An Effective Numerical Method for Linear Mode Conversion Problems

✍ Scribed by P.M. Bellan

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 296 KB
• Volume: 136
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1997.5792

✦ Synopsis

Linear mode conversion, an important issue in the physics of plasma waves, involves an ordinary differential equation of at least is easily solved for E(p), and then E(x) is found from the fourth order. Attempts to integrate this differential equation using Bromwich integral of E(p), i.e. from a contour integral in conventional numerical methods typically fail to provide a physithe complex p plane. Because Eq. ( 1) is fourth-order, there cally sensible result. This failure occurs because small, unavoidable are four distinct integration paths for the contour integral, truncation and differencing errors excite nonphysical, mathematieach giving one of the four independent solutions to Eq. cally allowed exponentially growing solutions which quickly overwhelm the desired physical solution. We present here a two-point

(1). The appropriate linear combination of solutions is boundary numerical method which avoids exciting these unwanted found by imposing four physically relevant boundary connonphysical solutions and so provides solutions that are physically ditions. This turns out to be equivalent to assigning the significant. The numerical algorithm is a generalization of the stanends of the integration paths, since analyticity within a dard tridiagonal method and provides single-pass solutions which satisfy the original difference equations to within the numerical region means that a given integration path with fixed end accuracy of the computer. ᮊ 1997 Academic Press points can be deformed in that region and still give the same result. The end points are typically determined using boundary conditions at x Ǟ Ϯȍ; these boundary condi-654