Relativistic acceleration of Landau resonant particles as a consequence of Hopf bifurcations

TL;DR

This paper demonstrates that relativistic particle acceleration occurs via Hopf bifurcations in a dynamical system, leading to efficient energization of electrons from keV to MeV energies in space plasmas.

Contribution

It introduces a bifurcation-based mechanism for relativistic acceleration of Landau resonant particles, linking Hopf bifurcations to particle energization in plasma physics.

Findings

Electrons can be accelerated from keV to MeV energies within milliseconds.

Hopf bifurcations enable uniform acceleration through wave-particle locking.

The mechanism explains efficient particle energization in space and astrophysical plasmas.

Abstract

Using bifurcation theory on a dynamical system simulating the interaction of a particle with an obliquely propagating wave in relativistic regimes, we demonstrate that uniform acceleration arises as a consequence of Hopf bifurcations of Landau resonant particles. The acceleration process arises as a form of surfatron established through the locking in pitch angle, gyrophase, and physical trapping along the wave-vector direction. Integrating the dynamical system for large amplitudes ($\delta B/B_0\sim0.1$) obliquely propagating waves, we find that electrons with initial energies in the keV range can be accelerated to MeV energies on timescales of the order of milliseconds. The Hopf condition of Landau resonant particles could underlie some of the most efficient energization of particles in space and astrophysical plasmas.