a conceptual design of the single stage multi-tev electron-positron pair beam collider
DESCRIPTION
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 PresentationTRANSCRIPT
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
Outline
Electron-positron pair-beam productionin strong laser fields
Laser Plasma Collider-type INonlinear Laser Plasma acceleration andPlasma lens final focus
Laser Plasma Collider-type IILaser Ponderomotive Acceleration and Focus
Multi-stage or Single stage?
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
T3
OPTICALDELAY
MARXGENERATOR
WATERCAPACITOR
MULTILTSG
YAG(Triger)
T3
OPTICALDELAY
MARXGENERATOR
WATERCAPACITOR
MULTILTSG
YAG(Triger)
T3
OPTICALDELAY
MARXGENERATOR
WATERCAPACITOR
MULTILTSG
YAG(Triger)
~1 m
2.5 TeV e- LWFA 2.5 TeV e+ LWFA
~1 km55GeV/m, 10GeV/stage
Parameters of 5TeV e+e- Linear Collider based on LWFA
Collider parameters
N 5x107/ bunch
CM Energy Ecm
Luminosity Lg
Emittance y
Beta at IP y
Beam size at IP y
Bunch length z
Number of particles
Collision frequency fc 50 kHz
Average beam power Pb 2 MW
Disruption parameter Dy 0.93
Beamstrahlung parameter 3485
0.32 m
0.1 nm22 m
2.2 nm
1035 cm-2s-1
5 TeV
LWFA parameters
Plasma density ne 3.5x1017cm-3
Acceleraion length Lac 20 cm
Accelerating gradient Ez 55GV/mEnergy gain/ stage W 10 GeV
Laser pulse energy
Laser power/ stage Pav 100 kW
EL 2 J
Laser pulse duration 100 fsLaser peak power P 20 TW
Number of stages 500Total laser power 50 MW
(M. Xie et al.,AIP CP398,AAC96,233,1997)
Total length ~ 1 km
Pair-beam production in nuclear fields The yield of pair production via trident process in plasma ions foris given by
γ >>3
Np ≈0.48π3
103 α 2a08Z3 nc
ne0
⎛
⎝ ⎜
⎞
⎠ ⎟
2r0λ
⎛ ⎝ ⎜
⎞ ⎠ ⎟
2 Δλ
⎛ ⎝ ⎜
⎞ ⎠ ⎟
2
Np ≈2.8×10−45Z3I W/cm2[ ]
4ne0
−2 cm−3[ ]r0
2 μm[ ]Δ2 μm[ ]
where r0 is the laser spot radius and is the plasma thickness.
≈0.8×10−6a08Z3 nc
ne0
⎛
⎝ ⎜
⎞
⎠ ⎟
2r0λ
⎛ ⎝ ⎜
⎞ ⎠ ⎟
2 Δλ
⎛ ⎝ ⎜
⎞ ⎠ ⎟
2
e.g. Z=54 (Xe)ne0 =1020cm−3
r0 =10μmΔ =100μmFor
I =1022W/cm2
Np ≈4.4×1014
Virtual photon
e-
e-
e- in the laser field
e+
Coulomb fieldof nuclear charge
Z
e+Z → ′ e e+e−Trident pair creation in plasma
γ >>3
€
It =2.6 ×1019
λ L μm( )[ ]2 W/cm2
Threshold intensity
A priori scaling for Nonlinear Wakefield Accelerator with self-channel guiding
€
Emax ≈ mec2a0
2 ncne
€
a0 = 6.8 P TW[ ]λR
The maximum energy by dephasing
Acceleration length
€
Lacc ≈ 0.6λa0ncne
⎛
⎝ ⎜
⎞
⎠ ⎟3 2
€
nc =mω2
4πe2 =π
reλ2 ≈
1.1×1021
λ μm[ ]cm−3
[ ]
Acceleration by driving laser pulse =30fs,=0.8m, R=10m
Using relativistic self-guiding condition
€
P TW[ ] ≥ 0.017ncne
P[TW] a0 nc/ne Lacc Emax
20 2.4 1176 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 NonlinearWakefield Accelerator with plasma channel
Maximum energy gainat the wave breaking limit:
€
γmax ≈ 4γg
3
Operating plasma density:
€
ne ≈ ncγ g−2 = nc
γ4
⎛ ⎝ ⎜
⎞ ⎠ ⎟−2 3
€
n0 cm−3[ ] ≈
1.1×1021
λ 0 μm[ ]
γ4
⎛ ⎝ ⎜
⎞ ⎠ ⎟−2 3
Required laser intensity:
€
a02 ≈ 4γg = 4
γ4
⎛ ⎝ ⎜
⎞ ⎠ ⎟
1 3
€
P TW[ ] ≈ 0.1γ4
⎛ ⎝ ⎜
⎞ ⎠ ⎟
1 3 r0λ 0
⎛
⎝ ⎜
⎞
⎠ ⎟2
Accelerating length:
€
Ld ≈ γg2γ⊥λ p ≈
24γλ 0
€
γ≈2 ⋅106
€
n0 ≈ 2.2 ⋅1017 cm−3
€
a0 ≈ 18
P ~ 1.2 PW
€
r0 =10μm,λ 0 = 0.8μmfor
€
Ld ≈ 71cm
E = 1 TeV
€
γg =ncne
Plasma lens final focusBoth electron and positron beams self-focus by a self-pinching effect in plasma.
Ft =−2πremec2nbr
Beam density: nb =N
2π( )3 2σbr2σbz
Focusing strength:
KF =Ft
γmec2r
=reN
2πγσbr2 σbz
=reN
2πεnβ0σbz
re =2.818×10−13cm : classical electron radius
for a Gaussian density profile: n r,z( ) =nb exp−r2
2σ br2 −
z2
2σbz2
⎡
⎣ ⎢ ⎤
⎦ ⎥
Self-focusing force for an overdense plasma
ne >nb
where
εn : Normalized beam emittance
β0 : Beta function at the plasma lens
Focal length: f =1
K Fl=
2πεnβ0σbz
reNl
σbr : rms beam radius σbz : rms bunch length
β0 =γσ br2 εn
l : Length of plasma lens
σbr
ne
nb
l
σbr∗
f
Particle bunch
Plasma
cτb =2 2ln2σbz ≈2.35σbz
FWHM bunch length
(P. Chen, PRD, 39, 2039, 1989)
Luminosity by plasma lens final focus
The beta function at the collision point β∗
β0 =β∗+s2 β∗≈ f 2 β∗
The spot size at the collision point
σ ∗2 =εβ∗≈εn f 2
γβ0
=2πεnσbrσ bz
reNl
⎛
⎝ ⎜
⎞
⎠ ⎟
2
The luminosity for a Gaussian beam
L =N2
4πσ 2 =1
8π2
reN2l
εnσ brσbz
⎛
⎝ ⎜
⎞
⎠ ⎟
2
=γ
8π2εnβ0
reN2l
εnσbz
⎛
⎝ ⎜
⎞
⎠ ⎟
2
εn ≈λL π β0 ≈πrL2 λL
€
rL ≈ 10μm
L =γ
8rL2
reN2l
λLσbz
⎛
⎝ ⎜
⎞
⎠ ⎟
2
Assuming
C.M. Energy 2x1TeV
Number of particles 1.4x1010 e-
Plasma lens length ~5mm
Laser spot size
Laser wavelength
€
L = 0.8μm
Luminosity 5x1035 cm-2/s-1
Repetition rate 10 Hz
Laser intensity distributions of Hermite-Gaussian modes
Radius
ElectronElectron
Intensity
Fpond Fpond
Scattering of the electrons
x-z plane
x-y plane
z
x
y
x
xz
x
Intensity
Radius
FpondFpond
Electrons confinement
TEM(0,0)
y
TEM(1,0)
xy
TEM(1,0)+TEM(0,1)
by S. Miyazaki, Utsunomiya Univ.
The momentum in the x, y and z direction
-50
0
50
100
150
200
250
300
350
400
0 10000 20000 30000 40000 50000
PxPy
Pz
t[λ/c]
P[m
c]
Electron acceleration by TEM01+TEM10
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
a)
-100
0
100
200
300
400
500
-10000 0 10000 20000 30000 40000 50000
Transverse
Sum
Longitudinal
Δγ
t[λ/c]
z
x
y
t=0
0
8 Lz
2w0
2w0
Electron bunch
Laser pulse
Simulation model
~200 MeV/cm
Ponderomotive acceleration energy for the laser intensity
1 10 100
1
10
100
1000
10000
100000
a0
γ f
Initial Velocity : 0Minimal spot size : 20λPulse length : 10λ
With radiationWithout radiation
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 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
CollisionFrequency 10Hz 10Hz 10Hz 14.1kHz 433MHz
Luminosity(cm-2s-1) 5x1035 5x1035 5x1035 1x1034 3x1035
LaserPeak Power/Duration
100x20TW/100fs
2x1.4PW/16ps
2x115PW/200fs
The key issue is luminosity for beam collisions.
Road Map toward TeV
1~10 MeV Proof-of-Principle
experiments
100~350 MeVdemonstration
Mono energetichigh quality beam
>1 GeV Channel Guided LWFA
10~100GeVSingle stage
1 TeV demonstration
1993
2003
2004
2006
2008
2010
2015
During the last decadehigh-quality beam up to near 1GeVwas achieved.
In the next decade worldwide Advanced Accelerator Communitywill aim at realizing1 TeV electron acceleration.
Multi TeV collider
Select single stageor multi-stage