Kyle Reger, University of Central Florida


Numerical Solutions to Hall Magnetohydrodynamics near an X-type Neutral Point

Abstract: The Hall Magnetohydrodynamic (MHD) model is the new paradigm to describe fast magnetic reconnection processes in space and laboratory plasmas. Current sheets form and store enormous amounts of magnetic energy at X-type magnetic neutral points, which is released as magnetic storms when the sheets break up. The fast magnetic reconnection process impacts solar flares and Earth's geomagnetic sub-storms, which affect global weather. The fast magnetic reconnection process also influences fusion reactors, which may be used as a future energy source. Numerical analysis of previously given approximate solutions to the Hall MHD equations at X-type magnetic neutral points is done to find insights into the solutions. The solutions to the Hall MHD equations must obey compatibility conditions like incompressibility and an exact invariant. The result, achieved through asymptotic analysis, correctly fits physical laws up to O(t). On the other hand, the exact invariant can be used to refine the asymptotics to any order of accuracy. The asymptotic solutions fully satisfy the plasma incompressibility condition. The most notable of changes between the MHD solutions and the Hall MHD solutions is the ability of the Hall term to prevent the finite-time singularity that appears in MHD. This leads to the prevention of the current density blow-up at long times in Hall MHD.

Mentor: Dr. Bhimsen Shivamoggi (University of Central Florida)