Kinetic Equilibrium of Two-dimensional Force-free Current Sheets

Abstract

Force-free current sheets are local plasma structures with field-aligned electric currents and approximately uniform plasma pressures. Such structures, widely found throughout the heliosphere, are sites for plasma instabilities and magnetic reconnection, the growth rate of which is controlled by the structure’s current-sheet configuration. Despite the fact that many kinetic equilibrium models have been developed for one-dimensional force-free current sheets, their two-dimensional (2D) counterparts, which have a magnetic field component normal to the current sheets, have not received sufficient attention to date. Here, using particle-in-cell simulations, we search for such 2D force-free current sheets through relaxation from an initial, magnetohydrodynamic equilibrium. Kinetic equilibria are established toward the end of our simulations, thus demonstrating the existence of kinetic force-free current sheets. Although the system currents in the late equilibrium state remain field aligned as in the initial configuration, the velocity distribution functions of both ions and electrons systematically evolve from their initial drifting Maxwellians to their final time-stationary Vlasov state. The existence of 2D force-free current sheets at kinetic equilibrium necessitates future work in discovering additional integrals of motion of the system, constructing the kinetic distribution functions, and eventually investigating their stability properties.

Thin Current Sheets in the Magnetotail at Lunar Distances: Statistics of ARTEMIS Observations

“…Therefore, our results confirm the idea of Liuzzo et al (2022), that the middle magnetotail is a natural plasma laboratory for in situ CS investigations across a wide range of plasma characteristics. Moreover, observations of such partially force-free CSs provide a unique opportunity for the verification of models describing equilibrium for CSs without a normal magnetic field component, B n = 0, (e.g., Allanson et al, 2015;Neukirch, Vasko, et al, 2020, and references therein) and with a finite B n ≠ 0 (e.g., An et al, 2023;Artemyev, 2011;Mingalev et al, 2012;Vasko et al, 2014).…”

“…Partially force-free CSs, which appear to make up a significant fraction of the middle magnetotail CSs, are rarely observed in the near-Earth magnetotail, where these CSs are usually associated with magnetic reconnection Nakamura et al, 2008). However, partially force-free CSs are much more typical in the solar wind (Artemyev, Angelopoulos, & Vasko, 2019;Lotekar et al, 2022;Neukirch, Vasko, et al, 2020), Earth magnetopause (e.g., Lukin et al, 2020;Panov et al, 2011), and planetary magnetospheres (e.g., Artemyev et al, 2014;DiBraccio et al, 2015;Rong et al, 2015), where their formation is associated with insufficient ion contribution to the pressure balance (see discussion in An et al, 2023). Therefore, our results confirm the idea of Liuzzo et al (2022), that the middle magnetotail is a natural plasma laboratory for in situ CS investigations across a wide range of plasma characteristics.…”

“…(b) To what extent are these characteristics influenced by solar wind conditions? The answer to the first question should provide important data for new CS models (see discussion in Sitnov & Arnold, 2022;Arnold & Sitnov, 2023;An et al, 2022An et al, , 2023). The answer to the second question should reveal if the solar wind is the main driver of thin CS formation in the middle tail.…”