Ambipolar diffusion: Self-similar solutions and MHD code testing. Cylindrical symmetry

Ambipolar diffusion is a process occurring in partially ionised astrophysical systems that imparts complicated mathematical and physical nature to Ohm's law. The numerical codes solve the magnetohydrodynamic (MHD) equations have be able deal with singularities are naturally created system by ambipolar term. global aim calculate set of theoretical self-similar solutions nonlinear equation cylindrical symmetry can used as tests for MHD which include First, following general methods developed applied mathematics literature, we obtained eigenfunctions ordinary differential equation. Phase-plane techniques were integrate through at locations nulls, correspond infinitely sharp current sheets. In second half paper, consider use these codes. To end, Bifrost code, thereby testing capabilities well (inversely) accuracy Bifrost's recently module. shown constitute demanding, but nonetheless viable, test incorporate diffusion. code reproduce sufficient up very advanced diffusive times. Using also explored asymptotic properties our time when initially perturbed either small or finite perturbations. functions this paper relevant They provide more stringent than simple Zeldovich-Kompaneets-Barenblatt-Pattle solution.