Magnetohydrodynamic stability comparison theorems revisited

Journal Article · Sat Jan 15 04:00:00 EST 2011 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.3535587· OSTI ID:21532176

Cerfon, Antoine J; Freidberg, Jeffrey P ^[1]

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1. Plasma Science and Fusion Center, Massachusetts Institute of Technology, 167 Albany Street, Cambridge, Massachusetts 02139 (United States)

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 ExB 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.

• OSTI ID: 21532176
• Journal Information: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 1 Vol. 18; ISSN PHPAEN; ISSN 1070-664X
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
BOLTZMANN-VLASOV EQUATION
DIFFERENTIAL EQUATIONS
DRIFT INSTABILITY
EQUATIONS
FLUID MECHANICS
HYDRODYNAMICS
INSTABILITY
MAGNETOHYDRODYNAMICS
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
PLASMA INSTABILITY
PLASMA MICROINSTABILITIES
STABILITY