Nonresonant Charged-Particle Acceleration by Electrostatic Waves Propagating across Fluctuating Magnetic Field

In this Letter, we demonstrate the effect of nonresonant charged-particle acceleration by an electrostatic wave propagating across the background magnetic field. We show that in the absence of resonance (i.e., when particle velocities are much smaller than the wave phase velocity) particles can be accelerated by electrostatic waves provided that the adiabaticity of particle motion is destroyed by magnetic field fluctuations. Thus, in a system with stochastic particle dynamics the electrostatic wave should be damped even in the absence of Landau resonance. The proposed mechanism is responsible for the acceleration of particles that cannot be accelerated via resonant wave-particle interactions. Simplicity of this straightforward acceleration scenario indicates a wide range of possible applications.

Figure 1

Schematic view of the system: (a) with the resonant wave-particle interaction, (b) without a resonant interaction, and (c) without a resonant interaction but with magnetic field fluctuations. Particle velocity and energy are shown for two periods of gyrorotation around the background magnetic field $2\pi /{\mathrm{\Omega }}_0$.

Figure 2

Five examples of particle trajectories in the momentum space for different amplitudes of magnetic field fluctuations, electrostatic wave, and induction electric field: (a) $ϵ=2$, $\delta =0$, $v_{\varphi }=0$; (b) $ϵ=2$, $\delta =2.5$, $v_{\varphi }=0$; (c) $ϵ=2$, $\delta =5.0$, $v_{\varphi }=0$; (d) $ϵ=0$, $\delta =2.5$, $v_{\varphi }=0.005c$; (e) $ϵ=2$, $\delta =2.5$, $v_{\varphi }=0.005c$. The corresponding profiles of the particle energy are shown in the bottom panels. Wave frequency is $\omega /{\mathrm{\Omega }}_0=100$, while the initial particle energy is $\gamma =1.5$. The resonant value of momentum $p_y/mc$ is $(\omega /kc)/\sqrt{1-(\omega /kc{)}^2}\approx 7.5$ (i.e., all five examples correspond to the nonresonant interaction).

Figure 3

Five examples of the averaged energy time profiles for particle ensembles ($10^4$ particles). System parameters are the same as in Fig. 2.

Figure 4

An example of the particle trajectory containing two acceleration regimes: the nonresonant acceleration precedes the resonant surfatron trapping. System parameters are the same as for Fig. 2, but $ϵ=10$, $\delta =2.5$, $v_{\varphi }=0$.