Nonlocal adiabatic theory. I. The action distribution function

Abstract

In this paper, we address the motion of charged particles acted upon by a sinusoidal electrostatic wave, whose amplitude and phase velocity vary slowly enough in time for neo-adiabatic theory to apply. Moreover, we restrict to the situation when only few separatrix crossings have occurred, so that the adiabatic invariant, $\mathcal{I}$, remains nearly constant. We insist here on the fact that $\mathcal{I}$ is different from the dynamical action, $I$. In particular, we show that $\mathcal{I}$ depends on the whole time history of the wave variations, while the action is usually defined as a local function of the wave amplitude and phase velocity. Moreover, we provide several numerical results showing how the action distribution function, $f(I)$, varies with time, and we explain how to derive it analytically. The derivation is then generalized to the situation when the wave is weakly inhomogeneous.

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Cited by in corpus (1)

• Self-consistent theory for the linear and nonlinear propagation of a sinusoidal electron plasma wave. Application to stimulated Raman scattering in a non-uniform and non-stationary plasma