Trapping scaling for bifurcations in Vlasov systems

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.

11 pages, 3 figures. Movies illustrating the numerical simulations available upon request

References in corpus (4)

• Statistical mechanics and dynamics of solvable models with long-range interactions
• Nonlinear response for external field and perturbation in the Vlasov system
• Pattern formation in Hamiltonian systems with continuous spectra; a normal-form single-wave model
• Instability conditions for some periodic BGK waves in the Vlasov-Poisson system

Cited by in corpus (5)

• Collisional relaxation in the inhomogeneous Hamiltonian-Mean-Field model: diffusion coefficients
• Particle number dependence in the non-linear evolution of N-body self-gravitating systems
• Discontinuous codimension-two bifurcation in a Vlasov equation
• Towards a classification of bifurcations in Vlasov equations
• Classification of bifurcation diagrams in coupled phase-oscillator models with asymmetric natural frequency distributions