Relativistic multistage resonant and trailing-field acceleration induced by large-amplitude Alfvén waves in a strong magnetic field

TL;DR

This work addresses how electrons can achieve highly relativistic energies in strongly magnetized plasmas through Alfvén-wave–driven acceleration. The authors introduce a multistage mechanism—counter-propagating wave-particle resonant acceleration (CWRA) initiated by decay instability, followed by modulational instability that creates $E_{ ext{mod}}$ and enables gyroresonant surfing acceleration (GRSA), then single-wave resonant acceleration (SWRA) as particles trap in the parent wave, with electrostatic trailing-field acceleration (TFA) augmenting energy gain. They validate the sequence with a 1D PIC simulation, showing that supercritical wave amplitudes ($b_w$ above a critical value $\approx 0.685$) drive CWRA and lead to GRSA and SWRA, achieving $\gamma_e$ up to $\sim 2.8\times 10^{3}$, while subcritical amplitudes yield modest energies; a monochromatic-wave analysis in the wave frame supports the resonance geometry and trapping dynamics that underpin the multistage process. The results offer a plausible pathway for generating high-energy cosmic-ray–like electrons in astrophysical environments and motivate further work on radiation losses, multidimensional effects, and realistic wave properties to refine energy limits and observational relevance.

Abstract

We propose a particle acceleration mechanism driven by large-amplitude Alfvén waves in a strong magnetic field. The acceleration process proceeds through multiple stages triggered by counterpropagating wave-particle resonant acceleration (CWRA) via decay instability. Initially, parent and daughter Alfvén waves resonantly accelerate particles perpendicular to the ambient magnetic field. The resultant modulational instability generates electrostatic fields within the wave packet, which are locally amplified by the ponderomotive force of the Alfvén wave packet. These fields subsequently drive further acceleration within a few relativistic gyroperiods via gyroresonant surfing acceleration (GRSA). During this, the v*B force facilitates momentum transfer from the perpendicular to the parallel direction. In the later stage, particles become trapped by the parent wave and gain additional energy through single wave resonant acceleration (SWRA). Furthermore, the accumulation of accelerated particles induces electrostatic trailing fields behind and at the tail of the wave packet, which drive trailing-field acceleration (TFA) of other electrons. The combined effects of these mechanisms, CWRA followed by GRSA and SWRA, result in highly relativistic electron energy. The electron energy accelerated through the above process is higher than that accelerated through TFA. This multistage acceleration process provides insights into the generation of high energy cosmic rays in astrophysical environments.

Figures (7)

• Figure 1: Results when the wave amplitude is supercritical $b_{w}=B_{w}/B_{0}=0.8$, where $B_{0}$ is the strength of the background magnetic field. Spatial profiles of the normalized wave magnetic field $b_{z}=eB_{z}/m_{e}\omega_{pe}$ (gray), the wave envelop $b_{\perp}=\sqrt{b_{y}^{2}+b_{z}^{2}}$ (black), the electrostatic field $e_{x}\times5=eE_{x}/m_{e}c\omega_{pe}\times5$ (magenta) and electron's perpendicular momentum ($p_{e\perp}$: blue dots) and energy ($\gamma_{e}$: red dots) are shown at (a) $\omega_{pe}t=0$, (b) $\omega_{pe}t=38$, (c) $\omega_{pe}t=98$ and (d) $\omega_{pe}t=215$. The large amplitude modulational electrostatic field ($E_{\text{mod}}$)
• Figure 2: Temporal evolution of $E_{x,\text{max}}$ for the cases of a Gaussian envelope and a plane wave.
• Figure 3: Temporal profiles of the energy gain from the $E_{x}$ ($\epsilon_{x}$) (green), $E_{y}$ ($\epsilon_{y}$) (gray), and $E_{z}$ ($\epsilon_{z}$) (blue) components, along with the total energy $\gamma_{e}$ (black) with logarithmic scale, for the three colored electrons; (a) green, (b) yellow, and (c) cyan, corresponding to Fig. \ref{['fig1']}. Each time region separated by the gray dotted line indicates a different acceleration process, namely CWRA, GRSA, SWRA, and TFA. The bottom panels display the trajectories of the (d) green, (e) yellow, and (f) cyan electrons in the $p_{y}-p_{z}$ momentum space, represented by colored lines with a time scale.
• Figure 4: The wave power spectra for (a) the $\hat{b}_{z}$ component and (b) the $\hat{e}_{x}$ component. The spectra in (a) reveal the parent wave (P) and two antiparallel propagating electromagnetic waves ($R_{\text{AD}}$ and $R_{\text{Lb}}$), and modulational wave near the parent wave ($F_{\text{mod}}$)
• Figure 5: The depdendence of the maximum electron energy on the wave amplitude at $\omega_{pe}t=447$. The critical amplitude $b_{\text{cr}}=0.685$ is estimated by $(1-\sqrt{2\nu})/v_{\text{ph}}$Isayama_1.