Parallel Collisionless Shocks in strongly Magnetized Electron-Ion Plasma. I. Temperature anisotropies

TL;DR

This study investigates how strong ambient magnetic fields modify parallel collisionless shocks in electron–ion plasmas by varying the ion magnetization parameter $\sigma_i$ in 1D3V PIC simulations with a realistic mass ratio. It finds that $\sigma_i \geq 1$ drives a low compression ratio $R \sim 2$, preserves perpendicular temperatures, and suppresses particle acceleration, while ions experience substantial parallel heating and large temperature anisotropy without triggering instabilities; electrons thermalize rapidly downstream, and supra-thermal populations emerge only in weakly magnetized cases. The work demonstrates clear deviations from ideal MHD predictions in strongly magnetized shocks and provides kinetic insights into the role of magnetic fields in shaping shock structure, anisotropy stability, and energy partition in astrophysical settings. These results have implications for understanding cosmic-ray acceleration and the magnetic-field-modulated dynamics of collisionless shocks in high-field environments.

Abstract

Collisionless electron-ion shocks are fundamental to astrophysical plasmas, yet their behavior in strong magnetic fields remains poorly understood. Using Particle-in-Cell (PIC) simulations with the SHARP-1D3V code, we investigate the role of the ion magnetization parameter $σ_i$ in parallel shock transitions. Strongly magnetized converging flows ($σ_i > 1$) exhibit lower density compression ratios ($R \sim 2$), smaller entropy jumps, and suppressed particle acceleration, while maintaining pressure anisotropy stability due to conserved perpendicular temperatures across the transition region, alongside increased parallel temperatures. In contrast, weakly magnetized shocks drive downstream mirror and firehose instabilities due to ion temperature anisotropy, which are suppressed in strongly magnetized cases. Additionally, weakly magnetized shocks exhibit the onset of a supra-thermal population induced by shock-drift acceleration, with most of the upstream kinetic energy thermalized for both electrons and ions in the downstream region. Our results demonstrate that perpendicular temperatures for both species are conserved in weakly and strongly magnetized cases and highlight deviations from standard ideal magnetohydrodynamic (MHD) behavior in strongly magnetized cases. These findings provide critical insights into the role of magnetic fields in parallel collisionless astrophysical shocks.

Figures (6)

• Figure 1: The spatial distribution of the number density (electron+ions) in various simulations at $t \omega_i = 9400$. This shows that for values of $\sigma_i^{\prime} > 4$ the compression ratio $R=n/n_0$ drops to $R \sim 2$ mean while it is $R>2$ for smaller values of $\sigma_i^{\prime}$. Dashed lines for each simulation represent the function in Equation \ref{['Eq:ndenjump']} using the best fit values of $R, \lambda_{\rm sh}$, and $x_{\rm sh}$ to number density profile. When plotting the density profile in simulations (solid lines) we filter all fluctuations on scales smaller than $4c/\omega_i$ using a moving average filter. The gray-shaded regions, which extend over about $115\,c/\omega_i$, define the regions where we compute the numerical entropy density in simulations (Figure \ref{['Fig:R_S']}, bottom panel).
• Figure 2: Top panel shows the dependence of the shock compression ration, $R$ on the value os $\sigma_i$. Bottom panel shows the entropy jump between upstream and downstream regions highlighted with gray regions in Figure\ref{['Fig:nden']}, i.e., $\Delta s = s_{\rm downstream} - s_{\rm upstream}$. In the bottom panel, dashed red (black) curves shows the entropy jump for ions (electrons) in various simulations. This is shown at $t \omega_i = 9400$, the same time used in Figure \ref{['Fig:nden']}.
• Figure 3: Electrons phase-space distribution in various simulations at $t \omega_i = 9400$ (the same time used in Figure \ref{['Fig:nden']}). The left panels show the spatial profile of parallel momenta, i.e., $f(u_x, x)$, while the right panels show that of perpendicular (y-component) momenta, i.e., $f(u_y, x)$.
• Figure 4: Ion phase-space distribution in various simulations at $t \omega_i = 9400$ (the same time used in Figure \ref{['Fig:nden']}). The left panels show the spatial profile of parallel momenta, i.e., $f(u_x, x)$, while the right panels show that of perpendicular (y-component) momenta, i.e., $f(u_y, x)$.
• Figure 5: The spatial profiles for parallel (top) and perpendicular (y-component; bottom) temperatures in various simulations (color-coded) at $t \omega_i = 9400$ (the same time used in Figure \ref{['Fig:nden']}). In all cases, the ion temperature is represented by dashed curves, while the electron temperature is represented by solid curves with dots indicating the locations of bin centers where these temperatures are computed, and we use an equally spaced bins that extend over $40\,c/\omega_i$.