Direct observations of anomalous resistivity and diffusion in collisionless plasma

The behavior of plasma, comprising ions and electrons governed by electromagnetic forces, is significantly different in low-density astrophysical plasmas where Coulomb collisions are rare. This means that traditional mechanisms for plasma resistivity and diffusion are ineffective. However, the scattering of particles by electromagnetic waves can introduce effective collisions, leading to anomalous resistivity. This anomalous resistivity, driven by wave-particle interactions, is believed to be crucial in various collisionless plasma processes, including magnetic reconnection, a fundamental process responsible for explosive energy releases in the universe. Theoretical and numerical studies suggest that waves could contribute both diffusion and resistivity to support the reconnection electric field, but this needs direct observational confirmation. Lower hybrid waves, found at frequencies between ion and electron cyclotron frequencies and driven by plasma gradients and associated cross-field currents, are considered a potential source of these anomalous effects. Previous attempts to calculate anomalous terms yielded conflicting results, partly due to limitations in measurement techniques relying on inferences from spacecraft potential and assumptions about electron behavior. Direct particle measurements are necessary to accurately assess the role of lower hybrid waves in anomalous resistivity, viscosity, and cross-field diffusion, thereby resolving the uncertainties surrounding their role in magnetic reconnection. This study directly measures and quantifies these anomalous plasma effects using high-resolution data from the four MMS spacecraft, offering a unique opportunity to investigate the impact of lower hybrid waves on magnetic reconnection, specifically addressing the outstanding question of their contribution to the reconnection electric field.

Past research on anomalous resistivity has explored various wave-particle interaction mechanisms, particularly focusing on lower hybrid waves. Early theoretical work by Drummond and Rosenbluth (1962) established the fundamental concept of anomalous diffusion arising from microinstabilities in plasma. Subsequent studies, such as Papadopoulos (1977), explored anomalous resistivity in the ionosphere. Davidson and Krall (1977) investigated anomalous transport in high-temperature plasmas, while Drake et al. (2003) explored electron hole formation and particle energization during reconnection. However, these studies often relied on theoretical models or numerical simulations with limitations in representing real-world conditions. Studies focusing on lower hybrid waves and their role in anomalous resistivity have also shown conflicting results. Some studies suggested a small contribution of anomalous resistivity (Shinohara et al., 1998; Mozer et al., 2011), while others highlighted significant cross-field particle diffusion (Vaivads et al., 2004; Graham et al., 2017). These discrepancies stem from the use of indirect measurements and assumptions about electron behavior. Recent work by Graham et al. (2019) showed electrons remaining mostly frozen in, but pressure fluctuations can lead to deviations from the ideal frozen-in condition. This highlights the need for direct measurements of particle distributions to accurately assess anomalous effects.

This research utilizes high-resolution data from the four Magnetospheric Multiscale (MMS) spacecraft. The study focuses on magnetopause reconnection events, specifically examining regions with strong density gradients where lower hybrid waves are expected to be prominent. The MMS spacecraft provide measurements of electric and magnetic fields, as well as high-resolution electron and ion distributions. This high temporal resolution (7.5 ms for electrons) allows for the detailed analysis of lower hybrid wave properties. The analysis involves separating measured quantities into fluctuating and quasi-stationary components. Anomalous terms – drag (resistivity), viscosity (momentum transport), and Reynolds stress – are calculated using a collisionless electron momentum equation. The anomalous electron flow and diffusion coefficient are determined from the electron continuity equation. The methodology leverages the multi-spacecraft nature of MMS to perform spatial averaging (approximated by four-spacecraft averaging), essential for calculating the anomalous terms. Specifically, the data analysis proceeds as follows: 1) Data is resampled to the highest-resolution electron moment sampling frequency. 2) Four-spacecraft timing analysis determines boundary normal velocity and time delays between spacecraft. 3) Time-shifted quantities are averaged to obtain non-fluctuating components using a low-pass filter. 4) Fluctuations associated with lower hybrid waves are extracted using a bandpass filter. 5) Spatial averaging of fluctuation products provides estimates for the anomalous terms. The uncertainties in the anomalous terms are estimated considering uncertainties in the electron moments and the electric field gain. The negligible contribution of the anomalous inertial term is confirmed by separate estimations, showing that its magnitude is much smaller compared to the drag and viscosity terms. The impact of the anomalous Reynolds stress is also evaluated using a method based on approximation of its variation primarily in the normal direction, showing it to be much less significant compared to the drag and viscosity components. A numerical simulation using the fully kinetic iPIC code was conducted to model a specific magnetopause reconnection event (the 06 December 2015 event). The simulation employed parameters consistent with the observations and included asymmetric initial conditions. This complements the observational data analysis and allows for cross-validation of the findings. The simulation utilizes a double periodic domain with two thin current sheets and initiates reconnection with a localized perturbation. The three-dimensional simulation was initialized using the steady-state solutions from a two-dimensional run.

The study's key findings center around the direct observation and quantification of anomalous terms associated with lower hybrid waves during magnetopause reconnection. The analysis reveals that the anomalous drag (resistivity) is balanced by the anomalous viscosity (momentum transport), meaning that their combined effect on the reconnection electric field is negligible. This indicates that lower hybrid waves do not directly contribute to the driving of reconnection. This result is further supported by the observation that electrons move closely with the magnetic field (frozen-in condition), making their contribution to the reconnection electric field small. Despite the negligible impact on the reconnection electric field, the study finds a significant anomalous electron flow and cross-field diffusion across the current layer associated with lower hybrid waves. This leads to a relaxation of density gradients and broadening of the current sheet on timescales comparable to the ion cyclotron period. The anomalous electron flow is directed from higher-density regions (magnetosheath) towards lower-density regions (magnetosphere), thus reducing the steepness of the density gradient. This process significantly affects the dynamics of the reconnection process by modifying the Hall electric and magnetic fields and potentially contributing to the electron heating observed in the magnetospheric inflow region. Statistical analysis of multiple magnetopause crossings (22 events) confirms these findings. In all cases, the anomalous drag and viscosity are comparable in magnitude but opposite in sign, resulting in a negligible net contribution to the electric field. The anomalous electron flow and diffusion coefficient show significant variability, with the largest values found near the electron diffusion regions (EDRs). The results also show that the diffusion coefficient increases with the amplitude of the anomalous electron flow, confirming the importance of lower hybrid waves in cross-field electron transport. The findings are further supported by the comparison between observational data and numerical simulation results. The simulation shows qualitatively similar behavior to the observations, with a balance between anomalous drag and viscosity and a significant anomalous electron flow across the current sheet. This corroborates the observational findings and increases their confidence.

The findings of this study directly address the long-standing question of the role of lower hybrid waves in magnetic reconnection. The observation that anomalous resistivity and viscosity balance each other provides strong evidence that these waves do not directly contribute to the reconnection electric field, contrary to some previous theoretical suggestions. This is a significant advancement in our understanding of collisionless reconnection, which is fundamental to many astrophysical processes. However, the significant anomalous electron diffusion across the current sheet highlights the importance of lower hybrid waves in modifying the reconnection dynamics. The relaxation of density gradients can alter the current sheet structure and influence other associated processes, such as electron heating. The observed broadening of the current sheet also has implications for the efficiency of magnetic energy conversion during reconnection. These findings underscore that lower hybrid waves, while not primarily driving reconnection, play a vital role in regulating the transport and distribution of electrons within the reconnection region. The variability of the anomalous electron flow and diffusion coefficient highlights the complexity of the interaction between lower hybrid waves and the reconnection process. Further research should investigate the dependence of these effects on different reconnection parameters and plasma conditions. This work also lays the groundwork for future studies investigating other types of waves and their roles in anomalous transport during magnetic reconnection.

This study presents the first direct observations and quantification of anomalous resistivity, viscosity, and cross-field electron diffusion associated with lower hybrid waves during magnetopause reconnection. The key finding is that lower hybrid waves do not significantly contribute to the reconnection electric field, but they drive considerable cross-field electron diffusion, modifying the reconnection process. These results refine our understanding of collisionless plasma processes and demonstrate the power of multi-spacecraft observations for revealing subtle but crucial aspects of fundamental plasma physics. Future studies should investigate the influence of various reconnection parameters and plasma conditions on this cross-field electron diffusion.

The primary limitation of this study is the reliance on four-spacecraft averaging to approximate spatial averaging, which can introduce some uncertainty in the calculation of the anomalous terms. The accuracy of this approximation depends on the spacecraft separation and the spatial scales of the fluctuations. However, the spacecraft separations are sufficiently small compared to the ion scales, making this a reasonable approximation. Additionally, the study focuses on a specific range of reconnection events and plasma conditions. The generalizability of the findings to other reconnection environments requires further investigation.