Lie symmetry analysis of the 3-dimensional reduced Hall MHD equations

To find symmetric Lie groups of a reduced form of the non-linear 3-dimensional Hall Magnetohydrodynamic equations, symmetry analysis was used to find determining equations and solve for the infinitesimal generating functions. Brian Cantwell’s Mathematica program was used to generate determining equations, and original Python code was written in order to simplify the process of reducing Mathematica output. Several symmetries were found, the most interesting of which are quadratic vortex tubes which extend through the plasma in the normal direction.