Martin V. Goldman

Electron-Scale Measurements of Magnetic Reconnection in Space

Probing magnetic reconnection in space Magnetic reconnection occurs when the magnetic field permeating a conductive plasma rapidly rearranges itself, releasing energy and accelerating particles. Reconnection is important in a wide variety of physical systems, but the details of how it occurs are poorly understood. Burch et al. used NASAs Magnetospheric Multiscale mission to probe the plasma properties within a reconnection event in Earths magnetosphere (see the Perspective by Coates). They find that the process is driven by the electron-scale dynamics. The results will aid our understanding of magnetized plasmas, including those in fusion reactors, the solar atmosphere, solar wind, and the magnetospheres of Earth and other planets. Science, this issue p. 10.1126/science.aaf2939; see also p. 1176 Magnetic reconnection is driven by the electron-scale dynamics occurring within magnetized plasmas. INTRODUCTION Magnetic reconnection is a physical process occurring in plasmas in which magnetic energy is explosively converted into heat and kinetic energy. The effects of reconnection—such as solar flares, coronal mass ejections, magnetospheric substorms and auroras, and astrophysical plasma jets—have been studied theoretically, modeled with computer simulations, and observed in space. However, the electron-scale kinetic physics, which controls how magnetic field lines break and reconnect, has up to now eluded observation. RATIONALE To advance understanding of magnetic reconnection with a definitive experiment in space, NASA developed and launched the Magnetospheric Multiscale (MMS) mission in March 2015. Flying in a tightly controlled tetrahedral formation, the MMS spacecraft can sample the magnetopause, where the interplanetary and geomagnetic fields reconnect, and make detailed measurements of the plasma environment and the electric and magnetic fields in the reconnection region. Because the reconnection dissipation region at the magnetopause is thin (a few kilometers) and moves rapidly back and forth across the spacecraft (10 to 100 km/s), high-resolution measurements are needed to capture the microphysics of reconnection. The most critical measurements are of the three-dimensional electron distributions, which must be made every 30 ms, or 100 times the fastest rate previously available. RESULTS On 16 October 2015, the MMS tetrahedron encountered a reconnection site on the dayside magnetopause and observed (i) the conversion of magnetic energy to particle kinetic energy; (ii) the intense current and electric field that causes the dissipation of magnetic energy; (iii) crescent-shaped electron velocity distributions that carry the current; and (iv) changes in magnetic topology. The crescent-shaped features in the velocity distributions (left side of the figure) are the result of demagnetization of solar wind electrons as they flow into the reconnection site, and their acceleration and deflection by an outward-pointing electric field that is set up at the magnetopause boundary by plasma density gradients. As they are deflected in these fields, the solar wind electrons mix in with magnetospheric electrons and are accelerated along a meandering path that straddles the boundary, picking up the energy released in annihilating the magnetic field. As evidence of the predicted interconnection of terrestrial and solar wind magnetic fields, the crescent-shaped velocity distributions are diverted along the newly connected magnetic field lines in a narrow layer just at the boundary. This diversion along the field is shown in the right side of the figure. CONCLUSION MMS has yielded insights into the microphysics underlying the reconnection between interplanetary and terrestrial magnetic fields. The persistence of the characteristic crescent shape in the electron distributions suggests that the kinetic processes causing magnetic field line reconnection are dominated by electron dynamics, which produces the electric fields and currents that dissipate magnetic energy. The primary evidence for this magnetic dissipation is the appearance of an electric field and a current that are parallel to one another and out of the plane of the figure. MMS has measured this electric field and current, and has identified the important role of electron dynamics in triggering magnetic reconnection. Electron dynamics controls the reconnection between the terrestrial and solar magnetic fields. The process of magnetic reconnection has been a long-standing mystery. With fast particle measurements, NASA’s Magnetospheric Multiscale (MMS) mission has measured how electron dynamics controls magnetic reconnection. The data in the circles show electrons with velocities from 0 to 104 km/s carrying current out of the page on the left side of the X-line and then flowing upward and downward along the reconnected magnetic field on the right side. The most intense fluxes are red and the least intense are blue. The plot in the center shows magnetic field lines and out-of-plane currents derived from a numerical plasma simulation using the parameters observed by MMS. Magnetic reconnection is a fundamental physical process in plasmas whereby stored magnetic energy is converted into heat and kinetic energy of charged particles. Reconnection occurs in many astrophysical plasma environments and in laboratory plasmas. Using measurements with very high time resolution, NASA’s Magnetospheric Multiscale (MMS) mission has found direct evidence for electron demagnetization and acceleration at sites along the sunward boundary of Earth’s magnetosphere where the interplanetary magnetic field reconnects with the terrestrial magnetic field. We have (i) observed the conversion of magnetic energy to particle energy; (ii) measured the electric field and current, which together cause the dissipation of magnetic energy; and (iii) identified the electron population that carries the current as a result of demagnetization and acceleration within the reconnection diffusion/dissipation region.

Upper‐hybrid solitons and oscillating‐two‐stream instabilities

A warm two‐fluid theory of soliton formation near the upper‐hybrid frequency is developed. Several forms of the nonlinear Schrodinger equation are obtained, depending on whether the electric field is completely perpendicular to the dc magnetic field or whether it has an additional small component parallel to the magnetic field. For the perpendicular case, the character of the soliton depends on its scale length, L, and on β. For low β, when L<c/ωpe, stationary envelope and hole solitons are found, whereas in the limit L≳c/ωpi the super‐Alvenic solitons described magnetohydromagnetically by Kaufman and Stenflo are obtained. However, the case E∥≠0 may be of more interest, since it couples the pump to the excited waves more efficiently. In the limit of linearization about an infinite wavelength pump, the nonlinear Schrodinger equations yield purely growing (oscillating‐two‐stream) instabilities in both cases.

Progress and problems in the theory of type III solar radio emission

The experimental and theoretical status of type III solar radio emission is considered in detail. We emphasize very recent developments which are relevant to the underlying plasma physics. In particular we discuss the identity of the sub-megahertz emissions as fundamental, or second harmonic, the degree of correlation between emissivities, electron streams, and plasma (Langmuir) waves, paradoxes concerned with the time-ordering of these phenomena, and the role of background density irregularities and ion-acoustic turbulence in the solar wind. From the theoretical point of view we discuss the current picture of the underlying Langmuir turbulence, including such effects as the interaction between Langmuir waves and stream electrons, induced scatter off ions, and strong turbulence effects such as modulational instability and soliton collapse.

Auroral particle acceleration by strong double layers: The upward current region

[1] Satellite observations have established that parallel electric fields of both upward and downward current regions of the aurora are supported, at least in part, by strong double layers. The purpose of this article is to examine the role of double layers in auroral electron acceleration using direct measurements of parallel electric fields and the accompanying particle distributions, electrostatic waves, and nonlinear structures; the concentration is on the upward current region. Direct observations of the ionospheric boundary of the auroral cavity suggest that a stationary, oblique double layer carries a substantial, albeit a minority fraction (∼10% to ∼50%) of the auroral potential. An order of magnitude density gradient results in an asymmetric electric field signature. Oblique double layers with amplitudes greater than 100 mV/m have been verified in ∼3% and may occur in up to 11% of auroral cavity crossings, so it is feasible that strong double layers are a principal acceleration mechanism. In this article we also present a second type of double layer that has a symmetric electric field signature and is seen inside of the auroral cavity. These structures are a possible signature of a midcavity or high-altitude acceleration mechanism. Numerical solutions of the Vlasov-Poisson equations support the possibility of midcavity double layers and indicate that trapped electrons can play an important role in the double-layer structure.

Nonlinear Langmuir waves during type III solar radio bursts

Type III solar radio bursts are thought to be associated with intense levels of electron beam excited Langmuir waves. We numerically study the nonlinear evolution of these waves, in time and in two spatial dimensions, due to their coupling to other waves. For parameters appropriate to one-half the Earth-Sun distance, we find nonlinear effects to be important, as in previous one-dimensional work. However, a new and important phenomenon, two-dimensional soliton collapse, is found to occur. This collapse, induced directly by the wave packet nature of the beam excited waves, produces two-dimensional wave spectra extending over a much broader range of wavenumbers than has been predicted by inhomogeneous quasi-linear theory. Our results compare favorably with certain aspects of recent observations. We neglect the background magnetic field; while substantially justified for the present parameters, this neglect may require reexamination at locations closer to the Sun.

Parallel electric fields in the upward current region of the aurora: Numerical solutions

Direct observations of the parallel electric field by the Fast Auroral Snapshot satellite and the Polar satellite suggest that the ionospheric boundary of the auroral cavity is consistent with an oblique double layer that carries a substantial fraction (roughly 5% to 50%) of the auroral potential. A numerical solution to the Vlasov–Poisson equations of a planar, oblique double layer reproduces many of the properties of the observed electric fields, electron distributions, and ion distributions. The solutions indicate that the electron and ion distributions that emerge from the ionospheric side dominate the structure of the double layer. The ionospheric electron distribution includes scattered and reflected (mirrored) primaries, auroral secondaries, photoelectrons, and a cold population. A large fraction of the ionospheric electrons is reflected by the parallel electric field whereas the ionospheric ions are strongly accelerated. The steep density gradient between the ionosphere and the auroral cavity resu...

Quenching of the beam-plasma instability by large-scale density fluctuations in 3 dimensions

A model is presented to explain the highly variable yet low level of Langmuir waves measured in situ by spacecraft when electron beams associated with type III solar bursts are passing by; the low level of excited waves allows the propagation of such streams from the Sun to well past 1 AU without catastrophic energy losses. The model is based, first, on the existence of large-scale density fluctuations that are able to efficiently diffuse small-k beam-unstable Langmuir waves in phase space, and, second, on the presence of a significant isotropic non-thermal tail in the distribution function of the background electron population, which is capable of stabilizing larger k modes. The strength of the model lies in its ability to predict various levels of Langmuir waves depending on the parameters. This feature is consistent with the high variability actually observed in the measurements. The calculations indicate that, for realistic parameters, the most unstable, small k modes are fully stabilized while some oblique mode with higher k and lower growth rate might remain unstable; thus a very broad range of levels of Langmuir waves is possible from levels of the order of enhanced spontaneous emission to the threshold level for nonlinear processes. On the other hand, from in situ measurements of the density fluctuations spectrum by ISEE-1 and 2 in the vicinity of the Earth, it is shown that measured 100 km scale fluctuations may be too effective in quenching the instability. If such strong density fluctuations are common in the solar wind, we show they must be highly anisotropic in order to allow the build-up of Langmuir waves to the observed mV m−1 range. Moreover, the anisotropy must be such that the strongest variations of density occur in a plane perpendicular to the magnetic field.

Theory of Stability of Large Periodic Plasma Waves

A method is developed for examining the stability of a large‐amplitude periodic Bernstein‐Greene‐Kruskal wave, E0, in a collisionless plasma. Vlasovs equation is integrated by the method of characteristics to yield a polarization charge density response ρ1, linear in a small‐amplitude field E1, but nonlinear in E0. The susceptibility linking ρ1 and E1 is expressed in terms of the exact orbits of trapped and untrapped particles in the field E0, distributed in energy according to an assumed Bernstein‐Greene‐Kruskal distribution function f0. These susceptibilities couple the Fourier components of E1 in the usual mode‐coupling fashion, but trapping effects are now included. For fields E0 which are not too large, the mode‐coupling problem reduces to finding the zeroes of a 2 × 2 or 3 × 3 determinant. Trapped electron distribution functions which are localized at the bottom of the potential energy troughts of E0 give the growing side‐band instability of Kruer, Dawson, and Sudan.

Simulation of the collapse and dissipation of Langmuir wave packets

The collapse of isolated Langmuir wave packets is studied numerically in two dimensions using both particle‐in‐cell (PIC) simulations and by integrating the Zakharov partial differential equations (PDE’s). The initial state consists of a localized Langmuir wave packet in an ion background that either is uniform or has a profile representative of the density wells in which wave packets form during strong plasma turbulence. Collapse thresholds are determined numerically and compared to analytical estimates. A model in which Langmuir damping is significantly stronger than Landau damping is constructed which, when included in the PDE simulations, yields good agreement with the collapse dynamics observed in PIC simulations for wave packets with initial wave energy densities small compared to the thermal level. For more intense initial Langmuir fields, collapse is arrested in PIC simulations at lower field strengths than in PDE simulations. Neither nonlinear saturation of the density perturbation nor fluid elec...

Electron phase-space holes and the VLF saucer source region

The Fast Auroral SnapshoT (FAST) satellite has identified new properties of VLF saucers that are important to understanding their generation and the physical processes in the source region. The most significant finding is a frequent occurrence (∼79%) of electron phase-space holes on flux tubes of the VLF saucer source in the downward current region. This finding implies either a common energy source or a direct association between the two phenomenon. FAST observations also demonstrate that VLF saucer vertices are strongly correlated with up-going electron fluxes associated with diverging DC electric field structures. These observations imply parallel electric fields along the source flux tube of VLF saucers.