Focusing of electromagnetic beams in collisional plasmas, with finite thermal conduction

Abstract

In this paper we present a theoretical investigation of the focusing of coaxial Gaussian electromagnetic beams and of a Gaussian ripple on an electromagnetic beam of uniform irradiance in a collisional plasma (in thermal equilibrium in the absence of the beams). A self consistent solution of the electromagnetic wave equation, the energy balance equation, and Fourier’s equation of heat conduction has been obtained in the paraxial approximation. The nonuniform distribution of the electron density and thereby the dielectric function on account of the nonuniform electron temperature/density distribution causes the focusing/defocusing of the beams. The effect of thermal conduction on the temperature distribution of the electrons, on the critical curves, and the nature of focusing has been specifically studied. In common with earlier studies, three regions in the initial beam width—initial axial irradiance plane, corresponding to steady divergence, self focusing and oscillatory divergence have been characterized. Numerical computations have been made for an ionic collisions dominated plasma.

Self-focusing of a Gaussian electromagnetic beam in a multi-ions plasma

“…However, the non-uniform collisional heating of electrons due to non-uniform irradiance distribution along the wavefront causes a redistribution of electron density, 6 and consequently, dielectric function leading to the self-focusing of the beam; the characteristic time for this nonlinearity to get manifested is 1=d c e ; where d c is the fraction of excess energy lost by an electron in a collision and e is the electron collision frequency. The phenomenon of thermal conduction by electrons also affects the redistribution of carriers; a theory, taking into account both collisions as well as thermal conduction has been given by Sodha et al 7 The ponderomotive force on a charge in a nonuniform electric field is a well known phenomenon in classical electrodynamics. Hora 8 is the first researcher to point out that the ponderomotive force on electrons leads to a nonuniform distribution of electron density (and consequently, dielectric function) along the wavefront of an electromagnetic beam; this nonlinearity has been considered in most of studies of self-focusing.…”

Interaction between parallel Gaussian electromagnetic beams in the ionosphere

“…The balancing of these pressure gradients by the space charge field in the steady-state results in a nonuniform field-dependent distribution of electron density and hence the dielectric function. The present analysis to determine the space-dependent distribution of the electron temperature and thereby the dielectric function is similar to a recent study of Sodha et al (2006b), which investigates self-focusing of a single beam in a collisional plasma with significant thermal conduction.…”

Interaction between parallel Gaussian electromagnetic beams in a plasma with weakly relativistic-ponderomotive regime

“…Two beams attract each other when the condition 2x 0 < ωr 0 is satisfied and repel each other for 2x 0 > ωr 0 . Sodha et al [46] have similarly obtained the space-dependent distribution of the electron temperature and thereby the dielectric function for the case of self-focusing of single beam in a collisional plasma with thermal conduction.…”