# Dielectric kernels for Maxwellian tokamak plasmas

## TL;DR

This paper introduces new integral kernels for the dielectric response of Maxwellian tokamak plasmas, enabling more accurate and flexible wave equation solutions without relying on traditional Fourier mode expansions.

## Contribution

It presents a novel formulation of dielectric kernels using special functions, improving numerical evaluation and allowing detailed local mesh refinements in plasma wave modeling.

## Key findings

- New integral kernels account for rotational transform and wave dispersion.
- Efficient evaluation methods are developed for the generalized functions.
- Framework allows for detailed local resolution near resonance layers.

## Abstract

New integral kernels describing the full-wave dielectric response of Maxwellian tokamak plasmas are presented. They realistically account for the rotational transform and for wave dispersion in presence of equilibrium magnetic field parallel gradients. These kernels rely on special functions of three variables that generalize the standard plasma dispersion function; their main analytical properties are given, leading to efficient evaluation. This approach is free from the poloidal Fourier mode expansion of the HF fields which appears in earlier formulations and gives complete freedom for the numerical resolution of the wave equation: it will typically be applied to 2D finite element discretizations, allowing local mesh refinements as required near cyclotron resonance layers and in regions of rapid HF field variations. This first presentation is to lowest order in the Larmor radius for the sake of clarity but will readily generalize to all orders in ($\rho_{LT}/\lambda_\perp$).