VARIATIONAL THEORY OF THE CYCLOTRON-EMISSION SOURCE DISTRIBUTION FROM A MODE-CONVERSION LAYER

This paper presents the theory of an inhomogeneous source of cyclotron emission from a three-branch mode-conversion layer in a non-uniformly magnetized plasma. The physical formulation of the problem is based on the generalized Kirchhoff's law that relates, branch by branch, the emission to the absorption. General integral expressions for both absorbed and emitted energy fractions along each wave branch are obtained. A discrete multi-point model of absorbers and emitters is analysed. A variational principle for the integral of the emitted power is formulated. A regular analytical procedure for solving the variational problem with non-trivial generalized Kirchhoff's law constraints for obtaining a continuous source distribution is developed. Examples at harmonics of both the electron- and ion-cyclotron frequencies are given and analysed for both relativistic and non-relativistic plasmas.