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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  1045 Z 3 I W/cm2 ne0
cm 3 r02 mm2 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 PTW 


R
m 2
 1.11021
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
PTW  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
1.110

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 
PTW  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  2re 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: nr,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
2s 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
4s
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
Repetitionrate
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 1021 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
2b  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.
s0
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
4s 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 mmr02 mmN 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
4s 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 1027 I 2 W/cm2 30 mmr01mm 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.