Global change in action due to trapping: How to derive it whatever the rate of variation of the dynamics

Sideband growth rates for differentiable and discontinuous distribution functions

This article addresses the stability of a nonlinear electron plasma wave (EPW) against the growth of longitudinal sidebands. The electron distribution function consistent with the EPW is assumed to only depend on the dynamical action. Consequently, the EPW is either stationary (a so-called Berstein-Greene-Kruskal mode) or varies very slowly in space and time (a so-called adiabatic wave). The sideband growth rates and the unstable spectrum are calculated theoretically by accounting for the exact nonlinear electron orbits in the EPW. Our theoretical results are compared against those from previous theories, and also against those from Vlasov simulations when the distribution function is differentiable. The latter comparisons show that our theory may also apply when the electron distribution function depends on, both the action and the angle. Moreover, our theory allows for discontinuous distributions, which are consistent with important classes of EPWs, e.g., those resulting from stimulated Raman scattering. Addressing such distributions using kinetic codes remains a challenge. Nevertheless, using our theoretical results, in this article we discuss the impact of discontinuities on the unstable spectrum in the linear regime, and on the range of validity of the linear approximation.

Open system control of dynamical transitions under the generalized Kruskal-Neishtadt-Henrard theorem

Useful dynamical processes often begin through barrier-crossing dynamical transitions; engineering system dynamics in order to make such transitions reliable is therefore an important task for biological or artificial microscopic machinery. Here, we first show by example that adding even a small amount of back-reaction to a control parameter, so that it responds to the system's evolution, can significantly increase the fraction of trajectories that cross a separatrix. We then explain how a post-adiabatic theorem due to Neishtadt can quantitatively describe this kind of enhancement without having to solve the equations of motion, allowing systematic understanding and design of a class of self-controlling dynamical systems.

Full self-consistent Vlasov-Maxwell solution

Full self-consistent stationary Vlasov-Maxwell solutions of magnetically confined plasmas are built for systems with cylindrical symmetries. The stationary solutions are thermodynamic equilibrium solutions. These are obtained by computing the equilibrium distribution function resulting from maximizing the entropy and closing the equations with source terms that are then computed by using the obtained distribution. This leads to a self-consistent problem corresponding to solving a set of two coupled second order nonlinear differential equations. Relevant plasma parameters are introduced and a bifurcation leading to an improvement of plasma confinement is shown. Conversely, in the improved confinement setting, we exhibit the emergence of a separatrix in the integrable motion of a charged particle .