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

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

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

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

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

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

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

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??

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)

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

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

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!

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≥1.0-4.0 !?? qc=600 mrad small emittance

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 ~ -0.0065, single IP crab crossing resonance free!

(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

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

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)

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

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

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

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

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

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

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, 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

off-momentum cleaning - principle Yi-Peng Sun

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

off-momentum cleaning - simulation Yi-Peng Sun

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

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

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)

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