Nonlinear ideal MHD instabilities
Explosive phenomena such as internal disruptions and flares are difficult to explain in terms of linear instabilities. Like a particle moving in a potential proportional to x3, a plasma approaching a stability limit can be expected to become explosively unstable. Where an initial perturbation is not infinitesimally small, this is true even before the marginal point is reached. To investigate such problems, a nonlinear extension of the energy principle is helpful and was first achieved by Merkel and Schlüter within the framework of Cartesian coordinate systems. Here, an exact coordinate system independent formulation for the Lagrangian is obtained, allowing also equilibria with flow. For vanishing equilibrium flow velocity v(x), the Lagrangian contains the potential energy and quadratic, but no linear, terms in xi representing the kinetic energy. Nonlinear stability is therefore determinable by the potential energy. For potential energies consisting only of second- and nth-order contributions, linearly marginally stable systems are shown to be nonlinearly explosively unstable even with infinitesimally small initial perturbations. Also, linearly absolutely stable systems turn out to be explosively unstable, but finite initial perturbations are needed. For non-vanishing flow velocities, nonlinear instabilities relating to negative-energy modes are possible.
Bibliographic Reference: Report: IPP 6/306 EN (1992) 16 pp.
Availability: Available from Max-Planck-Institut für Plasmaphysik, 8046 Garching bei München (DE)
Record Number: 199210771 / Last updated on: 1994-12-02
Original language: en
Available languages: en