Effects of Unequal Electron-Ion Plasma Beta on Pressure-Strain Interaction in Turbulent Plasmas

TL;DR

This paper addresses how unequal electron–ion temperatures ($T_e \neq T_i$) influence energy conversion in weakly collisional turbulent plasmas. Using five fully kinetic 2.5D PIC simulations of decaying turbulence with varying $T_e/T_i$, the authors decompose the pressure-strain interaction into pressure dilatation and volume-preserving deformation components, ${\rm Pi\!- m D}$, further splitting ${\rm Pi\!- m D}$ into ${\rm Pi\!-D}_{\rm normal}$ and ${\rm Pi\!-D}_{\rm shear}$. They find that the deformation channel dominates the energy transfer, with electron heating mainly sourced by ${\rm Pi\!-D}_{\rm shear}$ localized in $d_e$-scale current sheets between ion-scale eddies, while ion heating is weaker due to strong anti-correlation between ${\rm Pi\!-D}_{\rm shear}$ and ${\rm Pi\!-D}_{\rm normal}$ and a smaller overall deformation amplitude. Lowering either species’ temperature modulates the amplitudes but preserves the qualitative trend, suggesting deformation-driven, species-specific heating that tends to maintain rather than erase the initial temperature imbalance. These results provide a framework for interpreting energy evolution in non-LTE space plasmas and have implications for solar wind, magnetosheath, and accretion-flow environments where unequal species temperatures are common.

Abstract

A common occurrence in weakly collisional space plasmas is the unequal electron-ion temperatures. The pressure-strain interaction provides a mechanism-agnostic pathway for increasing plasma internal energy through spatiotemporally local isotropic compression and volume preserving deformation, yet its behavior under thermal disequilibrium is largely unexplored. We investigate this using five fully kinetic two-dimensional particle-in-cell simulations of undriven decaying turbulence by varying the initial electron-to-ion temperature ratio. By analyzing the species' internal energy density alongside a decomposition of the pressure-strain term, with a focus on the volume-preserving deformation that contains normal and shear contributions, we quantify how the initial temperature imbalance modifies the channels through which turbulence increases each species' internal energy density. The cumulative pressure-strain interaction tracks the change in internal energy for both electrons and ions, with the total deformation channel of energy conversion dominating. We discover that local changes to electron internal energy density are governed primarily by the shear deformation power density, concentrated in electron-scale current sheets, while the ion shear and normal deformation components cancel, yielding a much smaller net deformation power density that peaks around, rather than within, those electron-scale current structures. We find that the amplitudes and localization of deformation change, but preserve these qualitative trends. Together, these results show how thermal disequilibrium could shape species-dependent turbulent "heating rate", measured via pressure-strain interaction and approximated via only its shear deformation part, and provide a framework for interpreting energy evolution and conversion in space plasmas where unequal species temperature is the norm.

Figures (7)

• Figure 1: Mean square current for electrons in red-purple shades and ions in blue-green shades is presented as it evolves in time as a function of initial electron-to-ion temperature. The vertical gray line denotes the time chosen for comparative analysis $t=30\approx 2\tau_{nl}$.
• Figure 2: Change in electrons [panels (a)-(e)] and ions [panels (f)-(j)] internal energy $\Delta \langle \mathcal{E}_{int} \rangle$ (in solid black) is shown for all five simulations and is compared to the cumulative sum of system-averaged pressure-strain interaction (in black dotted), its total deformation part ${\rm Pi-D}$ (in red dotted), and its shear deformation part ${\rm Pi-D}_{\rm shear}$ (in green dotted). The gray dotted line in each panel denotes $t=30$.
• Figure 3: The shear deformation [panels (a)-(e)], normal deformation [panels (f)-(j)], and their combination, total deformation [panels (k)-(o)] for all five $T_e/T_i$ cases are shown for electrons. The color bar value of each quantity is set by the absolute maximum of the minimum and maximum seen in all five simulations at $t=30$. The in-plane magnetic fields, a proxy for interacting eddies, are shown by dashed black lines.
• Figure 4: Figure \ref{['fig:PiD_decomp_electrons']} repeated for ions, for all five simulations at $t=30$.
• Figure 5: The shear deformation [panels (a)-(e)], normal deformation [panels (f)-(j)], and their combination, total deformation [panels (k)-(o)] for all five $T_e/T_i$ cases are shown for electrons after applying the strong current sheet conditioning to only capture regions electron shear, normal, and total deformation are non-zero in strong intermittent structures. The color bar value of each quantity is set by the absolute maximum of the minimum and maximum seen in all five simulations at $t=30$. The in-plane magnetic field lines, a proxy for interacting eddies, are removed for clarity.