Observations of a nonlinear interaction involving three electromagnetic waves in a laboratory magnetoplasma

Abstract

POLARISATION requirements and wave number matching dictate that a nonlinear interaction involving three electromagnetic waves that propagate in a magnetoactive plasma must necessarily be two-dimensional if one of the waves propagates parallel to the external magnetic field B0. We report here what we believe to be the first observation of a three wave interaction of this kind. Our experiment involved the production of a whistler mode wave (k3, ω3) (referred to as WMW) through the interaction of two beams of high frequency electromagnetic waves (k1, ω1) and (k2, ω2), propagating somewhat above the local plasma frequency ωp. The resonance condition for the interaction are If ω1,2 > ωp and ω3 is sufficiently small compared with the electron gyrofrequency ωe (ωe < ωp), the high frequency beams must be directed1 almost at right angles to B0 (Fig. 1 inset). The strength of the coupling of the beams is determined by two factors: first, the magnitude of the matrix element for the interaction; and second, the time in which a stationary state is established as a result of the convection of the WMW packet across the finite interaction region of width, l. An expression2,3 for the steady-state amplitude, E3 of the electric field of the WMW, can be obtained in terms of the amplitudes E1 and E2 of the beams where where e and m are the charge and mass of the electron, respectively, c the speed of light, μ, the refractive index for the WMW, and other symbols are as defined previously.