### Abstract

Taylor's relaxation theory is extended to plasmas with mass flow by using the cross helicity as a conserved quantity, similar to the magnetic helicity. Indeed, it is shown that the conservation of the cross helicity in magnetohydrodynamics is the result of the conservation of two magnetic-like helicities in two-fluid plasmas. In addition, the usually ignored toroidal flux is also held to be conserved. We also view plasma relaxation as attaining a maximum entropy state rather than Taylor's minimum energy state, but prove that maximizing the entropy subject to a given amount of energy is equivalent to minimizing the energy subject to a given amount of entropy. The resulting relaxed state is similar to the one discussed by Finn and Antonsen [Phys. Fluids 26, 3540 (1983)], and involves flow parallel to the magnetic field and constant temperature, but non-constant pressure. We show how to construct an asymptotic solution to the relaxed state based on the smallness of the Alfven Mach number of the flow.

Original language | English (US) |
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Article number | 044503 |

Journal | Physics of Plasmas |

Volume | 21 |

Issue number | 4 |

DOIs | |

State | Published - Apr 2014 |

### ASJC Scopus subject areas

- Condensed Matter Physics

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## Cite this

*Physics of Plasmas*,

*21*(4), [044503]. https://doi.org/10.1063/1.4871391