P. A. Cassak

Scaling of asymmetric magnetic reconnection: General theory and collisional simulations

A Sweet-Parker-type scaling analysis for asymmetric antiparallel reconnection (in which the reconnecting magnetic field strengths and plasma densities are different on opposite sides of the dissipation region) is performed. Scaling laws for the reconnection rate, outflow speed, the density of the outflow, and the structure of the dissipation region are derived from first principles. These results are independent of the dissipation mechanism. It is shown that a generic feature of asymmetric reconnection is that the X-line and stagnation point are not colocated, leading to a bulk flow of plasma across the X-line. The scaling laws are verified using two-dimensional resistive magnetohydrodynamics numerical simulations for the special case of asymmetric magnetic fields with symmetric density. Observational signatures and applications to reconnection in the magnetosphere are discussed.

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.

Ion heating resulting from pickup in magnetic reconnection exhausts

Received 25 August 2008; revised 20 January 2009; accepted 19 March 2009; published 30 May 2009. (1) The heating of ions downstream of the x-line during magnetic reconnection is explored using full-particle simulations, test particle simulations, and analytic analysis. Large-scale particle simulations reveal that the ion temperature increases sharply across the boundary layer that separates the upstream plasma from the Alfvenic outflow. This boundary layer, however, does not take the form of a classical switch-off shock as discussed in the Petschek reconnection model, so the particle heating cannot be calculated from the magnetohydrodynamic, slow-shock prediction. Test particle trajectories in the fields from the simulations reveal that ions crossing the narrow boundary into the exhaust instead behave like pickup particles: they gain both a directed outflow and an effective thermal speed given by the flow speed v0 of the exhaust. The detailed dynamics of these particles are explored by taking 1-D cuts of the simulation data across the exhaust, transforming to the deHoffman-Teller frame, and calculating explicitly the increment in the temperature, miv0 /3, with mi, the ion mass. We compare the model predictions with the temperature increment in solar wind exhausts measured by the ACE and Wind spacecraft, confirming that the temperature increment is proportional to the ion mass. The Wind data from 22 high-shear exhaust encounters confirm the scaling of the proton temperature increment with the square of the exhaust velocity. However, the temperature increments are consistently lower than the model prediction. Implications for understanding the production of high-energy ions in flares and the broader universe are discussed.

Catastrophe model for fast magnetic reconnection onset

A catastrophe model for the onset of fast magnetic reconnection is presented that suggests why plasma systems with magnetic free energy remain apparently stable for long times and then suddenly release their energy. For a given set of plasma parameters there are generally two stable reconnection solutions: a slow (Sweet-Parker) solution and a fast (Alfvénic) Hall reconnection solution. Below a critical resistivity the slow solution disappears and fast reconnection dominates. Scaling arguments predicting the two solutions and the critical resistivity are confirmed with two-fluid simulations.

Kinetic dissipation and anisotropic heating in a turbulent collisionless plasma

The kinetic evolution of the Orszag–Tang vortex is studied using collisionless hybrid simulations. In magnetohydrodynamics (MHD) this configuration leads rapidly to broadband turbulence. At large length scales, the evolution of the hybrid simulations is very similar to MHD, with magnetic power spectra displaying scaling similar to a Kolmogorov scaling of −5/3. At small scales, differences from MHD arise, as energy dissipates into heat almost exclusively through the magnetic field. The magnetic energy spectrum of the hybrid simulation shows a break where linear theory predicts that the Hall term in Ohm’s law becomes significant, leading to dispersive kinetic Alfven waves. A key result is that protons are heated preferentially in the plane perpendicular to the mean magnetic field, creating a proton temperature anisotropy of the type observed in the corona and solar wind.

Statistics of magnetic reconnection in two-dimensional magnetohydrodynamic turbulence

The nonlinear dynamics of magnetic reconnection in turbulence is investigated through direct numerical simulations of decaying, incompressible, two-dimensional magnetohydrodynamics. Recently, it was shown by Servidio et al. [Phys. Rev. Lett. 102, 115003 (2009)] that in fully developed turbulence complex processes of reconnection occur locally. Here, the main statistical features of these multiscale reconnection events are further described, providing details on the methodology. It is found that is possible to describe the reconnection process in turbulence as a generalized local Sweet–Parker process in which the parameters are locally controlled by the turbulence cascade, thus providing a step toward reconciling classical turbulence analysis with reconnection theory. This general description of reconnection may be useful for laboratory and space plasmas, where the presence of turbulence plays a crucial role.

A MAGNETIC RECONNECTION MECHANISM FOR ION ACCELERATION AND ABUNDANCE ENHANCEMENTS IN IMPULSIVE FLARES

The acceleration of ions during magnetic reconnection in solar flares is explored with simulations and analytic analysis. Ions crossing into Alfvenic reconnection outflows can behave like pickup particles and gain an effective thermal velocity equal to the Alfven speed. However, with a sufficiently strong ambient out-of-plane magnetic field, which is the relevant configuration for flares, the ions can become adiabatic and their heating is then dramatically reduced. The threshold for nonadiabatic behavior, where ions are strongly heated, becomes a condition on the ion mass-to-charge ratio, m{sub i}/m{sub p}Z{sub i}>10{radical}({beta}{sub 0x}/2)/{pi}, where m{sub i} and Z{sub i} are the ion mass and charge state, m{sub p} is the proton mass, and {beta}{sub 0x} = 8{pi}nT/B {sup 2}{sub 0x} is the ratio of the plasma pressure to that of the reconnecting magnetic field B{sub 0x}. Thus, during flares high mass-to-charge particles gain energy more easily than protons and a simple model reveals that their abundances are enhanced, which is consistent with observations.

Kinetic signatures of the region surrounding the X line in asymmetric (magnetopause) reconnection

Kinetic particle-in-cell simulations are used to identify signatures of the electron diffusion region (EDR) and its surroundings during asymmetric magnetic reconnection. A “shoulder” in the sunward pointing normal electric field (EN > 0) at the reconnection magnetic field reversal is a good indicator of the EDR and is caused by magnetosheath electron meandering orbits in the vicinity of the X line. Earthward of the X line, electrons accelerated by EN form strong currents and crescent-shaped distribution functions in the plane perpendicular to B. Just downstream of the X line, parallel electric fields create field-aligned crescent electron distribution functions. In the immediate upstream magnetosheath, magnetic field strength, plasma density, and perpendicular electron temperatures are lower than the asymptotic state. In the magnetosphere inflow region, magnetosheath ions intrude resulting in an Earthward pointing electric field and parallel heating of magnetospheric particles. Many of the above properties persist with a guide field of at least unity.

Scaling of Sweet-Parker reconnection with secondary islands

Sweet–Parker (collisional) magnetic reconnection at high Lundquist number is modified by secondary islands. Daughton et al. [Phys. Rev. Lett. 103, 065004 (2009)] suggested the Sweet–Parker model governs the fragmented current sheet segments. If true, the reconnection rate would increase by the square root of the number of secondary islands. High Lundquist number resistive magnetohydrodynamic simulations are presented which agree, in a time-averaged sense, with the predicted scaling. This result may have important implications for energy storage before a solar eruption and its subsequent release.

Comparison of secondary islands in collisional reconnection to Hall reconnection.

Large-scale resistive Hall-magnetohydrodynamic simulations of the transition from Sweet-Parker (collisional) to Hall (collisionless) magnetic reconnection are presented; the first to separate secondary islands from collisionless effects. Three main results are described. There exists a regime with secondary islands but without collisionless effects, and the reconnection rate is faster than Sweet-Parker, but significantly slower than Hall reconnection. This implies that secondary islands do not cause the fastest reconnection rates. The onset of Hall reconnection ejects secondary islands from the vicinity of the X line, implying that energy is released more rapidly during Hall reconnection. Coronal applications are discussed.