Nonlinear Amplification and Decay of Phase-mixed Waves in Compressing Plasma

Abstract

Through particle-in-cell simulations, we show that plasma waves carrying trapped electrons can be amplified manyfold via compressing plasma perpendicularly to the wave vector. These simulations are the first ab initio demonstration of the conservation of nonlinear action for such waves, which contains a term independent of the field amplitude. In agreement with the theory, the maximum of amplification gain is determined by the total initial energy of the trapped-particle average motion but otherwise is insensitive to the particle distribution. Further compression destroys the wave; electrons are then untrapped at suprathermal energies and form a residual beam. As compression continues, the bump-on-tail instability is triggered each time one of the discrete modes comes in resonance with this beam. Hence, periodic bursts of the electrostatic energy are produced until a wide quasilinear plateau is formed.

On Variational Methods In the Physics of Plasma Waves

“…Some supplementary calculations are included as appendixes. Extension of the (largely known previously, but reworked) results that are presented in this paper can also be found in the aforementioned references [2,[17][18][19][20][21] and publications cited therein.…”

“…The presentation is based on the results reported in Refs. [2,[17][18][19][20][21] and some earlier publications [22] and shows how a practical, albeit approximate, wave Lagrangian is constructed explicitly and concisely. As it turns out, the problem can be reduced to finding the so-called oscillation-center (OC) energies of individual particles in a strictly periodic field, and that is readily done by a quadrature both for passing and trapped trajectories.…”

“…This is a valid assumption for certain scenarios of WTP formation that produce deeply-trapped distributions (see, e.g., Refs. [20,43]). …”

“…Consider a WTP in a plasma undergoing compression transverse to the wave vector [20]. (For WTP parallel compression, see Ref.…”

“…Note that surveying the (prohibitively extensive) relevant literature, especially of applied nature, is deliberately withheld here, as dictated by the format of this work. For historical background and applications, one is instead referred to the preceding papers [2,[17][18][19][20][21] and Ref. [24], where related theories are also reviewed more formally.…”