Comparison of M3DC1 Finite-Elements Code to Analytic Asymptotic Matching Solutions of Tearing Modes

The M3DC1 implicit high-order two-fluid finite-element plasma-modeling code has been benchmarked in the linear resistive regime by comparison to an asymptotic matching solution for the case of a tearing mode instability in a circular cylindrical tokamak. The instability is driven by current and pressure gradients and involves reconnection of the magnetic field. The asymptotic matching technique combines the solution to the resistive magnetohydrodynamic (MHD) equations in the thin region around the mode rational surface with the solution to the ideal MHD equations beyond it. The M3DC1 and asymptotic matching results for the mode growth rate were compared over a wide range of Lundquist numbers $(10^{4}