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A conceptual design of the single stage multi-TeV electron-positron pair beam collider

A conceptual design of the single stage multi-TeV electron-positron pair beam collider. Kazuhisa NAKAJIMA KEK. International Workshop on H igh E nergy E lectron A cceleration U sing P lasmas 2005 HEEAUP 2005: 8-10 June 2005 -Institut Henri Poincaré, Paris, France. Outline.

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A conceptual design of the single stage multi-TeV electron-positron pair beam collider

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  1. 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

  2. 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

  3. 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.

  4. 5 TeV e+e- LWFA Linear Collider consisting of staged plasma channels 2.5 TeV e- LWFA 2.5 TeV e+ LWFA ~1 km 55GeV/m, 10GeV/stage ~1 m

  5. Parameters of 5TeV e+e- Linear Collider based on LWFA Collider parameters LWFA parameters CM Energy Ecm 5 TeV Plasma density ne 3.5x1017cm-3 Luminosity Acceleraion length Lac 20 cm 1035 cm-2s-1 Lg Emittance 2.2 nm Accelerating gradient Ez 55GV/m Ey Beta at IP 22 mm Energy gain/ stage W 10 GeV by 0.1 nm Beam size at IP Laser power/ stage Pav 100 kW sy 0.32 mm sz Bunch length Laser pulse energy EL 2 J Number of particles N 5x107/ bunch Laser pulse duration t 100 fs Collision frequency fc 50 kHz Laser peak power P 20 TW Average beam power Pb 2 MW Number of stages 500 Total laser power Disruption parameter Dy 0.93 50 MW Total length ~ 1 km Beamstrahlung parameter U 3485 (M. Xie et al.,AIP CP398,AAC96,233,1997)

  6. e- e+ e- Virtual photon Coulomb field of nuclear charge Z e- in the laser field Pair-beam production in nuclear fields The yield of pair production via trident process in plasma ions for is given by Trident pair creation in plasma where r0 is the laser spot radius and D is the plasma thickness. e.g. Z=54 (Xe) Threshold intensity For

  7. A priori scaling for Nonlinear Wakefield Accelerator with self-channel guiding Acceleration length The maximum energy by dephasing

  8. Acceleration by driving laser pulse t=30fs,l=0.8mm, R=10mm Using relativistic self-guiding condition

  9. A priori scaling for NonlinearWakefield Accelerator with plasma channel E = 1 TeV Maximum energy gain at the wave breaking limit: Operating plasma density: Required laser intensity: P ~ 1.2 PW for Accelerating length:

  10. Plasma Particle bunch 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 where : classical electron radius Beam density: for a Gaussian density profile: : rms beam radius : rms bunch length Focusing strength: : Normalized beam emittance FWHM bunch length : Beta function at the plasma lens Focal length: (P. Chen, PRD, 39, 2039, 1989) : Length of plasma lens

  11. Luminosity by plasma lens final focus The beta function at the collision point C.M. Energy 2x1TeV The spot size at the collision point Number of particles 1.4x1010 e- ~5mm The luminosity for a Gaussian beam Plasma lens length Laser wavelength Laser spot size Assuming Repetition rate 10 Hz Luminosity 5x1035 cm-2/s-1

  12. x x z y x y y x TEM(1,0) TEM(1,0)+TEM(0,1) z Laser intensity distributions of Hermite-Gaussian modes x-z plane x x-y plane TEM(0,0) Intensity Intensity Electron Electron Fpond Fpond Fpond Fpond Radius Radius Scattering of the electrons Electrons confinement by S. Miyazaki, Utsunomiya Univ.

  13. Electron acceleration by TEM01+TEM10 x Electron bunch Laser pulse 0 z 2w0 2w0 y 8 Lz t=0 The momentum in the x, y and z direction by S. Kawata & S. Miyazaki 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 P[mc] t[λ/c] Simulation model a) Δγ ~200 MeV/cm t[λ/c]

  14. Ponderomotive acceleration energy for the laser intensity γf With radiation Without radiation a0 Initial Velocity : 0 Minimal spot size : 20λ Pulse length : 10λ by S. Miyazaki & S. Kawata

  15. 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 for final energy scaling for a particle initially at rest. e.g. At

  16. Focusing by TEM00 + TEM01 +TEM10 Ponderomotive Potential The focusing force is given by Focusing strength at r=0, and z-ct=0 The beam envelope equation on the rms beam radius srb is Space charge force Thermal emittance where N is the number of electrons in the bunch, szb is the rms bunch length, eb is the geometric emittance, en the normalized emittance re is the classical electron radius.

  17. Focused beam size The space-charge-force dependent beam size The equilibrium radius is obtained from Assuming e.g. For

  18. Laser micro collider Two counter propagating laser-accelerated beams make a micro collider. The space charge limited luminosity is given by e.g. Required peak power and pulse energy P = 17 EW EL > 2×4 kJ

  19. 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 where Np is the number of accelerated e+e- pairs and frep is the repetition rate of laser pulses. E.g. For

  20. 1042 Emittance-limited luminosity 1039 10000 1000 1036 100 C.M. Energy [GeV] 10 Luminosity at 1 Hz [cm-2s-1] 1 C.M. energy 1033 1030 Space charge-limited luminosity 1027 1020 1021 1022 1023 1024 1025 Laser Intensity [W/cm2] Luminosity of laser micro-colliders

  21. A conceptual design of Laser Micro Collider Parameters of LMC C. M. Collision energy 1 TeV Initial beam energy 50 MeV Number of particles per bunch 1010 Laser wavelength 0.8 mm Laser spot size 10 mm Repetition frequency 10 Hz Required peak intensity 4.2×1022 W/cm2 Required peak power 660 PW Required pulse energy 8 kJ for h=10% Space charge limited luminosity 2×1035 cm-2s-1 Emittance limited luminosity 5×1038 cm-2s-1 (K. Nakajima, High Energy Accelerator Seminar OHO’03)

  22. A conceptual design of 2TeV Advanced Colliders The key issue is luminosity for beam collisions. Laser Pondero motive ILC+ Energy Doubler PBG Laser Collider Non Linear LWFA Linear LWFA ~200m ~2m ~2m 30+0.2km 2km Total length Accelerating Gradient 35MV/m +4GV/m 55GV/m 1TV/m 1TV/m 1GV/m Number of particles 1.4x1010 1.4x1010 1.4x1010 1.5x1010 105 Collision Frequency 10Hz 10Hz 10Hz 14.1kHz 433MHz Luminosity (cm-2s-1) 5x1035 5x1035 5x1035 1x1034 3x1035 Laser Peak Power /Duration 2x115PW /200fs 100x20TW /100fs 2x1.4PW /16ps

  23. Road Map toward TeV In the next decade worldwide Advanced Accelerator Community will aim at realizing 1 TeV electron acceleration. Multi TeV collider 2015 1 TeV demonstration 2010 Select single stage or multi-stage 10~100GeV Single stage 2008 >1 GeV Channel Guided LWFA 2006 Mono energetic high quality beam 2004 100~350 MeV demonstration 2003 During the last decade high-quality beam up to near 1GeV was achieved. 1~10 MeV Proof-of-Principle experiments 1993

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