Trapping scaling for bifurcations in Vlasov systems

TL;DR

This paper investigates bifurcations in Vlasov systems, revealing how resonances are suppressed and initial conditions influence whether instabilities saturate or grow, with implications for plasma and galactic models.

Contribution

It introduces a trapping scaling framework for bifurcations in Vlasov systems, highlighting the role of initial perturbations and resonance suppression.

Findings

Resonances are strongly suppressed in non homogeneous Vlasov bifurcations.

The instability can either saturate at small amplitude or grow large, depending on initial conditions.

Numerical simulations confirm the analytical predictions.

Abstract

We study non oscillating bifurcations of non homogeneous steady states of the Vlasov equation, a situation occurring in galactic models, or for Bernstein-Greene-Kruskal modes in plasma physics. We show that resonances are strongly suppressed, leading to very different phenomena with respect to the homogeneous case. Through an unstable manifold expansion, we show that the dynamics is very sensitive to the initial perturbation: the instability may saturate at small amplitude -generalizing the "trapping scaling" of plasma physics- or may grow to produce a large scale modification of the system. These analytical findings are illustrated and extended by direct numerical simulations with a cosine interaction potential.