A Conserved Cross Helicity for Non-Barotropic MHD

TL;DR

This paper introduces a new conserved cross helicity in non-barotropic MHD, extending the classical concept and applicable even in complex topologies where traditional variational principles fail.

Contribution

It proposes a novel form of cross helicity that remains conserved in non-barotropic MHD, broadening the understanding of invariants in plasma physics.

Findings

New cross helicity reduces to standard form under barotropic conditions

Conserved in topologies where variational principles do not apply

Extends the concept of cross helicity to non-barotropic MHD

Abstract

Cross helicity is not conserved in non-barotropic magnetohydrodynamics (MHD) (as opposed to barotropic or incompressible MHD). Here we show that variational analysis suggests a new kind of cross helicity which is conserved in the non barotropic case. The non barotropic cross helicity reduces to the standard cross helicity under barotropic assumptions. The new cross helicity is conserved even for topologies for which the variational principle does not apply.