A Gauge Condition for Studying the Origin of Intrinsic Magnetospheres
  We propose an analytical model based on the solution of the magnetohydrodynamics (MHD) equations for studying the origin of intrinsic magnetospheres. For this purpose, we reveal a new gauge condition for the electromagnetic vector potential, which eases the solution of such complex system of non-linear equations. Using this model, we analyse the deformation of the terrestrial magnetic field due to the presence of the solar wind. By comparing with experimental observations, we have found that the geometrical configuration of the magnetosphere, before, and after the magnetic field of the Earth started to deviate the solar wind, has not changed notably, and that the solar wind should have had a finite conductivity. This model can also be used to perform linear stability analysis of fluid and magnetic instabilities. 
M. Mendoza and J. Morales