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
Cooling force [eV/m]
Effective Coulomb log:
Cooling rate:
Relative ion velocity [m/s]
Longitudinal force (momentum spread ):

8. Beam Equilibria and Luminosities
Conservative design (protons)
e-Cooler parameter: E=8.2 MeV, I=3 A, B=0.2T, TT=1eV, TL=0.5meV, Br/B < 10-5, L=24m
RF parameter: f=52 MHz, U=300 kV
HESR / 15GeV p
eRing / 3GeV
L [ring circumference, m]
~ 576
norm / geo [mm mrad, rms]
≤ 2.1 / ≤ 0.13
Δp/p (rms)
~ 4 ·10-4
IP [m]
0.3
rIP [mm, rms]
≤ 0.2
l (bunch length) [m]
0.1
n (particle / bunch)
5.4·1010
23·1010
h (number of bunches)
100
fcoll (collision freq) [MHz]
~ 52
lcoll (bunch distance) [m]
~ 5.76
ΔQsc (space charge)
≥ 0.05
 (beam-beam parameter)
0.014
0.015
L (luminosity) [cm-2s-1]
~ 2 · 1032
BetaCool program
JINR Dubna

9. Beam Equilibria and Luminosities
Advanced design (protons)
e-Cooler parameter: E=8.2 MeV, I=3 A, B=0.2T, TT=1eV, TL=0.5meV, Br/B < 10-5, L=24m
RF parameter: f=104 MHz, U=300 kV
HESR / 15GeV p
eRing / 3GeV
L [ring circumference, m]
~ 576
norm / geo [mm mrad, rms]
≤ 2.3 / ≤ 0.14
Δp/p (rms)
~ 4 ·10-4
IP [m]
0.1
rIP [mm, rms]
≤ 0.1
l (bunch length) [m]
n (particle / bunch)
3.6·1010
23·1010
h (number of bunches)
200
fcoll (collision freq) [MHz]
~ 104
lcoll (bunch distance) [m]
~ 2.88
ΔQsc (space charge)
≥ 0.1
 (beam-beam parameter)
0.014
0.01
L (luminosity) [cm-2s-1]
~ 6 · 1032
BetaCool program
JINR Dubna

10. Beam Equlibria Protons vs. Deuterons
Analytic formula for 15 GeV/c beams: Cooling rate (electron cooling) ~ 1/(A*gamma2)
Factor of 2 larger for deuterons Heating rate (IBS) ~ 1/(A2*beta4*gamma)
Approx. factor of two smaller for deuterons
Beam equilibria of deuterons roughly a factor of three smaller
geo ~ 0.12 mm mrad (rms) for protons
geo ~ 0.04 mm mrad (rms) for deuterons
Relative momentum spread also much smaller: Δp/p (rms) ~ 4*10-4 (rms) for protons
Δp/p (rms) ~ 2*10-4 (rms) deuterons and half bunch length
Luminosity could be much higher with same number of particles
or cooling force can be reduced significantly
But space charge limit has to be considered
 Reduce Electron Current of the Cooler: Iecooler < 1 A

11. Beam Equilibria and Luminosities
Baseline design (deuterons)
e-Cooler parameter: E=4.1 MeV, I=0.5 A, B=0.2T, TT=1eV, TL=0.5meV, Br/B < 10-5, L=24m
RF parameter: f=89 MHz, U=300 kV
HESR / 15GeV d
eRing / 3GeV
L [ring circumference, m]
~ 576
norm / geo [mm mrad, rms]
≤ 2.4 / ≤ 0.15
Δp/p (rms)
~ 2.4 ·10-4
IP [m]
0.1
rIP [mm, rms]
≤ 0.1
l (bunch length) [m]
0.17 – 0.19
n (particle / bunch)
1.1·1010
23·1010
h (number of bunches)
173
172
fcoll (collision freq) [MHz]
~ 89.3
lcoll (bunch distance) [m]
~ 3.3
ΔQsc (space charge)
≥ 0.1
 (beam-beam parameter)
0.014
0.030
L (luminosity) [cm-2s-1]
~ 1.8 · 1032
BetaCool program
JINR Dubna 11

12. Beam Preparation
Goal: ·1012 polarized protons / deuterons in bunches
Injection:
2·1011 pol. Protons / deuterons per cycle from SIS18
approx. 20 injections and bunch compression in h=2 cavity
Pre-cooling?
Acceleration:
h=1 resp. h=2 system to 15 GeV/c
Beam preparation:
beam cooling to equilibrium and
„adiabatic “ bunching in h= system
Problem: Cooling time to equilibrium

13. Cooling Time to Equilibrium
Cooling time for 200 bunches:
At 3.8 GeV/c: 200s At 15 GeV/c: s with same initial long. and transv. emittances
With factor of 4 smaller initial emittance:100000s (27h!) Cooling time for one or two bunches:
At 15 GeV/c: s
With factor of 4 smaller initial emittance: s
Cooling time for unbunched beam:
At 15 GeV/c: 35000s
With factor of 4 smaller initial emittance: 1000s
 Low initial emittance (pre-cooling) and cooling of unbunched beams at 15 GeV/c
Pre-cooling at lower momentum could be limited by space charge

14. Summary Protons (conservative) : L = 2 · 1032 cm-2s-1
IP [m] = 0.3 m, ΔQsc ≥ 0.05, Eecooler = 8.2 MeV, Iecooler = 3 A,
Protons (advanced): L = 6 · 1032 cm-2s-1
IP [m] = 0.1 m, ΔQsc ≥ 0.1, Eecooler = 8.2 MeV, Iecooler = 3 A
Deuterons (baseline): L = 1.8 · 1032 cm-2s-1
IP [m] = 0.1 m, ΔQsc ≥ 0.1, Eecooler = 4.1 MeV, Iecooler = <1 A

15. Major Tasks Hardware extensions and modifications:
Extension of the Electron Cooler for protons
Additional MHz, 300 kV cavity required
Major modification of the interaction region
Beam dynamics simulations:
Accumulation, acceleration and bunching process in HESR
Ion-optical IP / detector integration
Beam – beam effect in low energy e-n collider
Space charge for Protons / Deuterons