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Nonlinear Propagation Of High Frequency Electromagnetic Wave Into The Underdense Plasma

A. R. Niknam1 and B. Shokri1,2
1 Laser-Plasma Research Institute of Shahid Beheshti University, Evin,Tehran,Iran
2Institute for Studies in Theoretical Phys. and Maths., P.O.Box 19395-1795, Tehran, Iran
Abstract: In this work, we studied the interaction of a high frequency electromagnetic wave with a plasma taking into account of
the ponderomotive force per unit volume acting on plasma electrons. We assumed the plasma is collisionless unmagnetized nonisothermal
which occupying the semi-space z > 0 . We found the nonlinear differential equation for the electric field using the
Maxwell and the hydrodynamic equations. The profiles of the electric and magnetic fields deviate from sinusoidal form and the
electron density oscillations appear highly peaked.
Keywords: Ponderomotive force, Nonlinear propagation , Underdense plasma, Electromagnetic wave
PACS: 52.35.Mw, 52.38.-r, 52.38.Kd, 52.40.Db
INTRODUCTION
The nonlinear interaction of a high frequency electromagnetic wave with a plasma are being widely investigated by
considering to the ponderomotive force [1-4]. In general, if the energy flux of the high frequency electromagnetic
wave is spatially inhomogeneous, this wave acts on the charged particles in a plasma with the ponderomotive force

where e n is the electron density , E is the electric field amplitude and ( k ) ijε ω, is the dielectric tensor.
This force can change the plasma density profiles and cause the acceleration of charged particles [5-8]. In this work,
we consider a high frequency electromagnetic wave normally incident on a collisionless unmagnetized nonisothermal
plasma, occupying the semi-space z > 0 . Also, we use the Maxwell and the hydrodynamic equations
with taking into account the average ponderomotive force per unit volume acting on the plasma electrons. Since, the
ion mass is much greater than the electron mass, we neglect the ponderomotive force exerted on the ions. We will
obtain the electron density distribution and the self-consistent distribution of the electromagnetic fields. Then, we
will plot the electric and magnetic field profiles and electron density variation in the plasma for the different values
of energy flux and initial electron density.
GENERAL EQUATIONS
In this section, by making use of the hydrodynamic equations and the Maxwell wave electric field equations, we
find the electron density distribution and the nonlinear differential equation for the electric field. We assume a
plasma (with permittivityε ) occupying the semi-space z > 0 is bounded by vacuum (with permittivity ε = 1).
The wave propagation is in z direction. In this case, the electric and magnetic fields being in xy plane are written.

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