Particle acceleration in plasma
By
Prof. C. S. Liu
Department of Physics, University of Maryland
in collaboration with V. K. Tripathi, S. H. Chen,
Y. Kuramitsu, L. C. Tai, S. Y. Chen, J. Wang,
N. Kumar, and B. Eliasson
Cosmic ray acceleration
Magnetosphere of the Earth
The Earth’s magnetic field and
magnetosphere
Cavity flow with reentrant jet
“Mono-energetic” electrons on
the Earth
Electron can be accelerated by plasma wave: v   p k
Acceleration gradient of plasma wave can be large
Maximum acceleration gradient limited by the wave breaking

v osc
eE
mc 2  p 
3

~ c or E 0 V /cm 
  0.96 n 0 cm  Non-relativistic wavee  c 
m p
breaking amplitude
giving, E 0  100 GV m , for n0 1018 cm3 ,mc 2  0.5MeV,.c / p 1m

SLAC on a slab !!!
Relativistic wave-breaking
amplitude

E R V / cm   E 0  p  1
E R  E 0
 p  (1 v ph 2 /c 2 )1/ 2 is the Lorentz factor for plasma wave
How to generate plasma wave ??
1. Mode conversion
2. Beat wave excitation with two laser pulses
3. Raman scattering
4. Relativistic wake plasma wave excitation by
electron beam or short pulse laser
1) Mode conversion
An EM wave obliquely propagates
into a plasma with density gradient.
eE x
E x  v 0x 
im 0
n
n
 v 0x 0
t
x

n
+
k 0
kx  0
x

0   p
An oscillatory current can cause
space charge oscillations.
EM wave → ES wave
+


at
  p


2) Beat wave excitation
– Two long laser pulses E0  E0 sin k0 x   0 t , E1  E1sin k1x  1t 
– Plasma wave excitation possible if,  0   1  p , k0  k1  k p
Backscattering,
 ,
 k1  k0, k p  2k
0
 p ,k p
k p  
k0  k1   p 
/c
– Maximum saturated amplitude of the plasma

 mass effect
wave due to relativistic
Forward scattering,
E max
 161 2 / 31/ 3  1
E0
j 
eE j
m j c
 p ,k p
, j
 1,2
(Rosenbluth and Liu, PRL, 1972)
Nonlinear frequency-amplitude
relation
3) Raman Scattering by Plasma Wave
Laser light: a0 ( 0 , k0)
Scattered light: a1 (1,k1 )
 
 
Plasma: n p
Feed back

Instability
Current: j  n p v
1/ 2
 p 
Growth rate:   kv0   ,  p   0
 0 

kmax  2k 0,
kmin   p /c
Raman heated electrons
Raman scattering causes electron acceleration
4) Relativistic wake plasma wave excitation
by electron beam or short pulse laser
Maximum electric field of the plasma wave
E max n b

E0
n0
Acceleration of a SLAC electron beam
Demonstration of acceleration in
beam driven wakefield (SLAC)
Hogan et.al. Phys. Rev. Lett. 95,
054802 (2005)
Mono-energetic electron beam by short pulse
laser
Observation of mono-energetic
beam of electrons with energy
50-170 MeV by three groups.
Mangles et.al, Nature, 431, 535 (2004),
Faure et.al., Nature, 431, 541 (2004),
Geddes et.al., Nature, 431, 538 (2004)
First direct measurement of acceleration gradient;
eE=2.5 GeV/m ~ 103 of linac.
Chen, et.al.(Particle accelerator group, Academia Sinica, NCU)
Laser wakefield acceleration and ion channel
formation in laser
Micro magnetosphere
Relativistic self focusing
Laser power, P  Pcr where
 2 
Pcr  17  2  GW
 
 p
Relativistic dielectric constant
p2
  1 2

Relativistic effect
  increases
Ponderomotive effect  p decreases
2
Resultant effect

ion channel formation
Electron trajectories
Number density of electrons on
axis
Wake field on axis
Injection and acceleration of mono-energetic
electrons by a self-modulated laser pulse
• Experiments at Academia
Sinica (PRL, 2006)
• OOPIC (object-oriented
particle-in-cell) code
– two spatial and three
velocity components
– pre-ionized electron-proton
plasma
– linearly polarized Gaussian
laser pulse
– s-polarization (normal to
the density perturbation)
– moving window
– immobile ions
• Parameters
– Peak laser intensity:
I0 = 8x1018 W/cm2
(a0 = 2.)
– Laser wavelength:
l = 0.81 m
– Pulse duration:
t = 45 fs
– Gas density:
n = 4x1019/cm3
(p/L = 0.15)
– Initial waist size:
w0 = 4 m
– Chirp bandwidth: 27 nm
Initial Plasma Density
Time = 0.735ps
Time = 0.829 ps
Time = 1 ps
Time = 1.1 ps
50 MeV mono energetic electron beam
The wake field bunches the electrons in real space.
Time = 1.1 ps
The modulated laser field traps electrons and push electrons
moving with the laser pulse.
Time = 1.1 ps
The modulated laser field traps electrons and push electrons moving
with the laser pulse.
(The plasma is turned off at time = 1.33 ps)
50 MeV mono energetic
electron beam
Time = 1.43 ps
Ez of laser pulse
Distribution function
t=0.70883 ps
10
-4
10
-6
f()
10
-2
f()
10
t=0.97471 ps
0
1
2
4
6 8
10
2
4

10
-1
10
-2
10
-3
10
-4
10
-5
6 8
100
1
2
10
-2
10
-3
10
-4
10
-5
10
1
2
4
6 8
10
2
-2
10
-4
4
10
-6

6 8
100
1
2
10
4
6 8
4
6 8
100
4
6 8
10
2
100
0
-1
10
-2
10
-4
10
-6
f()
f()
6 8
t=1.1519 ps
10
10
4

t=0.88610 ps
10
2
0
10
f()
f()
10
10
t=1.0633 ps
0
-1
6 8

t=0.79749 ps
10
4
-3
-5
1
2
4
6 8
10

2
4
6 8
100
1
2
4
6 8
10

2
100
px - x phase space
Weibel instability
Ey
u-
Bz
u+
kx
Growth rate:
Thank you
Outline
• Plasma universe
• Plasma wave excitation and trapping of
resonant electrons
• Laser driven acceleration and production of
the mono-energetic electrons beam
• Ion acceleration
• Concluding remark
Plasma universe
Three minutes after Big Bang ----- Plasma dominated
universe
Radio jets, X-ray sources, -ray bursts, pulsar,
accretion disk etc….
We observe our universe mostly by EM waves. Its
dispersion relation,
 2   2p  k 2c 2
v ph  c[1  p /2 2 ]  c
2
v g  c[1  p /2 2 ]  c
2
Ion bubble formation by different a