Direct in-situ Estimates of Energy and Force Balance in Near Earth Collisionless Plasmas

Fundamental processes in plasmas act to convert energies into different forms, e.g., electromagnetic, kinetic and thermal. Direct derivation from the Valsov-Maxwell equation yields sets of equations that describe the temporal evolution of the magnetic, kinetic and internal energies in either the monofluid or multifluid frameworks. In this work we focus on the main terms that affect the changes in the kinetic energy. These are pressure gradient-related terms and electromagnetic terms. The former account for plasma acceleration or deceleration from a pressure gradient, while the latter from an electric field. The overall balance between these terms is fundamental to ensure the conservation of energy and momentum. We use in-situ observations from the Magnetospheric MultiScale (MMS) mission to study the relationship between these terms. We perform a statistical analysis of those parameters in the context of magnetic reconnection by focusing on small-scale Electron Diffusion Regions and large-scale Flux Transfer Events. The analysis reveals a correlation between the two terms in the monofluid force balance, and in the ion force and energy balance. However, the expected relationship cannot be verified from electron measurements. Generally, the pressure gradient related terms are smaller than their electromagnetic counterparts. We perform an error analysis to quantify the expected underestimation of gradient values as a function of the spacecraft separation compared to the gradient scale. Our findings highlight that MMS is capable of capturing energy and force balance for the ion fluid, but that care should be taken for energy conversion terms based on electron pressure gradients.