Particle acceleration in plasma

By

Prof. C. S. LiuPresident, National Central University, Taiwan

&

Department of Physics, NCU & University ofMaryland

in collaboration with S. H. Chen, S. Y. Chen,

J. Wang, N. Kumar, Y. Kuramitsu, and B. Eliasson

Outline

• Plasma universe

• Plasma wave excitation

• Laser driven acceleration and production ofthe monoenergetic electrons beam

• Ion acceleration

• Concluding remark

Plasma universe

Three minutes after Big Bang ----- Plasma dominateduniverse

Radio jets, X-ray sources, -ray bursts, pulsar,accretion disk etc….

γ

We observed this universe mostly by EM waves,its dispersion, e.g. distance of pulsars by dispersionrelation, 222

p2 ck+ω=ω

Cosmic ray acceleration

“Why plasma is such a capitalistic societyin which so much energy is given to sofew electrons” ??

Eugene Parker

Monoenergetic 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 monoenergeticbeam of electrons with energy50-170 MeV by three groups.

Acceleration of a SLAC electron beam

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

Demonstration of acceleration inbeam driven wakefield (SLAC)

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

First direct measurement of acceleration gradient;

eE=2.5 GeV/m ~ 103 of linac.

Plasma as medium for wavesPlasma wave

Ion wave

EM wave 222p

2 ck+ω=ω

2s

22 ck=ω

€

ω 2 =ω p2 + 3k 2ve

2

2) Ponderomotive pressure:

€

−∇nmυ os

2

2

= −n∇ a

2 = −mc 2∇γ,

linear

cm

Eea

0ω=

Oscillatory velocity,

€

vosc = eE mω0c , j = nevosc

€

vph =ω /k = c[1+ω p2 /k 2c 2] > c,

vg = c 2 /vph ≈ c[1−ω p2 /ω 2] < c

€

ve = kBTe me

In linear theory, no acceleration is possible by direct light wavebut by plasma wave and ion wave: Cherenkov resonance,

€

v =ω k

Plasma effects on light;

1) Dispersion:

€

ω p2 = 4πne2 me

€

cs = γkBTe Mi

Acceleration gradient of plasma wave can be large

Maximum acceleration gradient limited by the wave breaking

€

vosc ≈eEmω p

~ c or

€

E0 V /cm[ ] =mc 2

eω p

c

= 0.96 n0 cm

−3[ ]

giving, mGV100E0 = , for

€

n0 =1018 cm−3[ ],mc 2 ≈ 0.5MeV ,.c /ω p ≈1µm

Non-relativistic wave-breaking amplitude

Relativistic wave-breaking amplitude

[ ] 1Ecm/VE p0R −γ=

€

γ p = (1− vph2 /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 =ω 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 byelectron beam or short pulse laser

1) Mode conversion

€

n

€

x

++

€

Ex → v0x =eEx

imω0

∂δn∂t

= −v0x∂n0∂x

at ω0 =ω p

€

kx = 0

€

k = 0€

ω =ω pAn 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 plasmawave due to relativistic mass effect

( ) 13/16E

E 3/121

0

max <<αα= 2,1, =ω

′=α j

cm

Ee

j

jj

(Rosenbluth and Liu, PRL, 1972)

€

E0 = ′ E 0sin k0x −ω0t( ),

€

E1 = ′ E 1sin k1x −ω1t( )

€

ω 0 =ω 1+ωp,

€

k0 = k1 + kp

€

k1 ≅ −k0,Backscattering,

€

kp = k0 − k1 =ω p /cForward scattering,

€

kp = 2k0,

€

ω p,kp

€

ω p,kp

Laser light:

€

(ω 0, k0)

€

(ω1,k1 )Scattered light:

3) Raman Scattering by PlasmaWave

€

a0

€

a1Plasma:

€

δnp

€

δj = δnpvCurrent:

Feed backInstability

Growth rate:

€

γ = kv0ω p

ω0

1/ 2

,

€

kmax = 2k0,kmin =ω p /c€

ω p <<ω0

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 excitationby electron beam or short pulse laser

Micro magnetosphere

Relativistic self focusing

crPP ≥ whereLaser power,

GW17P2p

2

cr

ω

ω=

2

2

1γω

ω−=ε p

Relativistic dielectric constant

Relativistic effect increasesγ→

Ponderomotive effect decreases2pω→

Resultant effect ion channel formation→

Laser wakefield acceleration and ion channelformation in laser

2D PIC Simulation of Injection and Acceleration of2D PIC Simulation of Injection and Acceleration ofMono-Energetic Electrons in a Laser Wake FieldMono-Energetic Electrons in a Laser Wake FieldAccelerator by Accelerator by S. H. Chen and L. C. TaiS. H. Chen and L. C. Tai

Academia Sinica

• Plasma Density = 4.0e25 m^-3

• Peak Laser Intensity = 8.0e+18 // W/cm

• Pulse Length (FWHM) = 45.0e-15 // s

• Laser Wavelength = 0.81e-06 // m

• Bandwidth = 0.027e-06 // m, for chirped pulse

• Waist Size = 4e-06 // m

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 electronsmoving with the laser pulse. Time = 1.1 ps

The modulated laser field traps electrons and push electrons movingwith 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

Large time τ ~ ωpi-1, ions move

Ion acceleration

Borghesi et.al, PRL, 94, 195003 (2005)

Concluding remark

• With the recent breakthroughs in the plasmaaccelerator research, we can envisage that21st century will be a century of plasmascience and technology.

Thank you