Magnetic Boundary Conditions at Non-Conducting Planetary Bodies: Applications to Ganymede

The interaction of planetary bodies with their surrounding magnetized plasma can often be described with the magneto-hydrodynamic (MHD) equations, which are commonly solved by numerical models. For these models it is necessary to define physically correct boundary conditions. Many planetary bodies have electrically non-conductive surfaces, which do not allow electric current to penetrate their surfaces. Magnetic boundary conditions, which correctly consider that the associated radial electric current at the planetary surface is zero, are however difficult to implement because they include the curl of the magnetic field. Here we derive new boundary conditions for the magnetic field at non-conducting surfaces by a decomposition of the magnetic field in poloidal and toroidal components and their spherical harmonics expansions. We find that the toroidal part of the magnetic field needs to vanish at the surface of the isolator. For the spectral spherical harmonics coefficients of the poloidal part we derive a Cauchy boundary condition, which includes the Gauss coefficients of a possible intrinsic field. Our non-conducting boundary condition can thus additionally include intrinsic dynamo fields as well as induction fields within electrically conductive subsurface layers such as subsurface oceans. We implement the new boundary condition in the MHD simulation code ZEUS-MP using spherical geometry. We apply these new magnetic boundary conditions to a model for Ganymede's plasma environment. With this model we can describe the in-situ observations by the Galileo spacecraft and Hubble Space Telescope observations of Ganmyede's aurora very well.