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

A benchmark exercise for the modeling of vertical displacement events (VDEs) is presented and applied to benchmark 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 rectangular resistive wall. 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 good agreement is found between the results including the plasma currents as well as eddy and halo currents in the wall.