An algorithm to solve the linear mode conversion problem in a weakly inhomogeneous plasma

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Abstract
In a previous article, the wave equation for electromagnetic and electrostatic waves propagating in a weakly inhomogeneous plasma was studied assuming an ordinary differential equation of the Laplace type. An algorithm was developed, based on the contour integral formalism, that gives a prescription for calculating the connection formulas between the set of fast and slow propagating waves. Physical problems connected to the evanescent solutions were not treated, however, so the complete set of solutions was not obtained. In this paper, the method is extended to include both propagating and nonpropagating waves so that a complete set of solutions is obtained, permitting the construction of the Green function and the inclusion of localized sources or sinks.