An Effective Numerical Method for Linear Mode Conversion Problems

Abstract

Linear mode conversion, an important issue in the physics of plasma waves, involves an ordinary differential equation of at least fourth order. Attempts to integrate this differential equation using conventional numerical methods typically fail to provide a physically sensible result. This failure occurs because small, unavoidable truncation and differencing errors excite nonphysical, mathematically allowed exponentially growing solutions which quickly overwhelm the desired physical solution. We present here a two-point boundary numerical method which avoids exciting these unwanted nonphysical solutions and so provides solutions that are physically significant. The numerical algorithm is a generalization of the standard tridiagonal method and provides single-pass solutions which satisfy the original difference equations to within the numerical accuracy of the computer.