In situ measurements of kinetic scale current sheets in the solar wind show that they are often approximately force-free although the plasma $\beta$ is of order one. They frequently display systematic asymmetric and anti-correlated spatial variations of their particle density and temperature across the current sheet, leaving the plasma pressure essentially uniform. These observations of asymmetries have previously been modelled theoretically by adding additional terms to both the ion and electron distribution functions of self-consistent force-free collisionless current sheet models with constant density and temperature profiles. In this article we present the results of a modification of these models in which only the electron distribution function has an additional term, whereas the ion distribution function is kept as a thermal (Maxwellian) distribution function. In this case the nonlinear quasineutrality condition no longer has a simple analytical solution and therefore has to be solved alongside Ampère’s law. We find that while the magnetic field remains approximately force-free, the non-zero quasineutral electric field gives rise to an additional spatial substructure of the plasma density inside the current sheet. We briefly discuss the potential relation between our theoretical findings and current sheet observations.
