C. Dimopoulou A. Dolinskii, T. Katayama, D. Möhl, F. Nolden, C. Peschke, M. Steck, L. Thorndahl Simulations of stochastic cooling of antiprotons in the collector ring CR TUIOB02 @ COOL'11 Alushta, Ukraine, September 2011
Jan 11, 2016
C. Dimopoulou
A. Dolinskii, T. Katayama, D. Möhl, F. Nolden, C. Peschke, M. Steck, L. Thorndahl
Simulations of stochastic cooling of antiprotons in the collector ring CR
TUIOB02 @ COOL'11Alushta, Ukraine, September 2011
Antiprotons3 GeV, 108 ions
Rare isotopes740 MeV/u, 109 ions
δp/p (rms) εh,v (rms)
π mm mrad
δp/p (rms) εh,v (rms)
π mm mrad
Before cooling 0.35 % 45 0.2 % 45
After cooling 0.05 % (*) 1.25 (*) 0.025 % 0.125
Phase space reduction 9x103 1x106
Cooling down time ≤ 9 s ≤ 1 s
Cycle time 10 s 1.5 s
Required performance of CR stochastic cooling Short bunch of hot secondary beam from production target into the CR After bunch rotation and adiabatic debunching the δp/p is low enough to apply stochastic cooling Fast 3D stochastic cooling required to profit from production rate of secondary beams
(*) 20% lower (if possible) for HESR as accumulator ring (instead of RESR)
C. Dimopoulou, COOL'11
Overview of the CR stochastic cooling systems
Systems in frequency band 1-2 GHz
Pickup Kicker pbars RIBs Method
PH KH hor. hor., final stage
difference PU
PV KV vert. vert., final stage
difference PU
PH+PV KH+KV long. long., final stage
Sum PU + notch filter
PP KH ----- hor. + long.,first stage
Palmer: difference PUat high D
PP KV ---- vert., first stage
difference PU
System in frequency band 2-4 GHz (future option)
P2-4 K2-4 long. -------- Sum PU + notch filter
Main issue for pbars: increase ratio
noise thermal
)Q ( signalSchottky 2
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1925-2011
Principle of betatron cooling & basic ingredients
Phase advance PU-K ≈ 900
Coherent term= cooling force x undesired mixing (PUK)
Diffusion= heating from Schottky noise (desired mixing (KPU)) + from thermal noise
''rms'' theory (analytical model)( Fokker-Planck equation for )JNtJ ),(
High amplification needed, electronic gain ~ 10 7 (140 dB)
System gain g = PU response x Electronic gain x K response ~ 10-2
C. Dimopoulou, COOL'11
UMggBN
W
dt
d
22211
Phase advance PU-K ≈ 900
High amplification needed, electronic gain ~ 10 7 (140 dB)
Good cooling for overlapping Schottky bands i.e. M=1 and low ratio thermal noise/Schottky signal U
B and M depend in a contradictory way on the spread ΔT/T= - Δf/f ~ - ηring/pk Δp/p of the beam particles, they vary during momentum cooling
In reality: choose ηring/pk for a compromise between B and M
To cool all the particles within the initial momentum distribution B ≥ 0
Principle of betatron cooling & basic ingredients
C. Dimopoulou, COOL'11
UMggBN
W
dt
d
22211
,
EDDF
Et ns
ENtE ),(
Principle of momentum cooling with notch filter
Fokker-Planck equation (solved with CERN code)
The response of the notch filter
provides the cooling force,induces extra undesired mixing
Coherent term= cooling force x undesired mixing (PUK)
System gain G = PU response x Filter response x Electronic gain x K response
p
δpi π π
i ep
pm e
i
sin1
2H 0f/f 2
notch
well-separated Schottky bands M>1B ≥ 0 for increased undesired mixing
very small |η|≈1%i.e. ring almost @ γtr
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Features and developments for the 1-2 GHz system
Optical notch filter (< 40 dB deep notches within 1-2 GHz )
PU/Kicker tank consists of 2 plates (up+down or left+right) with 64 electrodes/plate PH/KH=PV/KV rotated by 900
Plunging of PU electrodes i.e. moving closer to beam during cooling No plunging of KI electrodes
Slotline PU electrodes at 20-30 KCryogenic low-noise preamplifiers at 80 K (open option of preamplifiers in UHV at 20 K)Kickers at 300 K
Effective noise temperature at preamplifier input Teff =73 K
Beam
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1.0 1.2 1.4 1.6 1.8 2.00.6
0.7
0.8
0.9
1.0
1.1
1.2
f(GHz)0 10 20 30 40 50 60
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
ypu
(mm)
Longitudinal PU/K impedance, sensitivity, PU plunging
pk ZZ 4
S(f))()f(y)f,( c ySZZ pp
Relative measurements on prototype PU:
,2
rms bI
PZ p
p
,2
rms
kk P
UZ b
HFSS simulations, absolute values:
circuit convention:
)f((y))f(y)f,( c SSZZ kk 11.25)f( cpZ at yPU= ±60 mm
Simplify:
yslope1)( yS
75.37)f( cpZ at yPU= ±20 mm
S(f)
Plunging of PU electrodes:factor 1.8 in sensitivity (3.4 in Zp)from yPU=±60 mm ±20 mm
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Input parameters & requirementsCR Circumference 3 GeV antiprotons
221.45 mβ=0.9712, γ=4.197, rev. frequency f0=1.315 MHz
Ring slip factor η, slip factor PU-K ηpk
Distance PU-K/circumference-0.011, -0.033 0.378
Beam intensityInitial rms momentum spread Initial rms emittance εh,v
108
3.5 10-3, Gaussian/parabolic 45 π mm mrad
System bandwith 1-2 GHz
Number of PU, K (longitudinal cooling)Number of PU, K (transverse cooling)
128, 128 64, 64
PU, Kicker impedance at midband 1.5 GHz
PU/K sensitivity S(y)=1+slope* yPU/K sensitivity vs. frequency S(f)
no plunging considered, PU electrodes at ± 60 mm11.25 Ohm, 45 Ohm slope= 24.5 m-1
Effective temperature for thermal noise 73 K
ideal, infinitely deep notch filter + 900 phase shifter
Total installed power at kickers (limited by funding, can be upgraded)
4.8 kW
Goal: Cool longitudinally from σp/p= 3.5 10-3 4 10-4 in 9 sSimultaneous transverse cooling from εh,v = 45 ≈ 1 π mm mrad
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Momentum cooling: Cooling force and diffusion G|| = 150 dB (3.2 107); t=10 s
t=0, 2.5, 5, 7.5 and 10 s
Coherent term: • linear notch filter response around Δp/p=0 cooling force• momentum acceptance of system (undesired mixing ≥ 0) > total initial Δp/p Cooling of all particles
Schottky noise dominates long. cooling time ~ N
Notch filter cuts thermal noise around all harmonics
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It deforms the cooling force and suppresses Schottky noise within the distribution,cooling loop is stable (Nyquist plot)
),,(1
),G( ),G(
tEmS
EmEm
),,(),G( )()(n n),,( kp tEmBTFEmmZmZtEmS kp
-*
*
*
PV
20 dE
E
dE/d
d
df e),,(
E
i
EmtEmB
Feedback by the beam included:
Momentum cooling: Feedback by the beam
G|| = 150 dB (3.2 107); t=10 s
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Optimization:For a given signal/noise ratio there is a gain so as to reach the desired σp/p in the desired time.Lower gain leads to lower σp/p but cooling takes longer.
Momentum cooling: Results
For ultimate σp/p : increase signal/noise by plunging the PU electrodes during cooling
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Required installed power = 4 Pmax ( to account for signal fluctuations)
),( ),()(n ef22
1)(
2p
20s tEmEGmZtP
m Ep
Total cw power in bandwidth at kicker: Pmax = Ps(t=0)+ Pn
, decreases as σp/p shrinksSchottky
2||effn kT
4
1GWP filtered thermal
Betatron cooling rate: details
)(2cos)(
t
p
pxmtB pkpkc
)(
1)(
tpp
mtM
c
)(
1
)(
1
2
slope)( 0
20
2 tmZW
f
nfNe
TktU
m ppp
effB
)()(
|)sin(|)()( pk
tUtM
tBtgopt
Optimum gain
UMggBN
W
dt
d
2pk |)sin(|2
211
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long
t
ini
ep
pt
p
p
)(
Simultaneous notch filter momentum cooling ONAnsatz from Fokker-Planck results at dB 150|| G
Interplay between betatron & momentum cooling
Beyond power limits...cw Pmax= 950 W !
For precise treatment, feedback by the beam must be included
dB 141 initial )( cmG
Betatron cooling: First results
Reached εh = 4 π mm mrad in 9 s
M dominates the heating at all t: M~10 U in principle, need long cooling at very low gain (plunging helps only at the end)
Initially:
, 2.1U ! 11M and grows...
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0 2 4 6 8 100
5
10
15
20
25
30
35
40
45
h
p/p
rms p/
p (
10-4),
rms h
(m
m m
rad)
t(s)
Conclusions I
Pbar filter momentum cooling from σp/p= 3.5 10-3 4 10-4 in 9 s is possible in the 1-2 GHz band:
• with a gain around 150 dB (3.2 107),• required max. installed power ~ 2.6 kW (cw ~0.7 kW),• assuming unplunged PU electrodes (conservative case), plunging expected to help reaching lower σp/p,• feedback by the beam not negligible but loop stable.
The design η=-0.011 of CR is optimum for both 1-2 and 2-4 GHz bands (undesired mixing)
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Conclusions II
Preliminary results show that betatron cooling is possible
• with separately optimized simultaneous filter momentum cooling (150 dB,~2.6 kW),
• down to εrms ~ 4 π mm mrad within 9 s,
• with an electronic gain at midband around 140 dB (107),
• with max. required installed power ~ 4 kW (cw ~1 kW) per plane h/v i.e. beyond the foreseen available power,
• assuming unplunged electrodes.
As expected, betatron cooling suffers from large desired mixing M (required by filter momentum cooling) dominating the diffusion at all t. Way out: slow-down momentum cooling in the beginning
C. Dimopoulou, COOL'11
Outlook
Include feedback by the beam into betatron cooling model
Time-optimization of momentum and betatron cooling together, distribution of available power accordingly, e.g.,
• Initially, slower filter cooling to help the betatron cooling, then inversely to reach ultimate emittances and momentum spread.• Apply initially time-of-flight and later notch filter momentum cooling, with simultaneous betatron cooling.
Include plunging of PU electrodes, expected to reduce diffusion by factors 4-9, especially transversally
Additional filter momentum cooling in the 2-4 GHz band, study handshake between 2 bands
C. Dimopoulou, COOL'11
Circumference 221.45 m
Max. magnetic rigidity 13 Tm
Antiprotons Rare Isotopes Isochronous Mode
Max. particle number 108 109 1-108
Kinetic energy 3 GeV 740 MeV/u 790 MeV/u
Velocity v 0.971 c 0.830 c 0.840 c
Lorentz γ 4.20 1.79 1.84
Transition γT 3.85 2.82 1.67 – 1.84
Frequency slip factor η -0.011 0.186 0
Betatron tunes Qx and Qy 4.28, 4.84 3.19, 3.71 2.23, 4.64
Revolution frequency 1.315 MHz 1.124 MHz 1.137 MHz
CR Parameters
,
EDDF
Et ns
),,(1
),G(Re )()(n n f e 2),( kp
20 tEmS
EmmZmZtEF
mkp
2
k20effn ),,(1
),G( )(n f Tk
2
1),(
tEmS
EmmZtED
mk
2
kp030
2s ),,(1
),G(
1 )()(n n
11 f e),(
tEmS
Em
mmZmZEtED
mkp
Fokker-Planck & Formulae I
cohEF 0f incohns EDDD 20f
2
1
ENtE ),(
[D.Möhl et al., Physics Reports 58 (1980)]
),G(Re )()(n n f e 2),( kp20 EmmZmZtEF
mkp
2k
20effn ),G( )(n f Tk
2
1),( EmmZtED
mk
2kp0
30
2s ),G(
1 )()(n n
11 f e),( Em
mmZmZEtED
mkp
Fokker-Planck & Formulae II
),(H ),( )( notch||
u EmieEmGEmG
0
)( 2 )(
p
EpxE pku