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
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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. - PowerPoint PPT Presentation
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A conceptual design of the single stage multi-TeV electron-positron pair beam collider
Kazuhisa NAKAJIMAKEK
International Workshop onHigh Energy Electron Acceleration Using Plasmas 2005
HEEAUP 2005: 8-10 June 2005 -Institut Henri Poincaré, Paris, France
High energy booster acceleration of a pair-beam can be accomplished by the relativistic ponderomotive acceleration with focusing in vacuum ortenuous plasma.
The final energy is obtained approximately as
γ f ≈a02
for a particle initially at rest.
Ef GeV[ ] ≈0.37×10−21I W/cm2[ ]λ0
2 μm[ ]
I =1022W/cm2 Ef ≈2.4GeVe.g.
I =1023W/cm2 Ef ≈24GeV
I =1024W/cm2 Ef ≈240GeV
I =1025W/cm2 Ef ≈2.4TeV
Acceleration
λ0 =0.8μmAt
for final energy scaling
Focusing strength at r=0, and z-ct=0 KF =Ft
γmc2r=
2a12 −a0
2
γσ⊥02
The beam envelope equation on the rms beam radius rb is
d2σ rb
dz2+KFσ rb −
reN2πβ2γ3σ zbσrb
−εb
2
σ rb3 =0
where N is the number of electrons in the bunch, zb is the rms bunch length, b is the geometric emittance, n the normalized emittance re is the classical electron radius.
εb =εn γβ
Space charge force Thermal emittance
The focusing force is given by
Fr
mc2=
∂U∂r
= 2a12 −a0
2( )rσ⊥0
2
σ⊥4 −a1
2 r3σ⊥02
σ⊥6
⎡
⎣ ⎢ ⎢
⎤
⎦ ⎥ ⎥ exp−
r2
2σ⊥2 −
z−ct( )2
2σ⊥2
⎡
⎣ ⎢ ⎢
⎤
⎦ ⎥ ⎥
Focusing by TEM00 + TEM01 +TEM10 Ponderomotive Potential
The equilibrium radius is obtained fromd2σrb
dz2=0
Focused beam size The space-charge-force dependent beam size
σrb ≅reN
2π( )14KF12βγ32σ zb
12 ≅reN
2π( )14 2a12 −a0
2( )
14σ zb
12
σ⊥0
γ
a1 =a0Assuming σ⊥0 =r0 2 σ zb ≈λ 0
σrb ≈2π( )14
2r0
a05 2
reNλ0
σrb pm[ ] ≈2×1024 NI5 4 W/cm2
[ ]
r0 μm[ ]λ0
3 μm[ ]
e.g. For λ0 =0.8μm r0 =10μm Np =1×1010
€
I =1.0 ×1022
W/cm2
€
rb ≈ 1.2 nm
€
I =1.06 ×1025W/cm2
€
rb ≈ 0.2 pm
Laser micro colliderTwo counter propagating laser-accelerated beams make a micro collider.
The space charge limited luminosity is given by
L =Np
2frep
4πσ rb2 ≅
a05λ0Np frep
2π3 2rer02
L cm−2s−1[ ] ≈2×10−30I 52 W/cm2
[ ]λ06 μm[ ]r0
−2 μm[ ]Np frep
λ0 =0.8μm
r0 =10μm
Np =1×1010
I =1.06×1025W/cm2 EC.M. =5TeVe.g.
L ≈2×1040 frep cm−2s−1
P = 17 EW EL > 2×4 kJ
Required peak power and pulse energy
e+e- pair-beam micro-colliderTwo counter-propagating laser-accelerated pair beams will createa new e+e-, e-e-, e+e+ micro-size collider without beam disruption at collision.
L =Np
2frep
4πσ rb2 ≅
a04Np
2 frep
λ0r0
The emittance-limited luminosity is
where Np is the number of accelerated e+e- pairs and frep is the repetition rate of laser pulses.
L cm−2s−1[ ] ≈5.3×10−27I2 W/cm2
[ ]λ03 μm[ ]r0
−1 μm[ ]Np2 frep[Hz]
E.g. For
λ0 =0.8μmr0 =10μm
Np =1×1010
L ≈3×1042 frep cm−2s−1
I =1.06×1025W/cm2
Luminosity of laser micro-colliders
1042
1039
1036
1033
1030
1027
Lum
inos
ity a
t 1 H
z [c
m-2s-1
]
100
110
C.M
. Ene
rgy
[GeV
]
100010000
1020 1021 1022 1023 1024 1025
Laser Intensity [W/cm2]
C.M. energy
Emittance-limitedluminosity
Space charge-limitedluminosity
λ0 =0.8μm r0 =10μm Np =1×1010
A conceptual design of Laser Micro Collider
C. M. Collision energy 1 TeVInitial beam energy 50 MeVNumber of particles per bunch 1010 Laser wavelength 0.8 mLaser spot size 10 mRepetition frequency 10 HzRequired peak intensity 4.2×1022 W/cm2
Required peak power 660 PWRequired pulse energy 8 kJ for =10%Space charge limited luminosity 2×1035 cm-2s-1 Emittance limited luminosity 5×1038 cm-2s-1
Parameters of LMC
(K. Nakajima, High Energy Accelerator Seminar OHO’03)
A conceptual design of 2TeV Advanced Colliders
Linear LWFA
Non LinearLWFA
LaserPonderomotive
ILC+EnergyDoubler
PBGLaserCollider
Total length~200m ~2m ~2m 30+0.2km 2kmAcceleratingGradient 55GV/m 1TV/m 1TV/m
35MV/m+4GV/m 1GV/m
Number ofparticles 1.4x1010 1.4x1010 1.4x10101.5x1010 105