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.

Variational principles for dissipative (sub)systems, with applications to the theory of linear dispersion and geometrical optics

“…The advantages of VM become especially obvious when one deals with media such as plasmas, which can be nonstationary, inhomogeneous, anisotropic, and exhibit both temporal and spatial dispersion simultaneously [12][13][14][15][16][17][18]. First-principle differential equations are often unrealistic to handle in this case, whereas VM allow for simple and intuitive modeling.…”

“…If the medium response is adiabatic (e.g., if ξ[q] can be approximated with a local function), an effective LAP for q can be formulated simply as δA[q, ξ[q]] = 0, as will also be discussed below. This principle has enjoyed insightful applications, e.g., in the theory of generalized ponderomotive forces [16][17][18] and nonlinear plasma waves [12][13][14][15]. However, when the medium response is not adiabatic, the dynamics of q becomes dissipative.…”

“…Equations (15) and (16) are second-order equations for q(t) and ξ(t), so the mentioned BC provide just enough parameters to define a solution.…”

“…Although Eqs. (15) and (16) form a self-consistent system, it is also convenient to approach Eq. (16) formally as if q were as a prescribed function.…”

“…( 18) vanishes. In this case, by requiring that A is extremized, one arrives at the correct equation (15). However, such choice of C is inconvenient.…”