Abstract
This paper presents an analysis of the spatial growth of a transverse instability, corresponding to the propagation of an electromagnetic beam, with uniform irradiance along the wavefront in a collisional plasma, along the direction of a static magnetic field; expressions have been derived for the rate of growth, the maximum value of the rate of growth and the corresponding value of the wave number of the instability. The instability arises on account of the ejection of electrons from regions where the irradiance of the perturbation is large. The energy balance of the electrons taking into account ohmic heating and the power loss of electrons on account of (i) collisions with ions and neutral species and (ii) thermal conduction has been taken into account for the evaluation of the perturbation in electron temperature, which determines the subsequent growth of the instability. Further, the relationship between the electron density and temperature, as obtained from the kinetic theory, has been used. The filamentation instability becomes enhanced with the increase of the static magnetic field for the extraordinary mode while the reverse is true for the ordinary mode. Dependence of growth rate on irradiance of the main beam, magnetic field and a parameter proportional to the ratio of power loss of electrons by conduction to that by collisions has been numerically studied and illustrated by figures. The dependence of the maximum growth rate and the corresponding optimum value of the wave number of the instability on the irradiance of the main beam has also been studied. The paper concludes with a discussion of the numerical results, so obtained.