# Electromagnetic zonal flow residual responses

## TL;DR

This paper extends the calculation of electromagnetic zonal flow residuals in tokamak plasmas, providing new formulas and insights into the behavior of electromagnetic perturbations and their relaxation properties.

## Contribution

It generalizes the collisionless zonal flow residual calculation to include electromagnetic effects with fully self-consistent fields, offering new test expressions for gyrokinetic codes.

## Key findings

- Derived simple expressions for electromagnetic residual responses.
- Showed that certain magnetic perturbations do not relax to flux functions.
- Provided a comprehensive electromagnetic test for gyrokinetic simulations.

## Abstract

The collisionless axisymmetric zonal flow residual calculation for a tokamak plasma is generalized to include electromagnetic perturbations. We formulate and solve the complete initial value zonal flow problem by retaining the fully self-consistent axisymmetric spatial perturbations in the electric and magnetic fields. Simple expressions for the electrostatic, shear and compressional magnetic residual responses are derived that provide a fully electromagnetic test of the zonal flow residual in gyrokinetic codes. Unlike the electrostatic potential, the parallel vector potential and the parallel magnetic field perturbations need not relax to flux functions for all possible initial conditions.