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A conceptual design of the single stage multi-TeV electron-positron pair beam collider Kazuhisa NAKAJIMA KEK International Workshop on High Energy Electron Acceleration Using Plasmas 2005 HEEAUP 2005: 8-10 June 2005 -Institut Henri Poincaré, Paris, France Outline Multi-stage or Single stage? Electron-positron pair-beam production in strong laser fields Laser Plasma Collider-type I Nonlinear Laser Plasma acceleration and Plasma lens final focus Laser Plasma Collider-type II Laser Ponderomotive Acceleration and Focus Multi-stage or Single stage? Multi-staging technology of laser plasma accelerators makes it possible to extend a short acceleration cell toward a high energy accelerator in a complex, long system, though spatial alignment and temporal synchronization must be resolved from the viewpoint of accelerator physics. Technologically less attractive! Single-staging technology is based on violent acceleration in a single interaction without complex system, though an extremely high peak power laser will be required. 5 TeV e+e- LWFA Linear Collider consisting of staged plasma channels 2.5 TeV e- LWFA 2.5 TeV e+ LWFA ~1 km T3 OPTICAL DELAY T3 YAG (Triger) MARX GENERATOR OPTICAL DELAY WATER CAPACITOR T3 YAG (Triger) MARX GENERATOR MULTI LTSG MULTI LTSG ~1 m 55GeV/m, 10GeV/stage WATER CAPACITOR OPTICAL DELAY YAG (Triger) MARX GENERATOR MULTI LTSG WATER CAPACITOR Parameters of 5TeV e+e- Linear Collider based on LWFA Collider parameters CM Energy Luminosity Ecm Lg LWFA parameters 5 TeV 1035 cm-2s-1 Emittance 2.2 nm Ey Beta at IP 22 mm by 0.1 nm Beam size at IP sy 0.32 mm sz Bunch length Number of particles N 5x107/ bunch Collision frequency fc 50 kHz Average beam power Pb 2 MW Disruption parameter Dy 0.93 Beamstrahlung parameter U 3485 (M. Xie et al.,AIP CP398,AAC96,233,1997) Plasma density ne Acceleraion length 3.5x1017cm-3 Lac 20 cm Accelerating gradient Ez 55GV/m Energy gain/ stage W 10 GeV Laser power/ stage Pav 100 kW Laser pulse energy EL 2J Laser pulse duration t 100 fs Laser peak power P 20 TW Number of stages 500 Total laser power 50 MW Total length ~ 1 km Pair-beam production in nuclear fields The yield of pair production via trident process in plasma ions for 3 is given by 2 Trident pair creation in plasma 0.48 3 2 8 3 nc r0 2 2 Np 3 a0 Z 10 n e0 e Z e e e 2 + 2 2 e e n r 0.8 10 6 a08 Z 3 c 0 ne0 ewhere r0 is the laser spot radius and is the plasma thickness. 2 N p 2.8 1045 Z 3 I W/cm2 ne0 cm 3 r02 mm2 mm e.g. For 4 Z=54 (Xe) ne0 1020 cm 3 r0 10 mm 100mm I 10 22 W/cm2 N p 4.4 1014 Virtual photon Coulomb field of nuclear charge Z 3 Threshold intensity It 2.6 1019 L mm e- in the laser field 2 W/cm 2 A priori scaling for Nonlinear Wakefield Accelerator with self-channel guiding Acceleration length a0 nc 3 2 Lacc 0.6 ne a0 6.8 PTW R m 2 1.11021 3 nc cm 2 2 mm 4 e r e The maximum energy by dephasing Emax 2 2 nc me c a0 ne Acceleration by driving laser pulse t=30fs,=0.8mm, R=10mm Using relativistic self-guiding condition nc PTW 0.017 ne P[TW] 20 a0 2.4 nc/ne 1176 Lacc Emax 7.3 cm 3.5 GeV 100 5.4 5882 2.7 m 87 300 9.4 17647 32.4 m 797 500 12.2 29412 103 m 2237 A priori scaling for Nonlinear Wakefield Accelerator with plasma channel Maximum energy gain at the wave breaking limit: max 4 3g g nc ne E = 1 TeV 2 106 2 3 ne nc 2 nc Operating plasma density: g 4 2 3 21 17 3 1.110 3 n 2.2 10 cm n0 cm 0 0 mm 4 13 2 a a0 18 Required laser intensity: 0 4 g 4 4 2 P ~ 1.2 PW 1 3 r0 PTW 0.1 4 0 for r0 10mm, 0 0.8mm 2 2 L 0 Accelerating length: d g p Ld 71cm 4 Plasma lens final focus Both electron and positron beams self-focus by a self-pinching effect in plasma. Self-focusing force for an overdense plasma ne nb Ft 2re mec 2 nb r where re 2.818 10 Beam density: 13 cm nb : classical electron radius N 2 2 3 2 s br s bz s r 2 z 2 br for a Gaussian density profile: nr,z nb exp 2 2 2s br 2s bz s br : rms beam radius Focusing strength: KF l Plasma ne f nb s bz : rms bunch length Ft re N 2 2 me c r 2s br s bz re N 2 n b 0s bz s br Particle bunch n : Normalized beam emittance FWHM bunch length ct b 2 2 ln 2s bz 2.35s bz : Beta function at the plasma lens b 0 s br n 1 2 n b 0 s bz Focal length: f K Fl re Nl (P. Chen, PRD, 39, 2039, 1989) l : Length of plasma lens b0 2 Luminosity by plasma lens final focus The beta function at the collision point b b0 b s2 b f 2 b C.M. Energy The spot size at the collision point 2x1TeV 2 s 2 ns brs bz n f 2 b 2 b 0 re Nl Number of particles 1.4x1010 e- The luminosity for a Gaussian beam 2 Plasma lens length 2 re N 2 l 1 re N 2 l 2 L 2 2 4s 8 ns brs bz 8 n b 0 ns bz N2 Assuming n L b 0 rL2 L 2 re N 2 l L 2 8rL Ls bz Laser wavelength Laser spot size Repetitionrate Luminosity ~5mm L 0.8mm rL 10mm 10 Hz 5x1035 cm-2/s-1 Laser intensity distributions of Hermite-Gaussian modes x x z z x-z plane x x x x-y plane y TEM(0,0) Intensity Electron Fpond y y TEM(1,0) TEM(1,0)+TEM(0,1) Intensity Electron Fpond Radius Scattering of the electrons Fpond Fpond Electrons confinement Radius by S. Miyazaki, Utsunomiya Univ. Electron acceleration by TEM01+TEM10 The momentum in the x, y and z direction by S. Kawata & S. Miyazaki P[mc] Laser intensity : I = 1.23×1018[W/cm2] ⇒ a0 = 0.5 Wave length:λ~1.053[μm] Minimal spot size: w0=35λ Pulse length: Lz=10λ t[λ/c] Δγ a) Simulation model x Electron bunch ~200 MeV/cm Laser pulse 0 2w0 y t[λ/c] z 2w0 8 Lz t=0 Ponderomotive acceleration energy for the laser intensity 100000 γf 10000 1000 With radiation Without radiation 100 10 1 1 10 100 a0 Initial Velocity : 0 Minimal spot size : 20λ Pulse length : 10λ by S. Miyazaki & S. Kawata Ponderomotive acceleration and focusing in vacuum High energy booster acceleration of a pair-beam can be accomplished by the relativistic ponderomotive acceleration with focusing in vacuum or tenuous plasma. Acceleration The final energy is obtained approximately as f a02 for a particle initially at rest. for final energy scaling E f GeV 0.37 1021 I W/cm2 20 mm e.g. At 0 0.8mm I 10 22 W/cm2 E f 2.4GeV I 10 23 W/cm2 E f 24GeV I 10 24 W/cm2 E f 240GeV I 10 25 W/cm2 E f 2.4TeV Focusing by TEM00 + TEM01 +TEM10 Ponderomotive Potential The focusing force is given by 2 3 2 r 2 Fr U 2 z ct 2 2 rs 0 2 r s 0 2a1 a0 4 a1 6 exp 2 2 mc 2 r s s 2 s 2 s Ft 2a12 a02 KF Focusing strength at r=0, and z-ct=0 2 2 mc r s 0 The beam envelope equation on the rms beam radius srb is d 2s rb re N b2 3 0 2 K F s rb 2 3 dz 2b s zb s rb s rb Space charge force Thermal emittance where N is the number of electrons in the bunch, szb is the rms bunch length, b is the geometric emittance, b n b n the normalized emittance re is the classical electron radius. Focused beam size The space-charge-force dependent beam size d 2s rb The equilibrium radius is obtained from 2 0 dz s rb re N 2 1 4 K1F 2 b 3 2s 1zb2 Assuming a1 a0 s 0 r0 2 s zb 0 s rb 2 1 4 r0 re N 2 a05 2 0 s rb pm 2 1024 e.g. s0 14 2 1 4 2a12 a02 s 1zb2 re N I5 4 r0 mm N W/cm2 30 mm For 0 0.8mm r0 10 mm N p 1 1010 I 1.0 10 W/cm 2 s rb 1.2 nm I 1.06 1025 W/cm2 s rb 0.2 pm 22 Laser micro collider Two counter propagating laser-accelerated beams make a micro collider. The space charge limited luminosity is given by L N p2 frep 2 4s rb a05 0 N p frep 2 3 2 re r02 L cm 2 s 1 2 10 30 I 5 2 W/cm2 60 mmr02 mmN p frep e.g. I 1.06 1025 W/cm2 0 0.8mm r0 10 mm EC.M. 5TeV L 2 1040 frep cm 2s 1 N p 1 1010 Required peak power and pulse energy P = 17 EW EL > 2×4 kJ e+e- pair-beam micro-collider Two counter-propagating laser-accelerated pair beams will create a new e+e-, e-e-, e+e+ micro-size collider without beam disruption at collision. The emittance-limited luminosity is L N p2 frep 2 4s rb a04 N 2p frep 0 r0 where Np is the number of accelerated e+e- pairs and frep is the repetition rate of laser pulses. L cm 2 s 1 5.3 1027 I 2 W/cm2 30 mmr01mm N 2p frep [Hz] E.g. 25 2 For I 1.06 10 W/cm N p 1 1010 0 0.8mm r0 10 mm L 3 1042 frep cm 2 s 1 Luminosity of laser micro-colliders Luminosity at 1 Hz [cm-2s-1] 1042 Emittance-limited luminosity 1039 10000 1000 100 10 C.M. energy 1 1036 1033 1030 1027 Space charge-limited luminosity 1020 1021 1022 1023 1024 Laser Intensity [W/cm2] 1025 C.M. Energy [GeV] 10 0 0.8mm r0 10 mm N p 1 10 A conceptual design of Laser Micro Collider Parameters of LMC C. M. Collision energy Initial beam energy Number of particles per bunch Laser wavelength Laser spot size Repetition frequency Required peak intensity Required peak power Required pulse energy Space charge limited luminosity Emittance limited luminosity 1 TeV 50 MeV 1010 0.8 mm 10 mm 10 Hz 4.2×1022 W/cm2 660 PW 8 kJ for h=10% 2×1035 cm-2s-1 5×1038 cm-2s-1 (K. Nakajima, High Energy Accelerator Seminar OHO’03) A conceptual design of 2TeV Advanced Colliders The key issue is luminosity for beam collisions. Laser ILC+ PBG Non Linear Pondero Energy Laser Linear LWFA motive Doubler Collider LWFA ~2m ~2m 30+0.2km Total length ~200m Accelerating 35MV/m 55GV/m 1TV/m 1TV/m +4GV/m Gradient Number of 1.4x1010 1.4x1010 1.4x1010 1.5x1010 particles Collision 10Hz 10Hz 10Hz 14.1kHz Frequency Luminosity 35 35 35 34 5x10 5x10 5x10 1x10 -2 -1 (cm s ) Laser 2x1.4PW2x115PW Peak Power 100x20TW /100fs /16ps /200fs /Duration 2km 1GV/m 105 433MHz 3x1035 Road Map toward TeV In the next decade worldwide Advanced Accelerator Community will aim at realizing 1 TeV electron acceleration. Select single stage or multi-stage Multi TeV collider 2015 1 TeV demonstration 2010 10~100GeV Single stage 2008 >1 GeV Channel LWFA MonoGuided energetic high quality beam 100~350 MeV demonstration 1~10 MeV Proof-of-Principle experiments 200 3 1993 2006 2004 During the last decade high-quality beam up to near 1GeV was achieved.