A unified theory of a class of mode conversion problems

Abstract

Many radio-frequency heating methods involve conversion of an incoming wave to another mode which only propagates within the plasma and is ultimately damped. A method previously used to consider electron cyclotron heating by the O mode is extended to other mode conversion phenomena.From the properties of the dispersion relation in the neighborhood of the mode conversion point, differential equations for the mode amplitudes are constructed, in a well-defined way, which give energy conservation in the absence of damping. An analytic solution gives the transmission and conversion coefficients in terms of parameters defining the local behavior of the dispersion relation. The technique is applied to a number of problems, showing that they can all be solved by elementary algebraic manipulations of the local dispersion relation. The phenomenon of electron cyclotron emission also falls rather naturally into this mode conversion picture. It is also suggested that the method of dealing with cyclotron emission may have some relevance to the more general problem of energy transport across a magnetic field. The technique, therefore, brings together into a unified theory a number of problems which have been treated by diverse, and usually more complicated, mathematical techniques in the existing literature.