Kinetic Scale Energy Budget in Turbulent Plasmas: Role of Electron to Ion Temperature Ratio

TL;DR

This work analyzes energy dissipation in kinetic-scale turbulence of weakly collisional plasmas using scale-filtered Vlasov-Maxwell equations and fully kinetic PIC simulations across varying electron-to-ion temperature ratios $T_e/T_i$. It shows that the scale-filtered pressure-strain interaction, dominated by the shear part of Pi-D, accounts for energy transfer at kinetic scales, with the normal Pi-D component anticorrelated to maintain a balanced budget. The amplitudes of the anisotropic Pi-D terms scale with the temperatures of each species and inversely with the temperature of the other, while pressure dilatation remains subdominant but becomes more compressible as temperatures decrease. These findings imply that thermal disequilibrium governs which species dominates kinetic-scale energy transfer and have implications for energy dissipation in environments like the magnetosheath and solar wind; future work should explore broader parameter regimes and 3D effects.

Abstract

The dissipation mechanisms in weakly collisional plasmas have been a longstanding topic of investigation, where significant progress has been made in recent years. A recent promising development is the use of the "scale-filtered" Vlasov-Maxwell equations to fully quantify the scale-by-scale energy balance, a feature that was absent when using fluid models in kinetic plasmas. In particular, this method reveals that the energy transfer in kinetic scales is fully accounted for by the scale-filtered pressure-strain interaction. Despite this progress, the influence of ion-electron thermal disequilibrium on the kinetic-scale energy budget remains poorly understood. Using two-dimensional fully kinetic particle-in-cell simulations of decaying plasma turbulence, we systematically investigate the pressure-strain interaction and its components at sub-ion scales by varying electron-to-ion temperature ratios. Our analysis focuses on three key ingredients of the pressure-strain interaction: the normal and shear components of Pi-D and pressure dilatation. Our results demonstrate that the scale-filtered pressure-strain interaction is dominated by scale-filtered Pi-D across the kinetic range, with the shear component consistently providing the dominant contribution. We find that the scale-filtered normal and shear contributions of Pi-D exhibit persistent anticorrelation and opposite signs across all kinetic scales. We also discover that the amplitude of both anisotropic components for each species scales directly with their temperature and inversely with the temperature of the other species, while the scale-filtered pressure dilatation remains negligible compared to the Pi-D terms but shows enhanced compressibility effects as plasma temperatures decrease. We discuss the implications of these findings in thermally non-equilibrated plasmas, such as in the turbulent magnetosheath and solar wind.

Figures (6)

• Figure 1: Idealized schematic plot of different terms of the scale filtered energy transfer equation (Eqn. \ref{['eqn:symbolic']}) versus filtering width $\ell$. Each term (shown on top) is normalized to the total dissipation rate $\epsilon$, and different ranges where they dominate are shown by colored rectangles. Shaded rectangles of color blue, pink, and green represent the kinetic, inertial, and correlation range, respectively. Representative values of the correlation scale $\lambda_c$ and the Kolmogorov scale $\lambda_d$ are shown.
• Figure 2: A comparison of time evolution of scale-filtered domain averaged $\langle \overline{Pi}-\tilde{D}_{normal} \rangle$ for ions in panels (a)-(e) and electrons in panels (f)-(j) as a function of lag $\ell$ in systems with different electron to ion temperature ratios. A dashed line at $d_i$ and a green solid line at $d_e$ are drawn for reference.
• Figure 3: A comparison of time evolution of scale-filtered domain averaged $\langle Pi-D_{shear} \rangle$ for ions in panels (a)-(e) and electrons in panels (f)-(j) as a function of lag $\ell$. A dashed line at $d_i$ and a green solid line at $d_e$ are drawn for reference. Note that the colorbar is different than the one in Fig. \ref{['fig:pidnormal_final']} (See text for details).
• Figure 4: A comparison of time evolution of scale-filtered domain averaged $\langle \overline{p}\tilde{\theta} \rangle$ for ions in panels (a)-(e) and electrons in panels (f)-(j) as a function of lag $\ell$. A dashed line at $d_i$ and a green solid line at $d_e$ are drawn for reference.
• Figure 5: Comparison of the scale dependence of ingredients of ion pressure-strain interaction: (a) $\langle \overline{Pi}-\tilde{D}_{normal} \rangle$, (b) $\langle \overline{Pi}-\tilde{D}_{shear} \rangle$ and (c) pressure dilatation $\langle \overline{p} \tilde{\theta} \rangle$ for cases with different electron to ion temperature ratio.