Negative-energy modes in collisionless kinetic theories and their possible relation to nonlinear instabilities
To explain anomalous transport, it may be necessary to take nonlinear instabilities into account. Such instabilities can exist even for arbitrarily small initial amplitudes, if the system possesses linear negative-energy modes. After reformulating Cherry's oscillator example, which allows a simple physical interpretation of the nonlinear instabilities and shows the relation to continuum theories such as the Maxwell-Vlasov theory, the question of how to obtain energy expressions for various linearised theories is discussed. The known energy expressions are in general rather impractical. Two new methods are described that yield energy expressions which can be used similarly to the potential energy deltaW in ideal MHD. The simpler one allows the energy of the linearised Maxwell-Vlasov theory to be obtained; the more complicated one can be applied to any Maxwell-collisionless kinetic theory and even yields the whole energy-momentum and angular momentum tensors. The latter method is used to treat the collisionless drift kinetic theory. Only the main points of this treatment are presented. Some general results are derived for the Maxwell-Vlasov theory in the form of examples. For one example, a comparison between the Maxwell-Vlasov and the Maxwell-drift kinetic theories is made.
Bibliographic Reference: Report: IPP 6/299 EN (1991) 34 pp.
Availability: Available from Max-Planck-Institut für Plasmaphysik, 8046 Garching bei München (DE)
Record Number: 199111295 / Last updated on: 1994-12-02
Original language: en
Available languages: en