VARIATIONAL THEORY OF THE CYCLOTRON-EMISSION SOURCE DISTRIBUTION FROMA 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 o n the generalized Kirchhoff's law that relates, branch by branch, the emission to the absorption. General integral expressions for both abso rbed 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 formul ated. A regular analytical procedure for solving the variational probl em with non-trivial generalized Kirchhoff's law constraints for obtain ing a continuous source distribution is developed. Examples at harmoni cs of both the electron- and ion-cyclotron frequencies are given and a nalysed for both relativistic and non-relativistic plasmas.