Semi-analytical derivation of the 2D all-FLR ICRH wave equation as a high-order partial differential equation

TL;DR

This paper extends a semi-analytical method for deriving a high-order PDE form of the all-FLR ICRH wave equation from 1D to 2D, incorporating finite poloidal field effects for improved modeling accuracy.

Contribution

It provides a semi-analytical derivation of the 2D all-FLR ICRH wave equation with finite poloidal field, advancing from previous 1D models.

Findings

Derivation of 2D high-order PDE coefficients for all-FLR ICRH wave equation.

Extension of the method to include finite poloidal field effects.

Preparation for future numerical simulations of RF waves in plasma.

Abstract

For 1-dimensional applications, Bude's method [Bude et al, Plasma Phys. Control. Fusion, 63 (2021) 035014] has been shown to be capable of accurately solving the all-FLR (Finite Larmor Radius) integro-differential wave equation as a high-order differential equation allowing to represent all physically relevant (fast, slow and Bernstein) modes upon making a polynomial fit that is accurate in the relevant part of k-space. The adopted fit is superior to the Taylor series expansion traditionally adopted to truncate the series of finite Larmor radius corrections, while the differential rather than integro-differential approach allows for significant gain in required computational time when solving the wave equation. The method was originally proposed and successfully tested in 1D for radio frequency (RF) waves and in absence of the poloidal field [D. Van Eester & E. Lerche, Nucl. Fusion, 61 (2021) 016024]. In the present paper, the derivation of the extension of that procedure to 2D and for finite poloidal field - semi-analytically yielding the coefficients of the relevant high-order partial differential equation - is discussed in preparation of future numerical application.