laser-plasma interaction part i

8/3/2019 Laser-Plasma Interaction Part I

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Laser-Plasma Interaction

Part I


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Outline


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Nonlinear optics of plasmas in the relativistic regime

Definition:Interaction of electrons with a laser field which is highly intensesuch that the electron quiver motion in this field approaches thespeed of light in vacuum.

Physics:

when vc

Nonlinear quiver motion of electrons (harmonic generation)

m0 m0vB E

Modification of refractive index

where

2

0( , ) 1 ( , ) / 2r t a r t = +20

20

1( , )

pn

r t

= 1

210 2

0 ( , ) 8.5 10 [ ] [ / ]a r t m I W cm

=

Large ponderomotive force (optical pressure) intensity22

0 0

2

04 1 / 2

pond

m c a

F a

= +

for linear polarization


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Dispersion relation of EM wave and refractive index


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Dispersion relation of EM wave and refractive index

Index of refraction of plasma

plasma frequency

p0 [rad/sec] = 5.64x104 ne[cm

-3]1/2

phase velocity of a laser pulse in a plasma

vp = /k = c/n

group velocity of a laser pulse in a plasmavg = d/dk = cn


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Plasma waves

ion acoustic waveelectron plasma wave

plasma

ion

electron

v v


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Microscopic description of plasma dynamics and particle-in-cell simulation


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Kinetic description of plasma dynamics and Vlasov simulation

and


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Fluid description of plasma dynamics and plasma hydrodynamic simulation


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inverse bremsstrahlung heating

local average electron quiver velocitywhere

laser ponderomotive force

Collisional ionization is included via the atomic transition code.


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high-intensity correction


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Plasma radiation emission and atomic transition simulation

With a given electron temperature and density, solve the transitionrate equations including

collisional ionizationcollisional recombinationphoto-ionizationradiative recombinationcollisional excitationcollisional deexcitaionphoto-excitaionradiative decay and stimulated emission........

collisional-radiative model non-LTE

The coefficients (cross sections) may be generated by another

code (e.g., Cowan code).

Output: time-resolved x-ray emission spectrum

average atom model or not


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Optical-field ionization and semiclassical simulation

in a single active electron approximation under theinfluence of the laser field Ecos() of linear polarization

x is in the direction of laser polarization.

The macroscopic effects including the evolution of the laserpulse with propagation and phase matching have to beincluded self-consistently for a good quantitative comparisonwith the experiments.

Harmonic spectrum is obtained from Fourier transform ofx(t)=


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Nonlinear Thomson scattering


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x

z

y

incident field

scattered field n

Vz

electron

coordinates

-0.15 -0.10 -0.05 0.00 0.05 0.10 0.15-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

k 0x

a0 = 0.1a0 = 0.3a0 = 0.6

a0 = 0.9

figure-eight trajectory

Principle


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Setup for measuring the angular distribution and spectrum of harmonics

CCDcamera

narrowbandpass

filter (20 or 30)

gas jet

slit

1200 lines/mmgratingspectrometer

CCDcamera

apertureCCDcamera

narrowbandpassfilter (0)

/2 plate


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Angular pattern of the harmonics

0

30

60

90

120

150

180

n = 2, = 90

0

30

60

90

120

150

180

0

30

60

90

120

150

1800

30

60

90

120

150

180

n = 1, = 90

Scattered intensity as a function of for 0.8-J pulse energyand 6.21019-cm -3 plasma density

n = 2, = 50

n = 3, = 90

experiment theory (v = 0) theory (v = - 0.2 c)


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Relativistic self-guiding


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Ponderomotive self-channeling

resulting from expulsion of electrons on axis

Relativistic self-focusingresulting from relativistic modification of electron mass


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the combinational effect of relativistic self-focusing andponderomotive self-channeling overcomes the naturaldiffraction, leading to the self-guiding of the laser pulse.

At


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Setup for characterizing relativistic self-guiding and Raman forwardscattering


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Setup for characterizing relativistic self-guiding and Raman forwardscattering


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Side imaging of Thomson scattering for various laser powers


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Transverse profiles of the self-guided laser beam


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Waveguide formation by ponderomotive self-channeling


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Formation of plasma waveguide driven by ponderomotive self-channeling

r0

Electrons are expelled outward bythe laser ponderomotive force. Ionsare not affected due to their much

heavier mass.

r0 r0

Electron Density Depression Ion Coulomb Explosion Plasma Waveguide Formation

W hile th e laser pu lse keep selectrons outside, the ions start tom ove out due to C ou lom b

repulsion.

After the end of the laser pulse,ions continue to move away fromthe axis(due to its inertia) while

dragging electrons with them.

laser intensity

ion density

electron density

The mean velocity of ions after the passage of the laser pulse is roughly given by

where Z is the ion charge, is the pulse duration and r0 is the radius of the laser

channel. At 2.5-TW laser power and 50% guiding, the mean ion velocity is about 1

m/ps. The maximum kinetic e nergy of ions is roughly determined by the laser ponder-omotive potential, which in this case is about 200 keV. Because of the low collisional

cross section at such higher energy, the motion of the ions are in a regime betweenpure hydrodynamic and free streaming. Prodution of ions with energy > 100 keV hasbeen observed.

2 2 2 20 0( 1 / 2) / / ( 1 / 2 1) / e r i e i Zm c dt a m Zm c m a r + +


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Inteferograms of the plasma at various probe delays

The interferograms show the formation of a plasma waveguide onaxis and the radial expansion of the plasma column

P


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Temporal evolution of plasma density distribution

Both the radii of the plasma waveguide and the plasma columnexpand with a velocity of ~1 m/ps.P

0 6x1019 cm -3

T + 5 ps

T + 30 ps

T + 40 ps

T + 15 ps

800 m3-D plasma density distribution

-100 -50 0 50 1000

1

2

3

4

5

15 ps30 ps40 ps

radial position (m)

ele

ctr

on

de

ns

ity

(x10

19c

m-3

)

Transverse lineout at the positionindicated by an arrow

5 ps


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Optical-field ionization (OFI)

energy

x0

multi-photon

ionization

tunneling

ionization

bound state

over-barrier

ionization


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Above-threshold ionization (ATI) heating

OFI by stronglaser pulse

heating (accelerating)by the laser pulse

linear-polarizedlaser field

timeelectronv

e

locity

electron energy spectrumproduced by different polarized

laser pulse

energy

linearpolarization

circularpolarization

electron

distribution


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Ion population and electron energy

100001 10 100 1000

0.01

0.1

1

energy (eV)

d

d

n

E

e

/

(arb.

un

its)

-120 -90 -60 -30 0 300.0

0.2

0.4

0.6

0.8

1.0

time (fs)

re

lativep

opulation

Xe (1+)(2+)(4+)

(5+)

(6+)

(7+)

(8+)

pulse waveform

(810 nm, 60 fs)

(9+)

(3+)

Calculated evolution of the relative population of ion species andthe electron energy spectrum under a laser pulse of 1 9x10W/cm peak intensity.

.

17

2

using ADK theory


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Interaction of laser pulse with solid target

target surface

pedestal

pedestal intensity:

~10 W/cm13 2

plasma generationplasma heating

peak intensity:

4.3 10 W/cm18 2

ionization threshold:

~10 W/cm10 2


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Dominant heating mechanisms

L

a

laser wavelength > plasma scale length > e oscillation amplitude L a-

Inverse bremsstrahlung absorption

Resonance absorption

electron


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Inverse bremsstrahlung absorption


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Resonant absorption

ncrcos2


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Plasma and electron plasma wave

+

-

+

-

+

-

+

-

+

-

pump pulse

plasma wave driven by Ramanforward scattering instability

electrons injected by Ramanbackscattering instability

Raman forward scattering instability can drive an electron plasma wave

with a phase velocity close to c. Electrons with initial energy higher thana threshold can be trapped and accelerated by the plasma wave.

P


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Stimulated Raman scattering instability and Brillouin scattering instability


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Raman forward scattering in a plasma


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Raman forward scattering in a plasma


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The Raman satellites originate from a channel of


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Raman spectra for various plasma densities

attenuation film

stokes peakelectron density

(x10 cm )19 -3

intensity(logscale)

(x10 rad/s)14

0 -2 -4 -6 -8electron density (x10 cm )19 -3

plasmafrequency(x10rad/s)

14

00

1

1

2

2

3

3

4

3.7

3.3

2.9

2.5

2.1

1.7

1.3

0.90.5

The frequency shift is equal to plasma frequency.P


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Raman spectra for various laser powers

The frequency shift is independent of laser power.

We can conclude that the frequency shift is due to RFS.

P

P


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Dependence of RFS on the chirp of a laser pulse

Raman forward scattering is expected to be assisted by a positively chirpedpulse and suppressed by a negatively chirped pulse.


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Raman intensity vs. laser pulse duration and chirp


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Raman shift vs. laser pulse duration and chirp


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Raman spectra vs. laser pulse duration and chirp

laser-plasma interaction part i

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