Julia E. Stawarz

Highly-nonlinear fluctuations, known as turbulence, such as those in the simulation in Figure 1 (Slide 1), are found throughout the Universe – from the solar wind and planetary magnetospheres to accretion discs and galaxy clusters. These fluctuations transfer energy from large to small length scales, enabling particle energisation. However, the absence of collisions in many of these plasmas means there are many possible channels for dissipating the fluctuation energy and disentangling them is a major open problem. Spacecraft observations from near-Earth plasmas provide some of the best observations to explore this problem.

Electric fields play a central role in exchanging energy between electromagnetic fluctuations and particles, making them a key quantity for examining nonlinear turbulent dynamics and energy dissipation. In collisionless plasmas, the electric field is governed by a generalised Ohm’s Law shown in Figure 2 (Slide 2), where different terms correspond to different plasma dynamics. These terms include the MHD and Hall terms, describing ion and electron fluid flows being “frozen-in” to the magnetic field, as well as electron pressure, inertial, and finite electron mass corrections that are capable of breaking this frozen-in condition. NASA’s Magnetospheric Multiscale (MMS) is a four-spacecraft mission that is uniquely capable of computing nearly all the terms in generalised Ohm’s Law due to a combination of high-resolution and multipoint measurements.

In this study, we use MMS data to examine power spectra of the terms in generalised Ohm’s Law and determine how they shape the turbulent electric field at different scales for the first time. In Figure 4 (Slide 3), we show these spectra from an example interval downstream of the Earth’s bow shock, in what is known as the magnetosheath. Overall, there is good agreement between the spectra of the total of all Ohm’s Law terms and the directly measured electric field down to a few times the electron gyroradius. The MHD contribution dominates the spectrum at large scales, indicating the magnetic field is frozen-in to the ion flow, as expected at these scales. At sub-ion scales, both the Hall and electron pressure contributions govern the electric field with the Hall field providing the larger contribution. The transition between these two regimes occurs at the ion inertial length modulated by the relative amplitude of velocity to magnetic fluctuations. The remaining inertial electric fields and electron mass corrections are negligible across the observed scales.

Figure 5 (Slide 4) examines the interplay between the Hall and electron pressure contributions at sub-ion scales, which is important because the electron pressure can contribute a non-ideal electric field capable of energising electrons. It is found that the relative amplitude of the electron pressure contribution is larger than expected from typical kinetic Alfvén wave predictions, which may relate to the presence of small-scale reconnection events in the plasma. The two contributions also partially anti-align, which is related to the relative importance of ion and electron effects in supporting the turbulent sub-ion scale currents.

Figure 6 (Slide 4) examines the relative importance of linear and nonlinear contributions to the MHD and Hall electric fields. At large scales for the MHD field and across all scales for the Hall field, the ratio of nonlinear to linear contributions is constant and given by the magnetic fluctuation amplitude, suggesting a balance of linear and nonlinear timescales across MHD and sub-ion scales. Furthermore, at sub-ion scales the nonlinear MHD field is enhanced, providing insight into the changing alignment of velocity and magnetic fluctuations.

Overall, this novel analysis confirms a number of expectations about the turbulent electric field and highlights new features about its role in the nonlinear dynamics and dissipation that should be explored further theoretically.