Direct nonlinear coupling of electromagnetic waves and electrostatic waves in a plasma: Theory

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Abstract
Nonlinear coupling among small amplitude electromagnetic and electrostatic waves in a cylindrical plasma-column waveguide is analyzed theoretically. The warm plasma equations of motion, in the displacement/polarization format, are combined with the wave equation for guided transverse magnetic waves to derive the system dispersion relation and the coupled-mode equations for this configuration. The coupling coefficients predict the strength of a given multiwave interaction from the intrinsic properties of the plasma waveguide. When the frequency selection rule is satisfied, for wave numbers consistent with the system dispersion relation, off-resonance excitation will occur if the interaction is confined to a finite length of the waveguide. Typical interaction resonances are illustrated on the system dispersion diagram by an experimentally useful graphical construction. Numerical estimates of the coupling strengths of selected three-wave “scattering” and “radiation” interactions are made from data obtained with the aid of this diagram. The analytical results are then illustrated and interpreted.

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