Time-asymptotic amplitude analysis for nonlinear plasma waves
- Univ. of Virginia, Charlottesville, VA (United States)
A fundamental and difficult problem in the kinetic theory of plasmas is the study of wave solutions to the Vlasov- Poisson-Ampere (VPA) system, where E(x,t) is the self-consistent electric field and f{sub {alpha}}(x,v,t) is the distribution function for the species {alpha}. The classic linear analysis of this problem is known to be, in general, not uniformly valid at long times, when the effects of the nonlinear wave-particle interactions become important. Unfortunately, the mathematical analysis of the nonlinear problem is extremely difficult, and very few results are available. To gain new insight into this problem, the author carried out a new nonlinear analysis based on the decomposition E(x,t)=A(x,t)+T(x,t), where T and A are the transient and time-asymptotic parts of the electric field, respectively. In the simplest case, A can be taken to be a single traveling wave, and an approximate solution to the nonlinear Vlasov equation can be obtained by linearizing only the term containing the transient, and then integrating the resulting equation along the nonlinear characteristics of A. This leads, ultimately, to a nonlinear algebraic problem for the time-asymptotic wave amplitude in terms of the amplitude of the initial disturbance. Then, a simple bifurcation analysis establishes the existence of a critical initial amplitude, i.e., a threshold below which the electric field Landau damps to zero and above which it nonlinearly damps through phase mixing to a final state of finite amplitude.
- OSTI ID:
- 426403
- Report Number(s):
- CONF-961103--
- Journal Information:
- Transactions of the American Nuclear Society, Journal Name: Transactions of the American Nuclear Society Vol. 75; ISSN TANSAO; ISSN 0003-018X
- Country of Publication:
- United States
- Language:
- English
Similar Records
Time-asymptotic field amplitudes in nonlinear Landau damping
Plasma waves in Lagrangian coordinates