Abstract
The excitation of transverse plasma modes by non-linear interaction is analysed by forming the Hamiltonian in terms of creation and annihilation operators for the quasi-particles (waves). The lowest order interaction occurs at order three of creation and annihilation operators. To this order the Hamiltonian contains the effects due to the processes of (a) two longitudinal waves interacting to generate one transverse wave (b) one longitudinal wave interacting with one transverse wave yielding one transverse wave and (c) two transverse waves colliding to produce one longitudinal wave. However the processes (b) and (c) can be eliminated by taking sufficiently long wavelength electrostatic waves such that K « ωp/c, where K is the longitudinal wave vector, ωp the plasma frequency and c the velocity of light. The relaxation time for the transfer of energy from the longitudinal modes to transverse modes is calculated for an isotropic, homogeneous, collisionless electron plasma.