preparation of the concerned sectors for …...2. s eliezers. eliezer, the interaction of highthe...

Preparation of the concerned sectors for educational and R&D activities„Preparation of the concerned sectors for educational and R&D activities related to the Hungarian ELI project ”

Ion acceleration in plasmasIon acceleration in plasmas

Lecture 4. Interaction of intense laser pulse with plasmaplasma

Dr. Ashutosh SharmaZoltán Tibai

1TÁMOP-4.1.1.C-12/1/KONV-2012-0005 projekt

Contents

1 Laser Induced Ionization1. Laser Induced Ionization

2. Laser Transport in Plasma2. Laser Transport in Plasma

3. Relativistic Effects in Plasma

4. Wave Interaction with Plasmas

TÁMOP-4.1.1.C-12/1/KONV-2012-0005 projekt 2

Laser induced ionization

(4.1)

(4.2)

(4 3)


(4.3)


a) Bound electron state (marked b) Distortion of the atomic potentialgreen) in absence of an externalfield

by a strong laser field (red) enablingtunnel ionization


Laser induced Ionization

c) Complete barrier suppression inan even higher field is greatlyi i th i i ti tincreasing the ionization rate.



Multiphoton Ionization (MPI)If th f i l h t i ll th th i i ti t ti lIf the energy of a single photon is smaller than the ionization potential

of the bound state, an electron can still gain enough energy to overcome thepotential barrier of the nucleus by absorbing several lower frequency photons ona short timescale process called MPI.

Above-threshold ionization (ATI) is an extension of MPI, where anelectron is excited by more photons than strictly necessary to free it from thee ect o s e c ted by o e p oto s t a st ct y ecessa y to ee t o t eatom.

Tunneling IonizationTunneling IonizationWhen the intensity is increased further, the laser field is strong enough

to significantly distort the atomic potential. At a certain distance on the righthand side of the atom, the coulomb barrier is lowered beneath the bindingenergy of the electron. Thus, quantum mechanically the previously bound state isenabled to tunnel through this barrier with some finite probability, a mechanismwhich is referred to a tunneling ionization.



(4.4)


Linear Waves in a plasma

(4.5)

(4.6)



Neglecting thermal effects, and considering all electrons at a point ist h th l it th t d it i ipace to have the same velocity, the current density is given as,

(4.7)

where (neglecting nonlinearand relativistic terms)

(4.8)

Considering a monochromatic field:(4.9)

We obtain,

(4.10)

With plasma frequency

(4 11)


(4.11)


(4.12)

(4 13)(4.13)

(4.14)

(4.15)


(4.16)


The dispersion relation can be obtain (from (4.13)-(4.16)).

(4.17)

i i l ff d i

(4 18)

→ critical or cutoff density


(4.18)


(4.19)



From Eq. (4.17)Ph l itPhase velocity:

(4.20)

From Eq. (4.17)Group velocity:



Fig. 4.3 Schematic diagram of the typical electron density profile in the laserproduced plasma


Longitudinal Electrostatic Waves


Longitudinal Electrostatic Waves

From wave equation (4.13) one obtains,

or

Thus,

These electrostatic waves at the plasma frequency are called as plasma

→ arbitrary values

These electrostatic waves at the plasma frequency are called as plasmawaves or plasmons.

The plasma waves are associated with density perturbation and can bebt i d f P i ’ tiobtained from Poisson’s equation.


Dispersion relation for plasma waves in warm plasmawarm plasma

(4.21)

Fig 4 4: Dispersion relation for electron plasma


Fig. 4.4: Dispersion relation for electron plasmawaves (Bohm-Gross waves)

Relativistic Nonlinear Effects in Plasma

(4.22)



(4.23)

(4.24)

(4.25)


( )

Propagation of finite beam size laser pulse in plasmain plasma

(4.26)

(4.27)


Relativistic self-focusing: Geometric optics

(4.28)


Beam propagation in vacuum

(4.29)

(4.30)

(4.31)



(4 32)

(4 33)

(4.32)

(4.33)



(4.34)

(4.35)

TÁMOP-4.1.1.C-12/1/KONV-2012-0005 projekt 25Fig. 4.6

Nonlinear Schrödinger Equation

(4.36)

(4.37)



(4.36)



(4.39)

(4.40)

(4 41)(4.41)



(4.42)



(4.43)

(4.44)



(4.45)

(4.46)

(4.47)


Beam Focusing Threshold

(4.50)

where


Beam Focusing Threshold

(4.50)


Laser Pulse Dynamics in Relativistic PlasmaPlasma

Spatial and Temporal Evolution of Gaussian Laser p pPulse in Relativistic Plasma



Temporal Evolution of Gaussian Laser Pulse in Relativistic Plasma



Transverse Focusing of Gaussian Laser Pulse in Relativistic Plasma


Problems


References

1. F. F. Chen, Introduction to Plasma Physics, (Plenum Press, New York, 1974)1974).

2 S Eliezer The Interaction of High-Power Lasers with Plasmas (IOP2. S. Eliezer, The Interaction of High Power Lasers with Plasmas, (IOP Publishing, Bristol, 2002).

3. W. L. Kruer, The Physics of Laser Plasma Interactions, (Addison-Wesley Publishing Company, California, 1988).

4. P. Gibbon, Short Pulse Laser Interaction with Matter, (Imperial College Press, 2005).


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