Particle acceleration in plasma

By

Prof. C. S. Liu

Department of Physics, University of Marylandin 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

Acceleration gradient of plasma wave can be large

Maximum acceleration gradient limited by the wave breaking

vosc eE

m p

~ c or

E0 V /cm mc 2

e

p

c

0.96 n0 cm 3

giving, mGV100E0 , for

n0 1018 cm 3 ,mc 2 0.5MeV ,.c / p 1m

Non-relativistic wave-breaking amplitude

Relativistic wave-breaking amplitude

1Ecm/VE p0R

p (1 v ph2 /c 2) 1/ 2 is the Lorentz factor for plasma wave

0R EE

SLAC on a slab !!!

Electron can be accelerated by plasma wave:

v p k

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

n

x

++

Ex v0x eEx

im0

n

t v0x

n0

xat 0 p

kx 0

k 0

p

An EM wave obliquely propagates into a plasma with density gradient.

An oscillatory current can cause space charge oscillations.EM wave → ES wave

2) Beat wave excitation

– Two long laser pulses – Plasma wave excitation possible if,

– Maximum saturated amplitude of the plasma wave due to relativistic mass effect

13/16E

E 3/121

0

max 2,1,

j

cm

Ee

j

jj

(Rosenbluth and Liu, PRL, 1972)

E0 E 0sin k0x 0t ,

E1 E 1sin k1x 1t

0 1p,

k0 k1 kp

k1 k0,Backscattering,

kp k0 k1 p /cForward scattering,

kp 2k0,

p,kp

p,kp

Nonlinear frequency-amplitude relation

Laser light:

( 0, k0)

(1,k1 )Scattered light:

3) Raman Scattering by Plasma Wave

a0

a1

Plasma:

np

j npvCurrent:

Feed backInstability

Growth rate:

kv0

p

0

1/ 2

,

kmax 2k0,

kmin p /c

p 0

Raman heated electrons

Raman scattering causes electron acceleration

Maximum electric field of the plasma wave

0

b

0

max

n

n

E

E

4) Relativistic wake plasma wave excitation by electron beam or short pulse laser

Acceleration of a SLAC electron beam

Hogan Hogan et.al. et.al. Phys. Rev. Lett. Phys. Rev. Lett. 95, 054802 (2005)95, 054802 (2005)

Demonstration of acceleration in beam driven wakefield (SLAC)

Mono-energetic electron beam by short pulse laser

Mangles et.al, Nature, 431, 535 (2004),

Faure et.al., Nature, 431, 541 (2004),

Geddes et.al., Nature, 431, 538 (2004)

Observation of mono-energetic beam of electrons with energy 50-170 MeV by three groups.

Chen, et.al.(Particle accelerator group, Academia Sinica, NCU)

First direct measurement of acceleration gradient;

eE=2.5 GeV/m ~ 103 of linac.

Micro magnetosphere

Relativistic self focusing

crPP whereLaser power,

GW17P2p

2

cr

2

2

1

p

Relativistic dielectric constant

Relativistic effect increases

Ponderomotive effect decreases2p

Resultant effect ion channel formation

Laser wakefield acceleration and ion channel formation in laser

Electron trajectories

Number density of electrons on axis

Wake field on axis

Injection and acceleration of mono-energetic Injection and acceleration of mono-energetic electrons by a self-modulated laser pulseelectrons 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: = 0.81 m

– Pulse duration: = 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)

Time = 1.43 ps50 MeV mono energetic

electron beam

Ez of laser pulse

Distribution function

10-6

10

-4

10-2

10

0

f()

12 4 6 8

102 4 6 8

100

t=1.1519 ps

10-6

10

-4

10-2

10

0

f()

12 4 6 8

102 4 6 8

100

t=1.0633 ps

10-5

10-4

10-3

10-2

10-1

f()

12 4 6 8

102 4 6 8

100

t=0.97471 ps

10-5

10-3

10-1

f()

12 4 6 8

102 4 6 8

100

t=0.88610 ps

10-5

10-4

10-3

10-2

10-1

100

f()

12 4 6 8

102 4 6 8

100

t=0.79749 ps

10-6

10

-4

10

-2

10

0

f()

12 4 6 8

102 4 6 8

100

t=0.70883 ps

px - x phase space

Weibel instability

kx

Ey

Bz

u+u-

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 p2 k 2c 2

v ph c[1 p2 /2 2] c

vg c[1 p2 /2 2] c

Ion bubble formation by different a