Generalised Ohm’s Law in the Magnetosheath: How do plasma conditions impact turbulent electric fields?

Turbulence is a complex phenomenon whereby fluctuation energy is transferred between different scale sizes as a result of nonlinear interactions. Electromagnetic turbulence is ubiquitous within space plasmas, wherein it is associated with numerous nonlinear interactions. The dynamics of the magnetic field, which are widely studied in turbulence theory, are intimately linked to the electric field, which controls the exchange of energy between the magnetic field and the particles. Magnetospheric Multiscale (MMS) provides the unique opportunity to decompose electric field dynamics into contributions from different linear and nonlinear processes. The evolution of the electric field is described by generalised Ohm’s law, which breaks down the dynamics into components arising from different physical effects. Using high-resolution multipoint measurements, we compute the MHD, Hall and Electron Pressure terms of generalised Ohm’s law for 60 turbulent magnetosheath intervals. These terms, which have varying contributions to the dynamics as a function of scale, arise as a result of different physical effects related to a range of underlying turbulent phenomena. We examine how two characteristics of the turbulent electric field spectra depend on plasma conditions: the transition scale between MHD and Hall dominance (the ‘Hall scale’, k_Hall) and the relative amplitude of Hall and Electron Pressure contributions. Motivated by dimensional analysis arguments which appeal to characteristics of the plasma and the turbulence that can be quantified in a number of ways by MMS, we demonstrate the necessary refinements required to reproduce measured values. The scalar isotropic kinetic Alfven wave prediction for the ratio of Electron Pressure to Hall terms as a function of plasma beta is not consistent with measurements. We observe that the MHD and Hall terms are dominated by either nonlinear or linear dynamics, depending on the interval, while the Electron Pressure term is dominated by linear components only. Our work shows how contributions to turbulent dynamics change in different plasma conditions, which may provide insight into other turbulent plasma environments.