Complex space Newton-Raphson solution of the dispersion relation of low frequency Alfven waves in fusion plasmas

TL;DR

This paper applies the complex space Newton-Raphson method to efficiently solve the transcendental dispersion relation of low frequency shear Alfven waves in fusion plasmas, demonstrating high convergence and computational speed.

Contribution

It introduces the use of complex space Newton-Raphson method for solving dispersion relations in fusion plasma physics, highlighting its efficiency and reliability.

Findings

High convergence rate with few non-converging points

Fast computational solution of the dispersion relation

Identification of physically relevant basins of attraction

Abstract

Newton-Raphson method in complex space is used to numerically solve the transcendental dispersion relation of low frequency shear Alfven waves in fusion plasmas. The equation exhibits several physically relevant basins of attraction. The method is shown to be efficient and fast in solving this equation, with very small portion of non-converging points.