Counter-Streaming Beams in Collisionless Pair Plasma Instability Systems II: Spectral Cone and Spectral Wave Mode Analysis

TL;DR

The paper investigates the spectral structure of collisionless WI/TSI in counter-streaming $e^t$ pair plasmas using PIC simulations and spectral-cone analysis. Building on Paper I, it emphasizes electrostatic wave modes and their coupling to the dominant electromagnetic mode, tracking how filamentation, saturation, and mergers shape the spectrum across multiple parameter sets (S1–S4). The study reveals two persistent spectral modes (high- and low-frequency) and demonstrates that the emergent electrostatic TSI radiates energy away from the EM wave, linking spectral signatures to filament dynamics and energy redistribution. These insights advance understanding of radio to gamma-ray signatures in relativistic shocks and inform radiation mechanisms in high-energy astrophysical plasmas.

Abstract

Energetic astrophysical phenomena, such as $γ$-ray bursts, supernova explosions, and magnetar flares occur in collisionless plasmas and involve various plasma kinetic and magnetohydrodynamic instabilities. In this paper, we explore the spectral trends of the Weibel instability using spectral analysis of particle-in-cell simulations. Power dependence on viewing angle and frequency are explored and the relation to the results of the first paper in this series is discussed.

Figures (36)

• Figure 1: Illustration of a "cone" in the $k_x, k_y$ box. The box itself represents $\pi/2$ radians.
• Figure 2: A dual plotting of the total wave power $P_{Tot}(\omega_p t) = \int P(\omega) d\omega$ of both non- and wave-like perturbations of the wave amplitudes (blue) and the magnetic energy density (orange) of the simulations. The major events and characteristic times scales are visible in each panel. Each panel is a different simulation data set with the top left being the fiducial simulation (S$1$), top right the lower beam speed (S$2$), bottom left the higher density (S$3$), and bottom right the low skin depth (S$4$).
• Figure 3: All of the non-wave-like perturbation (NWL - Green) and wave-like perturbation (WL - Red) spectral signals in cones for the magnetic field for each $\omega$ frequency in each epoch are summed and plotted for $S1$ for $B_z$. While small behaviors cannot be seen from this wide view, the overall behavior of the system can be viewed as a whole and various relationships derived, much like the physical field power evolution.
• Figure 4: All of the non-wave-like perturbation (NWL - Green) and wave-like perturbation (WL - Red) spectral signals in cones for $E_x$ (solid) and $E_y$ (dashed) for each $\omega$ frequency in each epoch are summed and plotted for $S1$. These fields overlap, displaying only two trend lines. The control simulation sees all three component fields follow the same basic trends as each other.
• Figure 5: All of the non-wave-like perturbation (NWL - Green) and wave-like perturbation (WL - Red) spectral signals in cones for the magnetic field for each $\omega$ frequency in each epoch are summed and plotted for $S2$. The signal in the low beam speed shows evidence of the signal trending the same as $S1$, but slower (later) in the simulation, while also being smoother. The peak representing filament merger is comparable to $S1$ with the background spectral power being weaker than $S1$ due to beam velocity. The signal corresponding to filament merger is also much later in the simulation (epoch 9/10).