Electronic Resource
[S.l.]
:
American Institute of Physics (AIP)
Physics of Plasmas
4 (1997), S. 3141-3151
ISSN:
1089-7674
Source:
AIP Digital Archive
Topics:
Physics
Notes:
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 a 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 [Phys. Lett. 147, 28 (1990)] 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 DR〈0 in the incompressible limit, whereas the tearing mode criterion Δ′〈0 is shown to result from the conservation law of the bilinear concomitant in the resistive layer. © 1997 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.872453
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