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1. Helmholtz decomposition of pressure–strain interaction in kinetic plasma turbulence

   https://doi.org/10.1063/5.0295281  

   Adhikari, Subash; Yang, Yan; Matthaeus, William H (December 2025, Physics of Plasmas)

   In this study, we revisit the pressure–strain interaction in kinetic plasma turbulence. We reexamine the decomposition of pressure–strain interaction into compressive and incompressive parts using Helmholtz theorem. The pressure dilatation ingredient is clearly due to plasma compressions, but here, using 2.5 dimensional kinetic particle-in-cell (PIC) simulations of plasma turbulence, it is demonstrated that the remaining anisotropic part, often called Pi-D, also contains contributions due to compressive, non-solenoidal velocities of the particle species. The compressive Pi-D can play a significant role in systems with low plasma β even if the system starts with small density variations. In addition, the compressive ingredient of Pi-D is found to be strongly anticorrelated with both incompressive Pi-D and pressure dilatation along the current sheets. 

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2. Pressure–Strain Interaction as the Energy Dissipation Estimate in Collisionless Plasma

   https://doi.org/10.3847/1538-4357/ac5d3e  

   Yang, Y.; Matthaeus, W.; Roy, S.; Roytershteyn, V.; Parashar, T.; Bandyopadhyay, R.; Wan, Minping (April 2022, The Astrophysical journal)

   The dissipative mechanism in weakly collisional plasma is a topic that pervades decades of studies without a consensus solution. We compare several energy dissipation estimates based on energy transfer processes in plasma turbulence and provide justification for the pressure–strain interaction as a direct estimate of the energy dissipation rate. The global and scale-by-scale energy balances are examined in 2.5D and 3D kinetic simulations. We show that the global internal energy increase and the temperature enhancement of each species are directly tracked by the pressure–strain interaction. The incompressive part of the pressure–strain interaction dominates over its compressive part in all simulations considered. The scale-by-scale energy balance is quantified by scale filtered Vlasov–Maxwell equations, a kinetic plasma approach, and the lag dependent von Kármán–Howarth equation, an approach based on fluid models. We find that the energy balance is exactly satisfied across all scales, but the lack of a well-defined inertial range influences the distribution of the energy budget among different terms in the inertial range. Therefore, the widespread use of the Yaglom relation in estimating the dissipation rate is questionable in some cases, especially when the scale separation in the system is not clearly defined. In contrast, the pressure– strain interaction balances exactly the dissipation rate at kinetic scales regardless of the scale separation 

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3. Electron-scale current sheets and energy dissipation in 3D kinetic-scale plasma turbulence with low electron beta

   https://doi.org/10.1093/mnras/stad1931  

   Vega, Cristian; Roytershteyn, Vadim; Delzanno, Gian Luca; Boldyrev, Stanislav (July 2023, Monthly Notices of the Royal Astronomical Society)

   ABSTRACT Three-dimensional kinetic-scale turbulence is studied numerically in the regime where electrons are strongly magnetized (the ratio of plasma species pressure to magnetic pressure is βe = 0.1 for electrons and βi = 1 for ions). Such a regime is relevant in the vicinity of the solar corona, the Earth’s magnetosheath, and other astrophysical systems. The simulations, performed using the fluid-kinetic spectral plasma solver (sps) code, demonstrate that the turbulent cascade in such regimes can reach scales smaller than the electron inertial scale, and results in the formation of electron-scale current sheets (ESCS). Statistical analysis of the geometrical properties of the detected ESCS is performed using an algorithm based on the medial axis transform. A typical half-thickness of the current sheets is found to be on the order of electron inertial length or below, while their half-length falls between the electron and ion inertial length. The pressure–strain interaction, used as a measure of energy dissipation, exhibits high intermittency, with the majority of the total energy exchange occurring in current structures occupying approximately 20 per cent of the total volume. Some of the current sheets corresponding to the largest pressure–strain interaction are found to be associated with Alfvénic electron jets and magnetic configurations typical of reconnection. These reconnection candidates represent about 1 per cent of all the current sheets identified. 

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4. Scale Separation Effects on Simulations of Plasma Turbulence

   https://doi.org/10.3847/1538-4357/ad5cf5  

   Edyvean, Jago; Parashar, Tulasi N; Simpson, Tom; Juno, James; Delzanno, Gian Luca; Guo, Fan; Koshkarov, Oleksandr; Matthaeus, William H; Shay, Michael; Yang, Yan (September 2024, The Astrophysical Journal)

   Abstract Understanding plasma turbulence requires a synthesis of experiments, observations, theory, and simulations. In the case of kinetic plasmas such as the solar wind, the lack of collisions renders the fluid closures such as viscosity meaningless and one needs to resort to higher-order fluid models or kinetic models. Typically, the computational expense in such models is managed by simulating artificial values of certain parameters such as the ratio of the Alfvén speed to the speed of light (v_A/c) or the relative mass ratio of ions and electrons (m_i/m_e). Although, typically care is taken to use values as close as possible to realistic values within the computational constraints, these artificial values could potentially introduce unphysical effects. These unphysical effects could be significant at sub-ion scales, where kinetic effects are the most important. In this paper, we use the 10-moment fluid model in the Gkeyll framework to perform controlled numerical experiments, systematically varying the ion–electron mass ratio from a small value down to the realistic proton–electron mass ratio. We show that the unphysical mass ratio has a significant effect on the kinetic range dynamics as well as the heating of both plasma species. The dissipative process for both ions and electrons becomes more compressive in nature, although the ions remain nearly incompressible in all cases. The electrons move from being dominated by incompressive viscous-like heating/dissipation to very compressive heating/dissipation dominated by compressions/rarefactions. While the heating change is significant for the electrons, a mass ratio ofm_i/m_e∼ 250 captures the asymptotic behavior of electron heating. 

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5. Effects of unequal electron–ion temperature on pressure–strain interaction in nearly collisionless turbulent plasmas

   https://doi.org/10.1063/5.0316403  

   Barbhuiya, M Hasan; Adhikari, Subash (April 2026, Physics of Plasmas)

   A common occurrence in nearly collisionless 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 remains unexplored. We investigate this using five fully kinetic 2.5-dimensional particle-in-cell simulations of undriven decaying turbulence by varying the initial electron-to-ion temperature ratios. By analyzing the species' internal energy density alongside a decomposition of the pressure–strain interaction, 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 average internal energy density for both electrons and ions, where the total deformation channel dominates energy evolution. We discover that 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. By varying the initial temperature ratio, 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 now approximated via only its shear deformation part, and provide a framework for interpreting energy evolution and conversion in turbulent space plasmas where unequal species temperature is the norm. 

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