Direct numerical comparison of compressible Hall MHD and reduced Hall MHD.

L.N. MARTIN, P. DMITRUK, D.O. GOMEZ

Trieste, Italia

Workshop; ICTP Workshop on Plasma Physics; 2009

When a plasma is subject to a strong magnetic field its macroscopic dynamics tends to develop in the perpendicular plane to this field, the gradients of the magnetic and velocity field fluctuations are much smaller along the direction of the external magnetic field than along the perpendicular directions. This property plus the assumption of only considering the slow time dynamics allows for a simplification of the magnetohydrodynamic (MHD) equations, known as reduced magnetohydrodynamics (RMHD). Our investigation compares direct numerical simulations of a compressible MHD flow including the Hall effect with the recently introduced reduced Hall MHD equations, which are a set of equations equivalent to the RMHD system but also including the Hall effect (see D.O. Gomez, S.M. Mahajan and P. Dmitruk, Phys. Plasmas 15, Art 102303, 2008). Our study is performed in the turbulent regime of this system. In our simulations we compare the full MHD system with the reduced system for different initial conditions, analyzing the role of isotropic/anisotropic initial conditions in the global history of the flow dynamics.