Generalized χ and η Cross-Helicities in Non-Ideal Magnetohydrodynamics

Prachi Sharma, Asher Yahalom

Research output: Contribution to journalArticlepeer-review


We study the generalized (Formula presented.) and (Formula presented.) cross-helicities for non-ideal non-barotropic magnetohydrodynamics (MHD). (Formula presented.) and (Formula presented.), the additional label translation symmetry group, are used to generalize cross-helicity in ideal flows. Both new helicities are additional topological invariants of ideal MHD. To study there behavior in non-ideal MHD, we calculate the time derivative of both helicities using non-ideal MHD equations in which viscosity, finite resistivity, and heat conduction are taken into account. Physical variables are divided into ideal and non-ideal quantities separately during the mathematical analysis for simplification. The analytical results indicate that (Formula presented.) and (Formula presented.) cross-helicities are not strict constants of motion in non-ideal MHD and show a rate of dissipation that is comparable to the dissipation of other topological constants of motion.

Original languageEnglish
Article number2203
Issue number12
StatePublished - Dec 2023


  • MHD
  • non-ideal flows
  • topological constants of motion


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