A class of conservative tunneling problems

Abstract

A conservative generalization of the Budden wave tunneling problem in an inhomogeneous medium is considered. The model describes the interaction between an electromagnetic wave and a ‘‘ballistic,’’ wavelike perturbation mediating between the incident and reflected electromagnetic wave channels. The transmission and reflection coefficients of the electromagnetic wave passing the interaction region are the same as in the classical Budden problem, while the ballistic mode carries the remainder of the energy flux. The theory is illustrated in the case of a whistler mode passing a local cyclotron resonance by propagating along a magnetized electron beam. The theory is also generalized to include other types of couplings, as those occurring in wave transformation problems at ion-cyclotron resonances, when the magnitude of the magnetic field has gradients along the field itself. The minority ion cyclotron heating problem for arbitrary direction of the gradient of the cyclotron frequency is studied as an example of such a generalized problem.