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