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

Abstract

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.

Anisotropic Electron Heating in Turbulence-driven Magnetic Reconnection in the Near-Sun Solar Wind

“…Fully kinetic simulations of collisionless turbulent plasmas, which retain both ion and electron kinetic effects, represent an invaluable tool for investigating the turbulent energy cascade down to electron scales (e.g., Grošelj et al 2018;Cerri et al 2019;González et al 2019;Roytershteyn et al 2019), its interplay with magnetic reconnection (e.g., Karimabadi et al 2013;Pucci et al 2017Pucci et al , 2018aAdhikari et al 2021;Agudelo Rueda et al 2021), and the role of electron-scale coherent structures in dissipating energy and heating particles (e.g., Camporeale & Burgess 2011;Parashar et al 2015;Yang et al 2017;Arrò et al 2021;Bandyopadhyay et al 2021;Yang et al 2022). They have also provided numerical evidence for an enhancement of the electron parallel temperature anisotropy in the outflows of strong reconnection events, which occurred spontaneously as the result of the interactions between subproton-scale turbulent structures (Camporeale & Burgess 2011;Haynes et al 2014).…”

Observations of Cross Scale Energy Transfer in the Inner Heliosphere by Parker Solar Probe

“…[86] have included pressure strain interactions to modify the von Kármán equations. This modification extends the range of validity of these equations down to sub-proton scales implying the important role played by pressure-strain interactions in the kinetic range energy transfer; see also [85].…”

“…An alternative approach to studying scale-to-scale transfer of energy in the fully kinetic limit is to apply scale filtering techniques to the Vlasov equation [41,[82][83][84]. Starting with the Vlasov equation, applying scale filtering techniques, one arrives at [82,85]…”

“…where ¯represents a scale filtered quantity and ˜represents a density weighted filtered quantity. Ẽf α is the filtered fluid flow energy, Ēm is the filtered electromagnetic energy, J u α and J b are spatial transport terms, Π uu α , and Π bb α are the subgrid scale fluxes, Φ uT α is the rate of flow energy conversion to internal energy through pressure strain interactions (see the discussion of energy at kinetic scales below), and Λ uT α is the rate of energy conversion from electromagnetic fluctuations into fluid flow through filtered j α • E. For details of these equations see [85].…”

“…The scale filtered energy equations show good numerical energy conservation at all scales while energy conservation has to be imposed on the von Kármán Howarth equations given the lack of kinetic and compressive physics. (Reproduced with permission from[85]).…”