Particle dynamics in nonlinear electromagnetic waves: chaos onset, diffusive heating, and wave surfing

Abstract

We investigate the dynamics of charged particles interacting with ultra-intense electromagnetic X-modes in strongly magnetized plasmas. We demonstrate that particle motion becomes chaotic for relative wave intensities $\delta = B_w/B_0 \gtrsim 0.25$ (not above the field reversal threshold $\delta \geq 1$). The transition to chaos occurs via the Chirikov resonance overlap mechanism and the related destruction of Kolmogorov-Arnold-Moser (KAM) tori. The maximum Lyapunov exponent increases logarithmically with $\delta$, even though the unmagnetized $\delta \to \infty$ limit is strictly integrable. In the $\delta \gg 1$ regime, incomplete re-laminarization of the phase space flow leads to two distinct populations: (i) the majority of particles undergoing stochastic diffusion, and (ii) a fraction of particles that become phase-locked with the wave, experiencing macroscopic intermittent surfing (L\'evy flights). The 1D Particle-In-Cell simulations using the EPOCH code in the highly magnetized ($\sigma \gg 1$) and under-dense regime are generally consistent with the Hamiltonian single-particle theory. The dissipation fraction of the initial EM energy remains mild.