Other Crab Cavity Applications - LHC, RR-LHeC, RL-LHeC, HE-LHC, p-driven plasma accelerators …

Frank ZimmermannLHC-CC’10, Geneva, 16 December 2010

outline• crabbing of colliding beams at the IP

- 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

• 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

applications of crab cavities

x

zcR

2

;1

12

“Piwinski angle”

“luminosity reduction factor”without crab cavity

nominal LHC

qc/2

effective beam size: s*

x,eff ≈ sx*/Rf

“LPA” upgrade

“FCC” upgrade

improving geometric overlap

crab cavitiesmake Rf~1

primary motivation for HL-LHC & LHeC

improving overlap with crab cavities at LHeC? - several options

RR LHeC:new ring in LHC tunnel,with bypassesaround experiments

RR LHeCe-/e+ injector10 GeVLR LHeC:

recirculatinglinac withenergy recovery,or straightlinac

LHeC – general parameterse- beam RR LR ERL LR “p-140”e- energy at IP[GeV] 60 60 140luminosity [1032 cm-2s-1] 17.1 10.1 0.44polarization [%] 5 - 40 90 90bunch population [109] 26 2.0 1.6e- bunch length [mm] 10000 300 300bunch interval [ns] 25 50 50transv. emit. gex,y [mm] 0.58, 0.29 0.05 0.1rms IP beam size sx,y [mm] 30, 16 7 7e- IP beta funct. b*x,y [m] 0.18, 0.10 0.12 0.14full crossing angle [mrad] 0.93 0 0geometric reduction Hhg 0.77 0.91 0.94repetition rate [Hz] N/A N/A 10beam pulse length [ms] N/A N/A 5ER efficiency N/A 94% N/Aaverage current [mA] 131 6.6 0.27tot. wall plug power[MW] 100 100 100

p- beam RR LRbunch pop. [1011] 1.7 1.7tr.emit.gex,y [mm] 3.75spot size sx,y [mm] 30, 16 7b*x,y [m] 1.8,0.5 0.1$

bunch spacing [ns] 25 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

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)

S

zzeH

z

hg

erfc2

Szpe

pepze

2

,*

12

with

2*

22,

81

cpzS

V. Litvinenko, IPAC10crab cavities helpful for all future lepton-hadron colliders

~2 MV at ~1.5 GHz

~4 MV at ~0.8 GHz?

~20 MV at ~0.4 GHz

~200 MV at ~0.4 GHz??

nominal LHC HE-LHCbeam energy [TeV] 7 16.5dipole field [T] 8.33 20dipole coil aperture [mm] 56 40beam half aperture [cm] 2.2 (x), 1.8 (y) 1.3injection energy [TeV] 0.45 >1.0#bunches 2808 1404bunch population [1011] 1.15 1.29 1.30initial transverse norm. emittance [mm] 3.75 3.75 (x), 1.84 (y) 2.59 (x & y)initial longitudinal emittance [eVs] 2.5 4.0number of IPs contributing to tune shift 3 2initial total beam-beam tune shift 0.01 0.01 (x & y)beam circulating current [A] 0.584 0.328RF voltage [MV] 16 32rms bunch length [cm] 7.55 6.5rms momentum spread [10-4] 1.13 0.9IP 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)

improving IP overlap for High-Energy LHC?

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

crab cavities for High-Energy LHC

formula simplifies for round beams:

formulae for geometric overlap

S

zzeH

z

hg

erfc2

Sz

z *

*

22

41 czS

geometric overlap loss factor for equal beams including hourglass & crossing angle

with and

dsss

eH

yx

s

z

hg

x

c

z

2*

2

2*

2

4

1

11

1*

2

22

dsss

eH

yx

s

z

ephg

x

c

z

2*

2

2*

2

4

2

,

11

2*

2

22

ep collision with sze<<szp

boosting beam-beam tune shift

• primary motivation for KEKB crab cavitiesactual beam-beam tune shift increased by ~20%

• SPS collider experience weak dependence on crossing angle, butf 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!

additional benefit for HL-LHC

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

f≥0.7

qc=500 mrad

qc=600 mradsmall emittance

tests up to >0.7 fshowed (almost) noadditionalbeam-beam effect

present nominal LHC: ~0.64,fupgrade: f≥1.0-4.0 !??

SPS collider experience

parameters:ex,y =0.5 nm E = 7 TeVbx = 30 cm, by = 7.5 cm, sz = 11.8 cm, qc= 315 mrad (f =1.5), Nb = 4.0x1011,Qs =0.002, DQx,y ~ -0.0065,single IP

frequency map analysis of Lifetrac simulation

M. Zobov, D. Shatilov

collisions withcrossing angle

crab crossing

resonances

resonancefree!

HL-LHC: INFN-BINP simulation

collisions with 280 mradcrossing angle K. Ohmi

crab crossing

simulated luminosity lifetime with crab crossing is 10 times better than without crab crossing

(HL-)LHC: KEK simulation

2 IPs

2 IPs

luminosity leveling

• 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

second motivation for HL-LHC

w/o leveling L=const DQbb=const

luminosity evolutionbeam current evolutionoptimum run time

average luminosity

constLL 0 2/1

ˆ

efft

LtL

tN

NNeff

00 efft

NtN

/10

0

max

N

NT effrun

taeffrun TT

tab

IPtotave

TnNnL

LL

max

0

0

1

22/12/1

ˆ

taeff

effave

TLL

leveling 2 → exponential L decay, w decay time teff (not teff/2)

efftLtL expˆ

efftN

tN

exp0

effeffrunta

piw

effrun

TT

T

ln

,01ln min 2

effrunT

runta

effave e

TTL

1

optimum run time & av. luminosity

F. Zimmermann

no levelingDQ=constL=const

b*=14 cm, Nb=2.3x1011, Tta=5 h

no levelingDQ=constL=const

luminosity [1034 cm-2s-1]

time [h]

|DQ|

time [h]

leveling – example evolution

F. Zimmermann, Chamonix 2010

b*=14 cm, 25 ns spacing, Tta=5 h

no leveling L=const DQbb=const

Nb(0) [1011] 2.3 2.3 2.3 2.3L(0)[1034cm-2s-1] 7.5 7.1 12.3 7.1

|DQbb(0)| 0.0059 0.0056 0.01 0.0056

|DQbb(Trun)| 0.0036 0.0090 0.01 0.0056

qc(0) [mrad] 509 539 239 539

run time Trun [h] 7.74 4.74 2.72 11.9

<L>[1034cm-2s-1] 2.8 3.5 3.6 3.2events/#ing (0) 142 135 234 135

leveling – example numbers

F. Zimmermann, Chamonix 2010

b*=25 cm, 50 ns spac., “LPA” Tta=5 h

no leveling L=const DQbb=const

Nb(0) [1011] 4.2 4.2 4.2L(0)[1034cm-2s-1] 7.4 4.5 4.5

|DQbb(0)| 0.010 0.0056 0.0056

|DQbb(Trun)| 0.006 0.010 0.0056

qc(0) [mrad] 381 672 672

run time Trun [h] 7.45 6.0 23.2

<L>[1034cm-2s-1] 2.6 2.5 2.1events/#ing (0) 280 172 172

leveling – other example numbers

F. Zimmermann, Chamonix 2010

avoiding off-center collisions

• 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

second motivation for LHeC

LHC longitudinal bunch position due to beam loading(1 cm = 33 ps)

Joachim Tuckmantel, 2nd EuCARD AccNet RFTech workshop, 2 Dec. 2010

ultimate bunch intensity+/- 0.8 cm maximum offset

for example:8 mrad x 0.8 cm / 2 = 64 mm offset collision

• 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

applications of crab cavities

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~10-6-10-5 one has 1000-10,000 turns for excitation (Yi-Peng Sun)

• effective AC dipole frequency Qacc=fCC/f0 h d ;with fCC=800 MHz, =10d -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

Yi-Peng Sun

off-momentum cleaning - principle

excitation must be fast compared with energy loss from synchrotron radiation

Yi-Peng Sun

off-momentum cleaning - principle

Yi-Peng Sun

off-momentum cleaning - simulation

• 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

applications of crab cavities

crab cavities for bunch compression

conventionalRF cavity

chicane/arcwith momentumdependentpath length

conventional bunch compression [e.g. SLC, CTF-2/3]

deflecting RF cavity

chicanewith dispersion& momentumdependentpath length

x-z emittance exchange with crab cavity [P. Emma et al, for LCLS, 2002]

SPS:ez~4 mmex,y~8 nm

• 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)

perspectives

conclusion:many crabs in our future

thank you for your attention