Spatial Singularities of the Ideal MHD Continuum Modes
Abstract
The spatial singularities that characterize the ideal MHD continuum modes of a nonaxisymmetric toroidal plasma with closed nested magnetic surfaces ψ(r) = const are explored. It was recently reported that in axisymmetric toroidal geometry, the component of the plasma velocity normal to the magnetic surfaces v_ψ generally has an essential singularity (ψ-ψ_0)^iμ, where μ is a real number, about the resonant surface ψ = ψ0 rather than a logarithm.^1 The logarithmic singularity appears only if certain spatial symmetries exist in the plasma equilibrium or wave modes. In the present study, the analysis of Ref. 1 is extended to a nonaxisymmetric toroidal plasma with zero pressure. The continuum frequencies in this case are governed by a second order magnetic differential equation with quasiperiodic coefficients along the magnetic lines. The number of linearly independent quasiperiodic solutions of this equation influences the singularity. It is found that an essential singularity v_ψ ~ (ψ-ψ_0)^iμ generally characterizes the continuum modes provided that the toroidal asymmetry of the equilibrium is not too strong. [1pt] Supported in part by the U.S. DOE under grant No. DE-FG02-97ER54398. [1pt] 1. A. Salat and J.A. Tataronis, Phys. Plasmas, to appear (1999).
- Publication:
-
APS Division of Plasma Physics Meeting Abstracts
- Pub Date:
- November 1999
- Bibcode:
- 1999APS..DPP.CP199S