MHD Field Line Resonances and Global Modes in Three-Dimensional Magnetic Fields

Technical Report · Thu May 30 04:00:00 EDT 2002

DOI:https://doi.org/10.2172/798182· OSTI ID:798182

Cheng, C Z ^[1]

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1. Princeton Plasma Physics Laboratory

By assuming a general isotropic pressure distribution P = P (y,a), where y and a are three-dimensional scalar functions labeling the field lines with B = -y x -a, we have derived a set of MHD eigenmode equations for both global MHD modes and field line resonances (FLR). Past MHD theories are restricted to isotropic pressures with P = P (y only). The present formulation also allows the plasma mass density to vary along the field line. The linearized ideal-MHD equations are cast into a set of global differential equations from which the field line resonance equations of the shear Alfvin waves and slow magnetosonic modes are naturally obtained for general three-dimensional magnetic field geometries with flux surfaces. Several new terms associated with the partial derivative of P with respect to alpha are obtained. In the FLR equations, a new term is found in the shear Alfvin FLR equation due to the geodesic curvature and the pressure gradient in the poloidal flux surface. The coupling between the shear Alfvin waves and the magnetosonic waves is through the combined effects of geodesic magnetic field curvature and plasma pressure as previously derived. The properties of the FLR eigenfunctions at the resonance field lines are investigated, and the behavior of the FLR wave solutions near the FLR surface are derived. Numerical solutions of the FLR equations for three-dimensional magnetospheric fields in equilibrium with high plasma pressure will be presented in a future publication.

• Research Organization: Princeton Plasma Physics Lab., NJ (US)
• Sponsoring Organization: USDOE Office of Science (US)
• DOE Contract Number: AC02-76CH03073
• OSTI ID: 798182
• Report Number(s): PPPL-3696.pdf
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
DIFFERENTIAL EQUATIONS
EIGENFUNCTIONS
MAGNETIC FIELDS
MAGNETOACOUSTIC WAVES
MAGNETOHYDRODYNAMICS
NUMERICAL SOLUTION
PLASMA PRESSURE
PRESSURE GRADIENTS
RESONANCE