Parametric Excitation of Transverse Waves in a Plasma

It is shown that an externally-imposed, oscillating electric field excites transverse electromagnetic waves propagating perpendicularly to it, in a cold plasma. The mechanism is closely related to the parametric excitation of longitudinal plasma oscillations recently predicted by Aliev and Silin. The problem provides an application of nonsecular perturbation methods, when the equations of motion are expanded in powers of the external electric field. Arbitrarily small perturbations which arise spontaneously in the plasma are amplified by the action of the electric field, for a certain range of the driving frequency. The growth rate of the oscillations is calculated.