Reconnection In Current Sheets Research Articles

In Situ Detection of the Solar Eruption: Lay a Finger on the Sun

This paper is to introduce a proposed deep space mission, which aims to perform in situ detection of the central structure, namely the magnetic reconnection current sheet, which drives the large scale eruption on a star. The main focus of this mission is on the fine physical characteristics of the large scale magnetic reconnection taking place on the Sun, our nearest star, revealing the secret of the most violent energy release process, also known as the solar storm, in the solar system. The scientific goal of this mission, magnetic reconnection, is a kernel process of energy conversion occurring in the magnetized plasma in the universe, and has long been a fairly important research topic or even research area in solar physics, space science, plasma physics, and the related fields. In situ detection enhances the spatial resolution of the instruments used on the Earth 5~20 times, will provide us extra-clear images of the Sun and the related information. We are thus able to study, to learn, and to understand the Sun on an unprecedented platform, and further resolve the long-standing puzzle in the solar community regarding the fine physical property of the kernel process driving the solar eruption, as well as that of the corona heating.

Multi-thermal atmosphere of a mini-solar flare during magnetic reconnection observed with IRIS

Context. The Interface Region Imaging Spectrograph (IRIS) with its high spatial and temporal resolution facilitates exceptional plasma diagnostics of solar chromospheric and coronal activity during magnetic reconnection. Aims. The aim of this work is to study the fine structure and dynamics of the plasma at a jet base forming a mini-flare between two emerging magnetic fluxes (EMFs) observed with IRIS and the Solar Dynamics Observatory instruments. Methods. We proceed to a spatio-temporal analysis of IRIS spectra observed in the spectral ranges of Mg II, C II, and Si IV ions. Doppler velocities from Mg II lines were computed using a cloud model technique. Results. Strong asymmetric Mg II and C II line profiles with extended blue wings observed at the reconnection site (jet base) are interpreted by the presence of two chromospheric temperature clouds: one explosive cloud with blueshifts at 290 km s−1 and one cloud with smaller Doppler shift (around 36 km s−1). Simultaneously at the same location (jet base), strong emission of several transition region lines (e.g. O IV and Si IV), emission of the Mg II triplet lines, and absorption of identified chromospheric lines in Si IV broad profiles have been observed and analysed. Conclusions. Such observations of IRIS line and continuum emissions allow us to propose a stratification model for the white light, mini-flare atmosphere with multiple layers of different temperatures along the line of sight in a reconnection current sheet. It is the first time that we could quantify the fast speed (possibly Alfvénic flows) of cool clouds ejected perpendicularly to the jet direction via the cloud model technique. We conjecture that the ejected clouds come from plasma which was trapped between the two EMFs before reconnection or be caused by chromospheric-temperature (cool) upflow material similar to a surge during reconnection.

Magnetic Reconnection and Hot Spot Formation in Black Hole Accretion Disks

Abstract Hot spots, or plasmoids, which form due to magnetic reconnection in current sheets, are conjectured to power frequent X-ray and near-infrared flares from Sgr A*, the black hole in the center of our Galaxy. It is unclear how, where, and when current sheets form in black hole accretion disks. We perform axisymmetric general-relativistic resistive magnetohydrodynamics simulations to model reconnection and plasmoid formation in a range of accretion flows. Current sheets and plasmoids are ubiquitous features that form regardless of the initial magnetic field in the disk, the magnetization in the quasisteady-state phase of accretion, and the spin of the black hole. Within 10 Schwarzschild radii from the event horizon, we observe plasmoids forming, after which they can merge, grow to macroscopic scales of the order of a few Schwarzschild radii, and are ultimately advected along the jet’s sheath or into the disk. Large plasmoids are energized to relativistic temperatures via reconnection and contribute to the jet’s limb brightening. We find that only hot spots forming in magnetically arrested disks can potentially explain the energetics of Sgr A* flares. The flare period is determined by the reconnection rate, which we find to be between and in all cases, consistent with studies of reconnection in isolated Harris-type current sheets. We quantify magnetic dissipation and nonideal electric fields, which can efficiently inject nonthermal particles. We show that explicit resistivity allows for converged numerical solutions, such that the electromagnetic energy evolution and dissipation become independent of the grid scale for the extreme resolutions considered here.

Measurement of magnetic field and relativistic electrons along a solar flare current sheet

In the standard model of solar flares, a large-scale reconnection current sheet is postulated as the central engine for powering the flare energy release and accelerating particles. However, where and how the energy release and particle acceleration occur remain unclear due to the lack of measurements for the magnetic properties of the current sheet. Here we report the measurement of spatially-resolved magnetic field and flare-accelerated relativistic electrons along a current-sheet feature in a solar flare. The measured magnetic field profile shows a local maximum where the reconnecting field lines of opposite polarities closely approach each other, known as the reconnection X point. The measurements also reveal a local minimum near the bottom of the current sheet above the flare loop-top, referred to as a "magnetic bottle". This spatial structure agrees with theoretical predictions and numerical modeling results. A strong reconnection electric field of ~4000 V/m is inferred near the X point. This location, however, shows a local depletion of microwave-emitting relativistic electrons. These electrons concentrate instead at or near the magnetic bottle structure, where more than 99% of them reside at each instant. Our observations suggest that the loop-top magnetic bottle is likely the primary site for accelerating and/or confining the relativistic electrons.

Microwave Spectral Imaging of an Erupting Magnetic Flux Rope: Implications for the Standard Solar Flare Model in Three Dimensions

Abstract We report microwave spectral imaging observations of an erupting magnetic flux rope during the early impulsive phase of the X8.2-class limb flare on 2017 September 10, obtained by the Expanded Owens Valley Solar Array. A few days prior to the eruption, when viewed against the disk, the flux rope appeared as a reverse S-shaped dark filament along the magnetic polarity inversion line. During the eruption, the rope exhibited a “hot channel” structure in extreme ultraviolet and soft X-ray passbands sensitive to ∼10 MK plasma. The central portion of the flux rope was nearly aligned with the line of sight, which quickly developed into a teardrop-shaped dark cavity during the early phase of the eruption. A long and thin plasma sheet formed below the cavity, interpreted as the reconnection current sheet viewed edge on. A nonthermal microwave source was present at the location of the central current sheet, which extended upward encompassing the dark cavity. A pair of nonthermal microwave sources were observed for several minutes on both sides of the main flaring region. They shared a similar temporal behavior and spectral property to the central microwave source below the cavity, interpreted as the conjugate footpoints of the erupting flux rope. These observations are broadly consistent with the magnetic topology and the associated energy release scenario suggested in the three-dimensional standard model for eruptive solar flares. In particular, our detection of nonthermal emission at conjugate flux rope footpoints provides solid evidence of particle transport along an erupting magnetic flux rope.

Counterstreaming Strahls and Heat Flux Dropouts as Possible Signatures of Local Particle Acceleration in the Solar Wind

Abstract Suprathermal electrons with energies of ∼70 eV and above are observed at 1 au as dispersionless halo electrons and magnetic field-aligned beams of strahls. For a long time, it has been thought that both populations originate only from the solar corona, and that the only active process impacting their properties in the solar wind is scattering. This view has consequently impacted the interpretation of typical patterns of pitch-angle distributions (PADs) of suprathermal electrons. Meanwhile, recent observational studies supported by numerical simulations have shown that there is an unaccounted population of electrons accelerated to suprathermal energies at reconnecting current sheets (RCSs) and 3D dynamical plasmoids (or 2D magnetic islands (MIs)) directly in the heliosphere. We present multispacecraft observations of counterstreaming strahls and heat flux dropouts in PADs within a region filled with plasmoids and RCSs unaffected by interplanetary shocks, comparing observed PAD features with those predicted by particle-in-cell simulations. We show typical PAD patterns determined by local acceleration of thermal-core electrons up to hundreds of electron volts. Resulting PAD views depend on properties and topology of particular RCSs, MIs, and plasma/magnetic field parameters. Our study suggests that solar wind-borne suprathermal electrons coexist with those of solar origin. Therefore, some of heat flux dropout and bidirectional strahl events can be explained by local dynamical processes involving magnetic reconnection. Possible implications of the results for the interpretation of the actively debated decrease in the strahl/halo relative density with heliocentric distance and puzzling features of suprathermal electrons observed at crossings of the heliospheric current sheet and cometary comas are also discussed.

Modeling Observable Differences in Flare Loop Evolution due to Reconnection Location and Current Sheet Structure

Abstract Flare reconnection is expected to occur at some point within a large-scale coronal current sheet. The structure of the magnetic field outside this sheet is almost certain to affect the flare, especially its energy release. Different models for reconnection have invoked different structures for the current sheet’s magnetic field and different locations for the reconnection electric field within it. Models invoking Petschek-type reconnection often use a uniform field. Others invoke a field bounded by two Y-points with a field strength maximum between them and propose this maximum as the site of the reconnection electric field. Still other models, such as the collapsing trap model, require that the field strength peak at or near the edge of the current sheet and propose that reconnection occurs above this peak. At present there is no agreement as to where reconnection might occur within a global current sheet. We study the post-reconnection dynamics under all these scenarios, seeking potentially observable differences between them. We find that reconnection occurring above the point of strongest field leads to the highest density and the highest emission measure of the hottest material. This scenario offers a possible explanation of superhot coronal sources seen in some flares.

Parker Solar Probe In Situ Observations of Magnetic Reconnection Exhausts during Encounter 1

Abstract Magnetic reconnection in current sheets converts magnetic energy into particle energy. The process may play an important role in the acceleration and heating of the solar wind close to the Sun. Observations from Parker Solar Probe (PSP) provide a new opportunity to study this problem, as it measures the solar wind at unprecedented close distances to the Sun. During the first orbit, PSP encountered a large number of current sheets in the solar wind through perihelion at 35.7 solar radii. We performed a comprehensive survey of these current sheets and found evidence for 21 reconnection exhausts. These exhausts were observed in heliospheric current sheets, coronal mass ejections, and regular solar wind. However, we find that the majority of current sheets encountered around perihelion, where the magnetic field was strongest and plasma β was lowest, were Alfvénic structures associated with bursty radial jets, and these current sheets did not appear to be undergoing local reconnection. We examined conditions around current sheets to address why some current sheets reconnected while others did not. A key difference appears to be the degree of plasma velocity shear across the current sheets: the median velocity shear for the 21 reconnection exhausts was 24% of the Alfvén velocity shear, whereas the median shear across 43 Alfvénic current sheets examined was 71% of the Alfvén velocity shear. This finding could suggest that large, albeit sub-Alfvénic, velocity shears suppress reconnection. An alternative interpretation is that the Alfvénic current sheets are isolated rotational discontinuities that do not undergo local reconnection.

<em>In situ</em> evidence of resonant interactions between energetic electrons and whistler waves in magnetopause reconnection

In this paper, we analyze one reconnection event observed by the Magnetospheric Multiscale (MMS) mission at the earth’s magnetopause. In this event, the spacecraft crossed the reconnection current sheet from the magnetospheric side to the magnetosheath side, and whistler waves were observed on both the magnetospheric and magnetosheath sides. On the magnetospheric side, the whistler waves propagated quasi-parallel to the magnetic field and toward the X-line, while on the magnetosheath side they propagated almost anti-parallel to the magnetic field and away from the X-line. Associated with the enhancement of the whistler waves, we find that the fluxes of energetic electrons are concentrated around the pitch angle 90° when their energies are higher than the minimum energy that is necessary for the resonant interactions between the energetic electrons and whistler waves. This observation provides in situ observational evidence of resonant interactions between energetic electrons and whistler waves in the magnetic reconnection.

Particle acceleration in coalescent and squashed magnetic islands

Aims. Magnetic reconnection in large Harris-type reconnecting current sheets (RCSs) with a single X-nullpoint often leads to the occurrence of magnetic islands with multiple O- and X-nullpoints. Over time these magnetic islands become squashed, or coalescent with two islands merging, as has been observed indirectly during coronal mass ejection and by in-situ observations in the heliosphere and magnetotail. These points emphasise the importance of understanding the basic energising processes of ambient particles dragged into current sheets with magnetic islands of different configuration. Methods. Trajectories of protons and electrons accelerated by a reconnection electric field are investigated using a test particle approach in RCSs with different 3D magnetic field topologies defined analytically for multiple X- and O-nullpoints. Trajectories, densities, and energy distributions are explored for 106 thermal particles dragged into the current sheets from different sides and distances. Results. This study confirms that protons and electrons accelerated in magnetic islands in the presence of a strong guiding field are ejected from a current sheet into the opposite semiplanes with respect to the midplane. Particles are found to escape O-nullpoints only through the neighbouring X-nullpoints along (not across) the midplane following the separation law for electrons and protons in a given magnetic topology. Particles gain energy either inside O-nullpoints or in the vicinity of X-nullpoints that often leads to electron clouds formed about the X-nullpoint between the O-nullpoints. Electrons are shown to be able to gain sub-relativistic energies in a single magnetic island. Energy spectra of accelerated particles are close to power laws with spectral indices varying from 1.1 to 2.4. The more squashed the islands the larger the difference between the energy gains by transit and bounced particles, which leads to their energy spectra having double maxima that gives rise to fast-growing turbulence. Conclusions. Particles are shown to gain the most energy in multiple X-nullpoints between O-nullpoints (or magnetic islands). This leads to the formation of electron clouds between magnetic islands. Particle energy gains are much larger in squashed islands than in coalescent ones. In summary, particle acceleration by a reconnection electric field in magnetic islands is much more effective than in an RCS with a single X-nullpoint.

Onset of Secondary Instabilities and Plasma Heating during Magnetic Reconnection in Strongly Magnetized Regions of the Low Solar Atmosphere

Abstract We numerically study magnetic reconnection on different spatial scales and at different heights in the weakly ionized plasma of the low solar atmosphere (around 300–800 km above the solar surface) within a reactive 2.5D multifluid plasma–neutral model. We consider a strongly magnetized plasma (β ∼ 6%) evolving from a force-free magnetic configuration and perturbed to initialize formation of a reconnection current sheet. On large scales, the resulting current sheets are observed to undergo a secondary “plasmoid” instability. A series of simulations at different scales demonstrates a cascading current sheet formation process that terminates for current sheets with width of 2 m and length of ∼100 m, corresponding to the critical current sheet aspect ratio of ∼50. We also observe that the plasmoid instability is the primary physical mechanism accelerating the magnetic reconnection in this plasma parameter regime. After plasmoid instabilities appear, the reconnection rate sharply increases to a value of ∼0.035, observed to be independent of the Lundquist number. These characteristics are very similar to magnetic reconnection in fully ionized plasmas. In this low-β guide-field reconnection regime, both the recombination and collisionless effects are observed to have a small contribution to the reconnection rate. The simulations show that it is difficult to heat the dense weakly ionized photospheric plasmas to above 2 × 104 K during the magnetic reconnection process. However, the plasmas in the low solar chromosphere can be heated above 3 × 104 K with reconnection magnetic fields of 500 G or stronger.

Numerical study of the cascading energy conversion of the reconnection current sheet in solar eruptions

Magnetic reconnection plays an important role in the energy conversion during solar eruptions. In this work, we present a resistive magnetohydrodynamical study (2.5D) of a flux rope eruption based on the Lin and Forbes model regarding cascading reconnection. We use a second-order Godunov scheme code, to better understand the physical mechanisms responsible for high reconnection rates and the internal structure, particularly in chaotic or turbulent regions, of the coronal mass ejection (CME)/flare current sheet (CS). Two sets of simulations with Lundquist numbers of 1.18 x 10(5) and 2.35 x 10(5) in the vicinity of the CS, generating a slow CME and a moderate one, show global dynamic features largely consistent with the flare model. Looking into the fine structure of the CS, magnetic reconnection employs simultaneously the Sweet-Parker mode and time-dependent small-scale Petschek patterns in the early stage. As the flux rope rises, the outflow region becomes turbulent, which further enhances the reconnection rates. Our results show that coalescence and fusion processes of plasmoids provide a large number of small, transient local diffusion regions to dissipate magnetic energy, and confirm that the dissipation starts at macro-MHD scales rather than ion inertial lengths. The two runs have the same range of the local reconnection rates (10(-4)-0.3) relevant to CMEs. The fast rates are closely proportional to the square of the aspect ratio of multiple small-scale CSs. The topology of the magnetic field and the turbulence spectrum of the energy cascade are statistically addressed as well.

Reflection of Fast Magnetosonic Waves near a Magnetic Reconnection Region.

Magnetic reconnection in the solar corona is thought to be unstable with the formation of multiple interacting plasmoids, and previous studies have shown that plasmoid dynamics can trigger MHD waves of different modes propagating outward from the reconnection site. However, variations in plasma parameters and magnetic field strength in the vicinity of a coronal reconnection site may lead to wave reflection and mode conversion. In this paper we investigate the reflection and refraction of fast magnetoacoustic waves near a reconnection site. Under a justified assumption of an analytically specified Alfvén speed profile, we derive and solve analytically the full wave equation governing the propagation of fast-mode waves in a non-uniform background plasma without recourse to the small wavelength approximation. We show that the waves undergo reflection near the reconnection current sheet due to the Alfvén speed gradient and that the reflection efficiency depends on the plasma-β parameter, as well as on the wave frequency. In particular, we find that waves are reflected more efficiently near reconnection sites in a low-β plasma, which is typical under solar coronal conditions. Also, the reflection is larger for lower-frequency waves while high-frequency waves propagate outward from the reconnection region almost without the reflection. We discuss the implications of efficient wave reflection near magnetic reconnection sites in strongly magnetized coronal plasma for particle acceleration, and also the effect this might have on first ionization potential (FIP) fractionation by the ponderomotive force of these waves in the chromosphere.

Reconnection in the Post-impulsive Phase of Solar Flares

Abstract Using a recently developed analytical procedure, we determine the rate of magnetic reconnection in the “standard” model of eruptive solar flares. During the late phase, the neutral line is located near the lower tip of the reconnection current sheet, and the upper region of the current sheet is bifurcated into a pair of Petschek-type shocks. Despite the presence of these shocks, the reconnection rate remains slow if the resistivity is uniform and the flow is laminar. Fast reconnection is achieved only if there is some additional mechanism that can shorten the length of the diffusion region at the neutral line. Observations of plasma flows by the X-ray telescope on Hinode imply that the diffusion region is, in fact, quite short. Two possible mechanisms for reducing the length of the diffusion region are localized resistivity and MHD turbulence.

Electron magnetic reconnection without ion coupling in Earth's turbulent magnetosheath.

Magnetic reconnection in current sheets is a magnetic-to-particle energy conversion process that is fundamental to many space and laboratory plasma systems. In the standard model of reconnection, this process occurs in a minuscule electron-scale diffusion region1,2. On larger scales, ions couple to the newly reconnected magnetic-field lines and are ejected away from the diffusion region in the form of bi-directional ion jets at the ion Alfvén speed3-5. Much of the energy conversion occurs in spatially extended ion exhausts downstream of the diffusion region 6 . In turbulent plasmas, which contain a large number of small-scale current sheets, reconnection has long been suggested to have a major role in the dissipation of turbulent energy at kinetic scales7-11. However, evidence for reconnection plasma jetting in small-scale turbulent plasmas has so far been lacking. Here we report observations made in Earth's turbulent magnetosheath region (downstream of the bow shock) of an electron-scale current sheet in which diverging bi-directional super-ion-Alfvénic electron jets, parallel electric fields and enhanced magnetic-to-particle energy conversion were detected. Contrary to the standard model of reconnection, the thin reconnecting current sheet was not embedded in a wider ion-scale current layer and no ion jets were detected. Observations of this and other similar, but unidirectional, electron jet events without signatures of ion reconnection reveal a form of reconnection that can drive turbulent energy transfer and dissipation in electron-scale current sheets without ion coupling.

Unambiguous Evidence of Filament Splitting-induced Partial Eruptions

Abstract Coronal mass ejections are often considered to result from the full eruption of a magnetic flux rope (MFR). However, it is recognized that, in some events, the MFR may release only part of its flux, with the details of the implied splitting not completely established due to limitations in observations. Here, we investigate two partial eruption events including a confined and a successful one. Both partial eruptions are a consequence of the vertical splitting of a filament-hosting MFR involving internal reconnection. A loss of equilibrium in the rising part of the magnetic flux is suggested by the impulsive onset of both events and by the delayed onset of reconnection in the confined event. The remaining part of the flux might be line-tied to the photosphere in a bald patch (BP) separatrix surface, and we confirm the existence of extended BP sections for the successful eruption. The internal reconnection is signified by brightenings in the body of one filament and between the rising and remaining parts of both filaments. It evolves quickly into the standard current sheet reconnection in the wake of the eruption. As a result, regardless of being confined or successful, both eruptions produce hard X-ray sources and flare loops below the erupting but above the surviving flux, as well as a pair of flare ribbons enclosing the latter.

The Properties of Reconnection Current Sheets in GRMHD Simulations of Radiatively Inefficient Accretion Flows

Abstract Non-ideal magnetohydrodynamic (MHD) effects may play a significant role in determining the dynamics, thermal properties, and observational signatures of radiatively inefficient accretion flows onto black holes. In particular, particle acceleration during magnetic reconnection events may influence black hole spectra and flaring properties. We use representative general relativistic magnetohydrodynamic (GRMHD) simulations of black hole accretion flows to identify and explore the structures and properties of current sheets as potential sites of magnetic reconnection. In the case of standard and normal evolution (SANE) disks, we find that in the reconnection sites, the plasma beta ranges from 0.1 to 1000, the magnetization ranges from 10−4 to 1, and the guide fields are weak compared with the reconnecting fields. In magnetically arrested (MAD) disks, we find typical values for plasma beta from 10−2 to 103, magnetizations from 10−3 to 10, and typically stronger guide fields, with strengths comparable to or greater than the reconnecting fields. These are critical parameters that govern the electron energy distribution resulting from magnetic reconnection and can be used in the context of plasma simulations to provide microphysics inputs to global simulations. We also find that ample magnetic energy is available in the reconnection regions to power the fluence of bright X-ray flares observed from the black hole in the center of the Milky Way.

Magnetic Reconnection in Strongly Magnetized Regions of the Low Solar Chromosphere

Abstract Magnetic reconnection in strongly magnetized regions around the temperature minimum region of the low solar atmosphere is studied by employing MHD-based simulations of a partially ionized plasma within a reactive 2.5D multi-fluid model. It is shown that in the absence of magnetic nulls in a low β plasma, the ionized and neutral fluid flows are well-coupled throughout the reconnection region. However, non-equilibrium ionization–recombination dynamics play a critical role in determining the structure of the reconnection region, leading to much lower temperature increases and a faster magnetic reconnection rate as compared to simulations that assume plasma to be in ionization–recombination equilibrium. The rate of ionization of the neutral component of the plasma is always faster than recombination within the current sheet region even when the initial plasma β is as high as . When the reconnecting magnetic field is in excess of a kilogauss and the plasma β is lower than 0.0145, the initially weakly ionized plasmas can become fully ionized within the reconnection region and the current sheet can be strongly heated to above K, even as most of the collisionally dissipated magnetic energy is radiated away. The Hall effect increases the reconnection rate slightly, but in the absence of magnetic nulls it does not result in significant asymmetries or change the characteristics of the reconnection current sheet down to meter scales.

Quasi-periodic Oscillations in Flares and Coronal Mass Ejections Associated with Magnetic Reconnection

Abstract We propose a mechanism for quasi-periodic oscillations of both coronal mass ejections (CMEs) and flare loops as related to magnetic reconnection in eruptive solar flares. We perform two-dimensional numerical MHD simulations of magnetic flux rope eruption, with three different values of the global Lundquist number. In the low Lundquist number run, no oscillatory behavior is found. In the moderate Lundquist number run, on the other hand, quasi-periodic oscillations are excited both at the bottom of the flux rope and at the flare loop top. In the high Lundquist number run, quasi-periodic oscillations are also excited; in the meanwhile, the dynamics become turbulent owing to the formation of multiple plasmoids in the reconnection current sheet. In high and moderate Lundquist number runs, thin reconnection jets collide with the flux rope bottom or flare loop top and dig them deeply. Steep oblique shocks are formed as termination shocks where reconnection jets are bent (rather than decelerated) in the horizontal direction, resulting in supersonic backflows. The structure becomes unstable, and quasi-periodic oscillations of supersonic backflows appear at locally confined high-beta regions at both the flux rope bottom and flare loop top. We compare the observational characteristics of quasi-periodic oscillations in erupting flux ropes, post-CME current sheets, flare ribbons, and light curves with corresponding dynamical structures found in our simulation.

Double Hall instability: A catalyzer of magnetic energy release

A pictorial explanation for shear-Hall instability is suggested and shows that the shear flow is not necessary for the instability because its role can be played by the Hall effect of an inhomogeneous background magnetic field. Linear stability analysis for a simple model of magnetic field varying periodically in space confirms such a 'double Hall' instability. Numerical computations show a considerable increase in Ohmic dissipation rate at the nonlinear stage of instability development. Field dissipation has a spiky character associated with magnetic reconnection in current sheets and X-points. Double Hall instability can be significant for magnetic field dissipation in neutron star crusts and, possibly, in the solar corona.