Spectral resolution and solution of field problems in an anisotropic and compressible medium

It is shown that when source currents are present in a compressible and anisotropic plasma, the longitudinal components of the electric and magnetic fields and the pressure variation satisfy a coupled inhomogeneous equation. Based on the spectral resolution of a square matrix, a general method for the solution of such an equation is presented. The solution of the coupled-wave equation is thus reduced to the evaluation of some simple integrals. Formulas for the determination of the transverse components are given. To demonstrate the simplicity of the method, fields due to a magnetic line source are worked out in detail. Some numerical results are also included.