Structure-preserving discretisation for magneto-frictional equations in the Parker conjecture
Abstract
The Parker conjecture, which explores whether magnetic fields in perfectly conducting plasmas can develop tangential discontinuities during magnetic relaxation, remains an open question in astrophysics. Helicity conservation provides a topological barrier against topologically nontrivial initial data relaxing to a trivial solution. Preserving this mechanism is therefore crucial for numerical simulation.
This paper presents an energy- and helicity-preserving finite element discretization for the magneto-frictional system for investigating the Parker conjecture. The algorithm enjoys a discrete version of the topological mechanism and a discrete Arnold inequality.
We will also discuss extensions to domains with nontrivial topology.
This is joint work with Prof Patrick Farrell, Dr Kaibo Hu, and Boris Andrews