1. Frank Zimmermann LHC-CC’10, Geneva, 16 December 2010
Other Crab Cavity Applications - LHC, RR-LHeC, RL-LHeC, HE-LHC, p-driven plasma accelerators …
Frank Zimmermann
LHC-CC’10, Geneva, 16 December 2010

2. outline crabbing of colliding beams at the IP off-momentum cleaning
- improving geometric overlap
- boosting beam-beam tune shift
- luminosity leveling
- avoiding off-center collisions from beam loading
→ HL-LHC, RR LHeC, RL LHeC, HE-LHC, eRHIC,…
off-momentum cleaning
→ HL-LHC
bunch compression
→ PDPWA

3. applications of crab cavities
crabbing of colliding beams at the IP
- improving geometric overlap
- boosting beam-beam tune shift
- luminosity leveling
- avoiding off-center collisions from beam loading
off-momentum cleaning
bunch compression

4. improving geometric overlap
primary motivation for
HL-LHC & LHeC
“Piwinski angle”
“luminosity reduction factor”
without crab cavity
qc/2
nominal LHC
effective beam size:
s*x,eff ≈ sx*/Rf
“LPA” upgrade
crab cavities
make Rf~1
“FCC”
upgrade

5. improving overlap with crab cavities at LHeC? - several options
RR LHeC:
new ring in
LHC tunnel,
with bypasses
around
experiments
RR LHeC
e-/e+ injector
10 GeV
LR LHeC:
recirculating
linac with
energy
recovery,
or straight
linac

6. LHeC – general parameters
e- beam RR
LR ERL
LR “p-140”
e- energy at IP[GeV] 60
140
luminosity [1032 cm-2s-1]
17.1
10.1
0.44
polarization [%]
5 - 40 90
bunch population [109] 26
2.0
1.6
e- bunch length [mm]
10000
300
bunch interval [ns] 25 50
transv. emit. gex,y [mm]
0.58, 0.29
0.05
0.1
rms IP beam size sx,y [mm]
30, 16 7
e- IP beta funct. b*x,y [m]
0.18, 0.10
0.12
0.14
full crossing angle [mrad]
0.93
geometric reduction Hhg
0.77
0.91
0.94
repetition rate [Hz]
N/A 10
beam pulse length [ms] 5
ER efficiency
94%
average current [mA]
131
6.6
0.27
tot. wall plug power[MW]
100
p- beam RR LR
bunch pop. [1011]
1.7
tr.emit.gex,y [mm]
3.75
spot size sx,y [mm]
30, 16 7
b*x,y [m]
1.8,0.5
0.1$
bunch spacing [ns] 25
$ smaller LR p-b* value than for
nominal LHC (0.55 m):
reduced l* (23 → 10 m)
only one p beam squeezed
new IR quads as for HL-LHC
B. Holzer,
M. Klein,
F. Zimmermann
Baseline without crab cavities
With crab cavities (less SR!):
RL crossing angle ~8 mrad

7. LR-LHeC crossing angle
need to separate e/p beams by 6-9 cm at 10 m from IP (i.e. angle of 6-9 mrad) [constraint from magnet design]
w/o IR-dipoles, crab cavities need 20-30x HL-LHC crab voltage, or ~200 MV !
maximum allowed crossing angle for luminosity w/o crab crossing is < 0.5 mrad (see graph)
with

8. crab cavities helpful for all future lepton-hadron colliders
V. Litvinenko, IPAC10
~2 MV at ~1.5 GHz
~4 MV at ~0.8 GHz?
~20 MV at ~0.4 GHz
~200 MV at ~0.4 GHz??

9. improving IP overlap for High-Energy LHC?
nominal LHC
HE-LHC
beam energy [TeV] 7
16.5
dipole field [T]
8.33 20
dipole coil aperture [mm] 56 40
beam half aperture [cm]
2.2 (x), 1.8 (y)
1.3
injection energy [TeV]
0.45
>1.0
#bunches
2808
1404
bunch population [1011]
1.15
1.29
1.30
initial transverse norm. emittance [mm]
3.75
3.75 (x), 1.84 (y)
2.59 (x & y)
initial longitudinal emittance [eVs]
2.5
4.0
number of IPs contributing to tune shift 3 2
initial total beam-beam tune shift
0.01
0.01 (x & y)
beam circulating current [A]
0.584
0.328
RF voltage [MV] 16 32
rms bunch length [cm]
7.55
6.5
rms momentum spread [10-4]
1.13
0.9
IP beta function [m]
0.55
1 (x), 0.43 (y)
0.6 (x & y)
initial rms IP spot size [mm]
16.7
14.6 (x), 6.3 (y)
9.4 (x & y)
full crossing angle [mrad]
285 (9.5 sx,y)
175 (12 sx0)
188 (12 sx,y0)

10. crab cavities for High-Energy LHC
nominal LHC
HE-LHC
Piwinski angle
0.65
0.39
initial geometric luminosity loss w/o CC
0.84
0.93
crab voltage at 800 MHz [MV]
~10
~15
initial luminosity gain [%] 19 8
SR power per ring [kW]
3.6
65.7
66.0
arc SR heat load dW/ds [W/m/aperture]
0.21
2.8
energy loss per turn [keV]
6.7
201.3
critical photon energy [eV] 44
575
photon flux [1017/m/s]
1.0
1.3
longitudinal SR emit. damping time [h]
12.9
0.98
horizontal SR emit. damping time [h]
25.8
1.97
initial longit. IBS emit. rise time [h] 61 64
~68
initial horiz. IBS emit. rise time [h] 80
~80
~60
events per crossing 76
initial luminosity w/o CC [1034 cm-2s-1]
2.0
peak luminosity w/o CC [1034 cm-2s-1]
beam lifetime due to p consumption [h] 46
12.6
optimum run time tr [h] (tta=5 h)
15.2
10.4
opt. av. int. luminosity / day w/o CC [fb-1]
0.47
0.78
0.79

11. formulae for geometric overlap
geometric overlap loss factor for equal beams
including hourglass & crossing angle
ep collision with sze<<szp
formula simplifies for round beams:
and
with

12. boosting beam-beam tune shift
additional benefit for HL-LHC
primary motivation for KEKB crab cavities
actual beam-beam tune shift increased by ~20%
SPS collider experience
weak dependence on crossing angle, but
f range of interest was not explored, and
SPS experience not fully relevant for LHC
HL-LHC: INFN-BINP simulations (Lifetrac code)
resonance suppression by LHC crab cavities
HL-LHC: KEK simulations (BBWS code)
beam-beam lifetime boosted 10 times!

13. SPS collider experience
historical experiments
at SPS collider
K. Cornelis, W. Herr, M. Meddahi,
“Proton Antiproton Collisions at a
Finite Crossing Angle in the SPS”,
PAC91 San Francisco
f~0.45
qc=500 mrad
f≥0.7
tests up to f>0.7
showed (almost) no
additional
beam-beam effect
present nominal LHC: f~0.64,
upgrade: f≥ !??
qc=600 mrad
small emittance

14. HL-LHC: INFN-BINP simulation
M. Zobov, D. Shatilov
collisions with
crossing angle
frequency
map analysis
of Lifetrac simulation
resonances
parameters:
ex,y =0.5 nm
E = 7 TeV
bx = 30 cm,
by = 7.5 cm,
sz = 11.8 cm,
qc= 315 mrad
(f =1.5),
Nb = 4.0x1011,
Qs =0.002,
DQx,y ~ ,
single IP
crab crossing
resonance
free!

15. (HL-)LHC: KEK simulation
collisions with 280 mrad
crossing angle
crab crossing
K. Ohmi
2 IPs
2 IPs
simulated luminosity lifetime with crab crossing is 10 times better than without crab crossing

16. luminosity leveling changing b*, Dx*, or qc during the store
second motivation for HL-LHC
changing b*, Dx*, or qc during the store
→ to reduce event pile up & IR peak power deposition
→ to maximize integrated luminosity
leveling with crossing angle has advantages
increased average luminosity, operational simplicity
(J.-P. Koutchouk)
natural option for crab cavities
leveling with Dx* already used for ALICE in 2010
two leveling strategies for HL-LHC:
(1) constant luminosity
(2) constant beam-beam tune shift

17. optimum run time & av. luminosity
w/o leveling
L=const
DQbb=const
luminosity evolution
beam current evolution
optimum run time
average luminosity
F. Zimmermann
leveling 2 → exponential L decay, w decay time teff (not teff/2)

18. leveling – example evolution
b*=14 cm, Nb=2.3x1011, Tta=5 h
luminosity [1034 cm-2s-1]
|DQ|
F. Zimmermann, Chamonix 2010
time [h]
time [h]
no leveling
DQ=const
L=const
no leveling
DQ=const
L=const

19. leveling – example numbers
b*=14 cm, 25 ns spacing, Tta=5 h
no leveling
L=const
DQbb=const
Nb(0) [1011]
2.3
L(0)[1034cm-2s-1]
7.5
7.1
12.3
|DQbb(0)|
0.0059
0.0056
0.01
|DQbb(Trun)|
0.0036
0.0090
qc(0) [mrad]
509
539
239
run time Trun [h]
7.74
4.74
2.72
11.9
<L>[1034cm-2s-1]
2.8
3.5
3.6
3.2
events/#ing (0)
142
135
234
F. Zimmermann, Chamonix 2010

20. leveling – other example numbers
b*=25 cm, 50 ns spac., “LPA” Tta=5 h
no leveling
L=const
DQbb=const
Nb(0) [1011]
4.2
L(0)[1034cm-2s-1]
7.4
4.5
|DQbb(0)|
0.010
0.0056
|DQbb(Trun)|
0.006
qc(0) [mrad]
381
672
run time Trun [h]
7.45
6.0
23.2
<L>[1034cm-2s-1]
2.6
2.5
2.1
events/#ing (0)
280
172
F. Zimmermann, Chamonix 2010

21. avoiding off-center collisions
second motivation for LHeC
RF beam loading in LHC will shift longitudinal bunch position across each bunch train and around the ring (abort gap)
offset is almost ±1 cm at ultimate intensity
LHeC e- beam will not experience the same beam loading
with crossing angle longitudinal p offset translates into transverse offset of e-p collision point by ±5 mm/ mrad
p crab cavities keep the collision centered for all bunches despite beam loading

22. LHC longitudinal bunch position due to beam loading
(1 cm = 33 ps)
ultimate bunch intensity
+/- 0.8 cm maximum offset
for example:
8 mrad x 0.8 cm / 2 = 64 mm
offset collision
Joachim Tuckmantel, 2nd EuCARD AccNet RFTech workshop, 2 Dec. 2010

23. applications of crab cavities
crabbing of colliding beams at the IP
- improving geometric overlap
- boosting beam-beam tune shift
- luminosity leveling
- avoiding off-center collisions from beam loading
off-momentum cleaning
bunch compression

24. off-momentum cleaning
at top energy use LHC crab cavity as “AC dipole” for off-momentum particles (Stephane Fartoukh, 2009)
collimate only in IR7, and use IR3 phase to push b*
energy loss per turn ~10-9 ; with resonance width of
Dd~ one has ,000 turns for excitation (Yi-Peng Sun)
effective AC dipole frequency Qacc=fCC/f0 h d ;
with fCC=800 MHz, d=10-3: Qacc≈0.025 ;
8 GHz crab cavity excites around Q≈0.03
(Stephane Fartoukh , Yi-Peng Sun)
must exploit higher-order resonance to use 800 MHz
collimation efficiency to be verified

25. off-momentum cleaning - principle
Yi-Peng Sun

26. off-momentum cleaning - principle
Yi-Peng Sun
excitation must be fast compared with energy loss from synchrotron radiation

27. off-momentum cleaning - simulation
Yi-Peng Sun

28. applications of crab cavities
crabbing of colliding beams at the IP
- improving geometric overlap
- boosting beam-beam tune shift
- luminosity leveling
- avoiding off-center collisions from beam loading
off-momentum cleaning
bunch compression

29. crab cavities for bunch compression
conventional bunch compression [e.g. SLC, CTF-2/3]
chicane/arc
with momentum
dependent
path length
conventional
RF cavity
x-z emittance exchange with crab cavity [P. Emma et al, for LCLS, 2002]
deflecting
RF cavity
chicane
with dispersion
& momentum
dependent
path length
SPS:
ez~4 mm
ex,y~8 nm

30. perspectives
numerous intriguing applications of crab cavities enable various future colliders or can push their performance to new limits:
LHC, HL-LHC, LHeC, HE-LHC, eRHIC, EIC,...
crab cavities improve geometric overlap, boost the beam-beam limit (with negligible effect of parasitic collisions), level the luminosity, mitigate beam loading, assist in beam cleaning and help to shorten bunches for even more advanced colliders (PD-PWA)

31. conclusion:
many crabs in our future
thank you for your attention