LYAPUNOV'S STABILITY CRITERIA FOR PLASMAS
The orbit stability theory of Lyapunov was adapted to the Vlasov- Boltzmann equation governing plasmas. Both linear and nonlinear stability are considered. The theory is characterized by a search for Lyapunov functions, whose existence implies stability in analogy with particles trapped in a potential well, as in the energy principle. The most important result is an existence theorem for Lyapunov functions quadratic in perturbations in all linearly stable cases in which perturbations damp asymptotically. As a corollary, without damping, the existence of a quadratic Lyapunov function is necessary and sufficient to prevent exponential growth of perturbations. A prescription is given for finding Lyapunov functions that are constants of motion. An example is treated. The implication of nonlinear stability from linear stability with damping is discussed, and a direct proof of nonlinear stability of a Maxwellian plasma by Lyapunov's method is reported. (auth)
- Research Organization:
- Oak Ridge National Lab., Tenn.
- Sponsoring Organization:
- USDOE
- NSA Number:
- NSA-17-024584
- OSTI ID:
- 4717131
- Journal Information:
- Journal of Mathematical Physics (New York) (U.S.), Journal Name: Journal of Mathematical Physics (New York) (U.S.) Vol. Vol: 4; ISSN JMAPA
- Country of Publication:
- Country unknown/Code not available
- Language:
- English
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