On the existence and uniqueness of dissipative plasma equilibria in a toroidal domain
A one-fluid, dissipative magnetohydrodynamic model of plasma equilibrium in a torus is considered. The equations include inertial forces, finite resistivity and viscosity, and a particle source which sustains the pressure gradient in the plasma. Viscosity is described by the Braginskii operator. Plasma density, resistivity and viscosity coefficents are assumed to be uniform. A boundary-value problem in a general toroidal domain is formulated, no further assumption on the domain being made besides a sufficient regularity of its boundary. A functional setting of the equations is established and a problem for weak solutions is formulated, which is shown to be equivalent to solving a nonlinear equation in a separable Hilbert space. Then, by analysing the Braginskii viscosity in the established functional framework, properties are found which make it possible to write the above equation as a fixed-point equation. The main results of the analysis are presented.
Bibliographic Reference: Report: IPP 2/312 EN (1991) 26 pp.
Availability: Available from Max-Planck-Institut für Plasmaphysik, 8046 Garching bei München (DE)
Record Number: 199111296 / Last updated on: 1994-12-02
Original language: en
Available languages: en