An Exact, Timedependent Analytical Solution for the Magnetic Field in the Inner Heliosheath
Abstract
We derive an exact, timedependent analytical magnetic field solution for the inner heliosheath, which satisfies both the induction equation of ideal magnetohydrodynamics in the limit of infinite electric conductivity and the magnetic divergence constraint. To this end, we assume that the magnetic field is frozen into a plasma flow resembling the characteristic interaction of the solar wind with the local interstellar medium. Furthermore, we make use of the ideal Ohm's law for the magnetic vector potential and the electric scalar potential. By employing a suitable gauge condition that relates the potentials and working with a characteristic coordinate representation, we thus obtain an inhomogeneous firstorder system of ordinary differential equations for the magnetic vector potential. Then, using the general solution of this system, we compute the magnetic field via the magnetic curl relation. Finally, we analyze the wellposedness of the corresponding Dirichlet boundary value problem, specify compatibility conditions for the boundary values, and outline the implementation of boundary conditions.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.12893
 Bibcode:
 2021arXiv211012893R
 Keywords:

 Astrophysics  Solar and Stellar Astrophysics;
 Physics  Plasma Physics;
 Physics  Space Physics
 EPrint:
 14 pages