Time-asymptotic field amplitudes in nonlinear Landau damping
- Univ. of Virginia, Charlottesville, VA (United States)
The behavior of an electrostatic plasma wave of initial amplitude Ei in a collisionless electron plasma depends crucially on the ratio [delta] = [gamma]L/[omega]B, where [gamma]L is the damping coefficient calculated from linear plasma kinetic theory and [omega]B = (ekEi/m)[sup 1/2] is the [open quotes]bounce[close quotes] frequency for trapped electrons. For sufficiently small E[sub i], i.e., [delta] [much gt] 1, the wave damps away completely; conversely, a wave of large initial amplitude, for which [delta] [much lt] 1, saturates at a finite final amplitude due to the nonlinear effects of particle trapping. In this paper, we report results concerning the transition region [delta] [approximately] 0(1), which separates these two regimes. For the case of weak damping, i.e., [vert bar][gamma]L/[omega]p[vert bar][much lt]1, where [omega]p is the plasma frequency, we calculate analytically the critical value [delta][sub i,e] below which complete damping occurs and derive the first explicit analytic relationship between E[sub i] and E[sub f], the time-asymptotic amplitude, for E[sub i] above the critical value E[sub i,c] = (m,ek)([gamma]L/[delta][sub i,c]). The results predict an interesting phenomenon - a finite jump [delta]E in the final field amplitude as E[sub i] is increased through E[sub i,c]. We have corroborated the reality of this phenomenon through large-scale numerical simulations of the Vlasov-Poisson system, carried out using the spectral splitting code of Klimas. These important new results establish a detailed picture of the fundamental transition between linear and nonlinear Landau damping and, in particular, show that the onset of essentially nonlinear behavior occurs very abruptly as the initial wave amplitude increases through its critical value.
- OSTI ID:
- 6904430
- Report Number(s):
- CONF-931160-; CODEN: TANSAO
- Journal Information:
- Transactions of the American Nuclear Society; (United States), Vol. 69; Conference: American Nuclear Society (ANS) winter meeting, San Francisco, CA (United States), 14-18 Nov 1993; ISSN 0003-018X
- Country of Publication:
- United States
- Language:
- English
Similar Records
A kinetic theory of trapped-electron-driven drift wave turbulence in a sheared magnetic field
Collisionless reversed magnetic shear trapped electron instability and contribution of sidebands to anomalous transport