# Axisymmetric simulations of vertical displacement events in tokamaks: A benchmark of M3D-C$^1$, NIMROD and JOREK

## TL;DR

This paper benchmarks three advanced 3D nonlinear magneto-hydrodynamic codes—M3D-C$^1$, NIMROD, and JOREK—in simulating vertical displacement events in tokamaks, demonstrating strong agreement in linear and nonlinear phases.

## Contribution

It provides a comprehensive comparison of M3D-C$^1$, NIMROD, and JOREK codes for VDE modeling, highlighting their consistency and validating their use for tokamak stability analysis.

## Key findings

- Linear VDE growth rates depend on wall resistivity.
- Good agreement in linear phase simulations among the codes.
- Excellent agreement in nonlinear simulations of plasma behavior.

## Abstract

A benchmark exercise for the modeling of vertical displacement events (VDEs) is presented and applied to the 3D nonlinear magneto-hydrodynamic codes M3D-C$^1$, JOREK and NIMROD. The simulations are based on a vertically unstable NSTX equilibrium enclosed by an axisymmetric resistive wall with rectangular cross section. A linear dependence of the linear VDE growth rates on the resistivity of the wall is recovered for sufficiently large wall conductivity and small temperatures in the open field line region. The benchmark results show good agreement between the VDE growth rates obtained from linear NIMROD and M3D-C$^1$ simulations as well as from the linear phase of axisymmetric nonlinear JOREK, NIMROD and M3D-C$^1$ simulations. Axisymmetric nonlinear simulations of a full VDE performed with the three codes are compared and excellent agreement is found regarding plasma location and plasma currents as well as eddy and halo currents in the wall.