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A formalism for the construction of energy principles for dissipative systems is presented. It is shown that dissipative systems satisfy a conservation law for the bilinear Hamiltonian provided the Lagrangian is time invariant. The energy on the other hand , differs from the Hamiltonian by being quadratic and by having a negative definite time derivative (positive power dissipation). The energy is Lyapunov functional whose definiteness yields necessary and sufficient stability criteria. The stability problem of resistive magnetohydrodynamic MHD is addressed: the energy principle for ideal MHD is generalized and the stability criterion by Tasso is shown to be necessary in addition to sufficient for real growth rates. An energy principle is found for the inner layer equations that yields the resistive stability criterion D(R) is less then 0 in the incompressible limit, whereas the tearing mode criterion Delta' is less than 0 is shown to result from the conservation law of the bilinear concomitant in the resistive layer.

Additional information

Authors: PLETZER A, Centre de Recherches en Physique des Plasmas, Ecole Polytechnique de Lausanne (CH)
Bibliographic Reference: Article: Physics of Plasmas (1997)
Record Number: 199710654 / Last updated on: 1997-06-09
Original language: en
Available languages: en