Nonlinear scattering from a warm plasma column

Abstract

When a plane electromagnetic wave impinges normally on a plasma column, with its magnetic field vector parallel to the axis of the column, a series of (Tonks-Dattner) resonances are excited which have been described previously in the linear regime, by a warm plasma analysis using a scalar electron pressure and an inhomogeneous radial electron density profile. In this paper, the theory is extended to the weakly nonlinear regime, assuming a parabolic electron density profile. The nonlinear scattered power is obtained. The excitation of dipole resonances at two different frequencies produces a predominantly quadrupolar radiation pattern with minima in the direction of the incident wave vectors and approximately at right angles to it. In general, there is no nonlinear power radiated in the forward and backward directions. Numerical results for the nonlinear scattering coefficients are obtained in the special case of second-harmonic generation at dipole resonance.