Extended-MHD modeling of diamagnetic-drift tearing instabilities

We use analytics and computations with the NIMROD code to examine tearing stability in large-guide-field slab cases with a nonzero equilibrium pressure gradient. A well known result from drift-reduced MHD is the diamagnetic drift associated with the pressure gradient has a stabilizing influence were the dispersion relation becomes $(\gamma+i\omega_{*e})^{3}\gamma(\gamma+i\omega_{*i})=\gamma_{rMHD}^{5}$ [1]. Here $\omega_{*i}$ and $\omega_{*e}$ are the ion- and electron-diamagnetic frequencies and $\gamma_{rMHD}$ is the tearing growth rate with a resistive-MHD model. Preliminary computational results with an unreduced extended-MHD model do not produce the expected drift-reduced result. For moderate values of $\omega_{*i}$ ($\omega_{*i}\leq3\gamma_{rMHD}$), the computations follow the dispersion relation that would result if the $\nabla{p}_{e}$ term were not included in the drift-reduced parallel Ohm's law: $(\gamma+i\omega_{*e})^{4}(\gamma+i\omega_{*i})=\gamma_{rMHD}^{5}$. Analytics, guided by computational diagnostics, are used to examine the significant terms in the flux evolution equation and investigate the discrepancy with the drift-reduced result.\\[4pt] [1] For example Coppi, PoF 7, 1501 (1964); Biskamp, NF 18, 1059 (1978).