### Abstract

Magnetohydrodynamic (MHD) stability comparison theorems are presented for several different plasma models, each one corresponding to a different level of collisionality: a collisional fluid model (ideal MHD), a collisionless kinetic model (kinetic MHD), and two intermediate collisionality hybrid models (Vlasov-fluid and kinetic MHD-fluid). Of particular interest is the re-examination of the often quoted statement that ideal MHD makes the most conservative predictions with respect to stability boundaries for ideal modes. Some of the models have already been investigated in the literature and we clarify and generalize these results. Other models are essentially new and for them we derive new comparison theorems. Three main conclusions can be drawn: (1) it is crucial to distinguish between ergodic and closed field line systems; (2) in the case of ergodic systems, ideal MHD does indeed make conservative predictions compared to the other models; (3) in closed line systems undergoing perturbations that maintain the closed line symmetry this is no longer true. Specifically, when the ions are collisionless and their gyroradius is finite, as in the Vlasov-fluid model, there is no compressibility stabilization. The Vlasov-fluid model is more unstable than ideal MHD. The reason for this is related to the wave-particle resonance associated with the perpendicular precession drift motion of the particles (i.e., the E×B drift and magnetic drifts), combined with the absence of any truly toroidally trapped particles. The overall conclusion is that to determine macroscopic stability boundaries for ideal modes for any magnetic geometry using a simple conservative approach, one should analyze the ideal MHD energy principle for incompressible displacements.

Original language | English (US) |
---|---|

Article number | 012505 |

Journal | Physics of Plasmas |

Volume | 18 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2011 |

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### ASJC Scopus subject areas

- Condensed Matter Physics

### Cite this

*Physics of Plasmas*,

*18*(1), [012505]. https://doi.org/10.1063/1.3535587

**Magnetohydrodynamic stability comparison theorems revisited.** / Cerfon, Antoine; Freidberg, Jeffrey P.

Research output: Contribution to journal › Article

*Physics of Plasmas*, vol. 18, no. 1, 012505. https://doi.org/10.1063/1.3535587

}

TY - JOUR

T1 - Magnetohydrodynamic stability comparison theorems revisited

AU - Cerfon, Antoine

AU - Freidberg, Jeffrey P.

PY - 2011/1

Y1 - 2011/1

N2 - Magnetohydrodynamic (MHD) stability comparison theorems are presented for several different plasma models, each one corresponding to a different level of collisionality: a collisional fluid model (ideal MHD), a collisionless kinetic model (kinetic MHD), and two intermediate collisionality hybrid models (Vlasov-fluid and kinetic MHD-fluid). Of particular interest is the re-examination of the often quoted statement that ideal MHD makes the most conservative predictions with respect to stability boundaries for ideal modes. Some of the models have already been investigated in the literature and we clarify and generalize these results. Other models are essentially new and for them we derive new comparison theorems. Three main conclusions can be drawn: (1) it is crucial to distinguish between ergodic and closed field line systems; (2) in the case of ergodic systems, ideal MHD does indeed make conservative predictions compared to the other models; (3) in closed line systems undergoing perturbations that maintain the closed line symmetry this is no longer true. Specifically, when the ions are collisionless and their gyroradius is finite, as in the Vlasov-fluid model, there is no compressibility stabilization. The Vlasov-fluid model is more unstable than ideal MHD. The reason for this is related to the wave-particle resonance associated with the perpendicular precession drift motion of the particles (i.e., the E×B drift and magnetic drifts), combined with the absence of any truly toroidally trapped particles. The overall conclusion is that to determine macroscopic stability boundaries for ideal modes for any magnetic geometry using a simple conservative approach, one should analyze the ideal MHD energy principle for incompressible displacements.

AB - Magnetohydrodynamic (MHD) stability comparison theorems are presented for several different plasma models, each one corresponding to a different level of collisionality: a collisional fluid model (ideal MHD), a collisionless kinetic model (kinetic MHD), and two intermediate collisionality hybrid models (Vlasov-fluid and kinetic MHD-fluid). Of particular interest is the re-examination of the often quoted statement that ideal MHD makes the most conservative predictions with respect to stability boundaries for ideal modes. Some of the models have already been investigated in the literature and we clarify and generalize these results. Other models are essentially new and for them we derive new comparison theorems. Three main conclusions can be drawn: (1) it is crucial to distinguish between ergodic and closed field line systems; (2) in the case of ergodic systems, ideal MHD does indeed make conservative predictions compared to the other models; (3) in closed line systems undergoing perturbations that maintain the closed line symmetry this is no longer true. Specifically, when the ions are collisionless and their gyroradius is finite, as in the Vlasov-fluid model, there is no compressibility stabilization. The Vlasov-fluid model is more unstable than ideal MHD. The reason for this is related to the wave-particle resonance associated with the perpendicular precession drift motion of the particles (i.e., the E×B drift and magnetic drifts), combined with the absence of any truly toroidally trapped particles. The overall conclusion is that to determine macroscopic stability boundaries for ideal modes for any magnetic geometry using a simple conservative approach, one should analyze the ideal MHD energy principle for incompressible displacements.

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U2 - 10.1063/1.3535587

DO - 10.1063/1.3535587

M3 - Article

VL - 18

JO - Physics of Plasmas

JF - Physics of Plasmas

SN - 1070-664X

IS - 1

M1 - 012505

ER -