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 ω_p. The resonance condition for the interaction are If ω_1,2 > ω_p and ω₃ is sufficiently small compared with the electron gyrofrequency ω_e (ω_e < ω_p), 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 expression^2,3 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.