Slow-mode Shocks Research Articles

Magnetohydrodynamic Perspective on the Disappearance of Mercury’s Bow Shock by Helios Data Exploration

In the magnetohydrodynamic (MHD) perspective, the planet’s bow shock would disappear when the fast-mode Mach number (M F) of the solar wind is less than one. Compared to Earth, Mercury is subject to a lower M F solar wind due to its proximity to the Sun, resulting in a higher possibility of the disappearance of its bow shock. To examine the variability of Mercury’s bow shock in response to the solar wind properties, analyses of the observations by the Helios spacecraft at 0.30–0.50 au during 1975–1983, covering solar cycle 21, together with the theoretical solutions and MHD simulations are conducted in this study. Our observational analyses show that more solar wind data with extremely low fast-mode Mach numbers (say, M F ≤ 1.5) are observed during the rising and maximum phases and are characterized by a significantly low proton number density. It is also found that approximately 35% of the extremely low fast-mode Mach number solar wind events (M F ≤ 1.5) occur within the main body of interplanetary coronal mass ejections (ICMEs), while about 58% of them are unrelated to ICMEs. Three of these events are selected to demonstrate that the occurrences of the solar wind with M F ≤ 1.5 may not be necessarily affected by ICMEs. Our theoretical and numerical results indicate that when Mercury encounters the solar wind with M F ≤ 1.5, its bow shock would move farther away, become flattened, and even disappear. Furthermore, our calculations suggest that Mercury’s bow shock would become a slow-mode shock with a concave-upward structure under such extreme solar wind conditions.

Change of Spectral Properties of Magnetic Field Fluctuations across Different Types of Interplanetary Shocks

The interaction between interplanetary (IP) shocks and the solar wind has been studied in the past for the understanding of energy dissipation mechanisms within collisionless plasmas. Compared to the study of fast shocks, other types of IP shocks, including slow mode shocks (i.e., fast forward, fast reverse, slow forward, and slow reverse shocks) remained largely unnoticed. We analyze magnetic field fluctuations observed by the Wind spacecraft from 1995 to 2021 upstream and downstream of the IP shocks using a continuous wavelet transform. The evolution of spectral indices in the ion inertial and transition ranges and the changes in distributions of characteristic ion length scales with respect to the spectral break and proton beta are presented. We found that spectral indices in both inertial and transition ranges and the characteristic length scale distributions are statistically conserved across three types of IP shocks, suggesting that mechanisms associated with the energy dissipation are unaffected by the shocks. The results obtained for the transition range of fast reverse shocks show a larger difference between upstream and downstream plasmas and this will be further studied.

Partially ionized two-fluid shocks with collisional and radiative ionization and recombination – multilevel hydrogen model

ABSTRACT Explosive phenomena are known to trigger a wealth of shocks in warm plasma environments, including the solar chromosphere and molecular clouds where the medium consists of both ionized and neutral species. Partial ionization is critical in determining the behaviour of shocks, since the ions and neutrals locally decouple, allowing for substructure to exist within the shock. Accurately modelling partially ionized shocks requires careful treatment of the ionized and neutral species, and their interactions. Here we study a partially ionized switch-off slow-mode shock using a multilevel hydrogen model with both collisional and radiative ionization and recombination rates that are implemented into the two-fluid (PIP) code, and study physical parameters that are typical of the solar chromosphere. The multilevel hydrogen model differs significantly from magnetohydrodynamic (MHD) solutions due to the macroscopic thermal energy loss during collisional ionization. In particular, the plasma temperature both post-shock and within the finite-width is significantly cooler that the post-shock MHD temperature. Furthermore, in the mid to lower chromosphere, shocks feature far greater compression than their single-fluid MHD analogues. The decreased temperature and increased compression reveal the importance of non-equilibrium ionized in the thermal evolution of shocks in partially ionized media. Since partially ionized shocks are not accurately described by the Rankine-Hugoniot shock jump conditions, it may be incorrect to use these to infer properties of lower atmospheric shocks.

Nonequilibrium Ionization Modeling of Petschek-type Shocks in Reconnecting Current Sheets in Solar Eruptions

Nonequilibrium ionization (NEI) is essentially required for astrophysical plasma diagnostics once the plasma status departs from the assumption of ionization equilibrium. In this work, we perform fast NEI calculations combined with magnetohydrodynamic (MHD) simulations and analyze the ionization properties of a Petschek-type magnetic reconnection current sheet during solar eruptions. Our simulation reveals Petschek-type slow-mode shocks in the classical Spitzer thermal conduction models and conduction flux-limitation situations. The results show that under-ionized features can be commonly found in shocked reconnection outflows and thermal halo regions outside the shocks. The departure from equilibrium ionization strongly depends on plasma density. In addition, this departure is sensitive to the observable target temperature: the high-temperature iron ions are strongly affected by the effects of NEI. The under-ionization also affects the synthetic SDO/AIA intensities, which indicates that the reconstructed hot reconnection current sheet structure may be significantly underestimated either for temperature or apparent width. We also perform an MHD-NEI analysis on the reconnection current sheet in the classical solar flare geometry. Finally, we show the potential reversal between the under-ionized and over-ionized states at the lower tip of reconnection current sheets where the downward outflow collides with closed magnetic loops, which can strongly affect multiple SDO/AIA band ratios along the reconnection current sheet.

Numerical simulations of the laser-driven Petschek-type magnetic reconnection

This paper describes a numerical study of the magnetic reconnection between two magnetic fields of opposite polarity. The magnetic fields are created by an electric current in a coil connected to two metal disks. One of the disks is irradiated by a strong laser beam, whereby large amounts of free electrons flow toward the other disk, constituting a closed circuit for the electric current flowing through the coil. Two parallel coils are arranged to connect the two disks, and irradiation of the laser beam on one disk results in parallel electric currents in the two coils, inducing two magnetic fields of opposite polarity in the region between them. The magnetic reconnection that occurs in this region is three-dimensional. This three-dimensional magnetic reconnection is investigated via magnetohydrodynamic numerical simulations. The characteristics of the Petschek-type magnetic reconnection are observed for the first time in such numerical simulations of magnetic reconnection. Changes in the shape of the magnetic field lines form the boundary of the dissipation region and the outflow region. Moreover, the thermal plasma generated by reconnection is strongly confined to the region where the reconnecting current sheet and the slow-mode shock are located, and no leaks of thermal plasma are observed. Comparisons with existing laboratory experiment results confirm that our numerical simulations reproduce the experimental outcomes and provide reasonable explanations for the results observed in laboratories.

Coronal Mass Ejection Deformation at 0.1 au Observed by WISPR

Although coronal mass ejections (CMEs) resembling flux ropes generally expand self-similarly, deformations along their fronts have been reported in observations and simulations. We present evidence of one CME becoming deformed after a period of self-similar expansion in the corona. The event was observed by multiple white-light imagers on 2021 January 20–22. The change in shape is evident in observations from the heliospheric imagers from the Wide-Field Imager for Solar Probe Plus (WISPR), which observed this CME for ∼44 hr. We reconstruct the CME using forward-fitting models. In the first hours, observations are consistent with a self-similar expansion, but later on the front flattens, forming a dimple. Our interpretation is that the CME becomes deformed at ∼0.1 au owing to differences in the background solar wind speeds. The CME expands more at higher latitudes, where the background solar wind is faster. We consider other possible causes for deformations, such as loss of coherence and slow-mode shocks. The CME deformation seems to cause a time-of-arrival error of 16 hr at ∼0.5 au. The deformation is clear only in the WISPR observations; thus, it would have been missed by 1 au coronagraphs. Such deformations may help explain the time-of-arrival errors in events where only coronagraph observations are available.

Stability of two-fluid partially ionized slow-mode shock fronts

ABSTRACT A magnetohydrodynamic (MHD) shock front can be unstable to the corrugation instability, which causes a perturbed shock front to become increasingly corrugated with time. An ideal MHD parallel shock (where the velocity and magnetic fields are aligned) is unconditionally unstable to the corrugation instability, whereas the ideal hydrodynamic (HD) counterpart is unconditionally stable. For a partially ionized medium (for example, the solar chromosphere), both HD and MHD species coexist and the stability of the system has not been studied. In this paper, we perform numerical simulations of the corrugation instability in two-fluid partially ionized shock fronts to investigate the stability conditions, and compare the results to HD and MHD simulations. Our simulations consist of an initially steady two-dimensional parallel shock encountering a localized upstream density perturbation. In MHD, this perturbation results in an unstable shock front and the corrugation grows with time. We find that for the two-fluid simulation, the neutral species can act to stabilize the shock front. A parameter study is performed to analyse the conditions under which the shock front is stable and unstable. We find that for very weakly coupled or very strongly coupled partially ionized system the shock front is unstable, as the system tends towards MHD. However, for a finite coupling, we find that the neutrals can stabilize the shock front, and produce new features including shock channels in the neutral species. We derive an equation that relates the stable wavelength range to the ion-neutral and neutral-ion coupling frequencies and the Mach number. Applying this relation to umbral flashes gives an estimated range of stable wavelengths between 0.6 and 56 km.

Collisional ionisation, recombination, and ionisation potential in two-fluid slow-mode shocks: Analytical and numerical results

Context.Shocks are a universal feature of warm plasma environments, such as the lower solar atmosphere and molecular clouds, which consist of both ionised and neutral species. Including partial ionisation leads to the existence of a finite width for shocks, where the ionised and neutral species decouple and recouple. As such, drift velocities exist within the shock that lead to frictional heating between the two species, in addition to adiabatic temperature changes across the shock. The local temperature enhancements within the shock alter the recombination and ionisation rates and hence change the composition of the plasma.Aims.We study the role of collisional ionisation and recombination in slow-mode partially ionised shocks. In particular, we incorporate the ionisation potential energy loss and analyse the consequences of having a non-conservative energy equation.Methods.A semi-analytical approach is used to determine the possible equilibrium shock jumps for a two-fluid model with ionisation, recombination, ionisation potential, and arbitrary heating. Two-fluid numerical simulations are performed using the (PIP) code. Results are compared to the magnetohydrodynamic (MHD) model and the semi-analytic solution.Results.Accounting for ionisation, recombination, and ionisation potential significantly alters the behaviour of shocks in both substructure and post-shock regions. In particular, for a given temperature, equilibrium can only exist for specific densities due to the radiative losses needing to be balanced by the heating function. A consequence of the ionisation potential is that a compressional shock will lead to a reduction in temperature in the post-shock region, rather than the increase seen for MHD. The numerical simulations pair well with the derived analytic model for shock velocities.Conclusion.Multi-fluid effects can lead to a significant departure from MHD results. The results in this paper are applicable to a wide range of partially ionised plasmas, including the solar chromosphere and molecular clouds.

The Formation and Dissipation of Current Sheets and Shocks due to Compressive Waves in a Stratified Atmosphere Containing a Magnetic Null

We study the propagation and dissipation of magnetohydrodynamic waves in a set of numerical models that each include a solar--like stratified atmosphere and a magnetic field with a null point. All simulations have the same magnetic field configuration but different transition region heights. Compressive wave packets introduced in the photospheric portion of the simulations refract towards the null and collapse it into a current sheet, which then undergoes reconnection. The collapsed null forms a current sheet due to a strong magnetic pressure gradient caused by the inability of magnetic perturbations to cross the null. Although the null current sheet undergoes multiple reconnection episodes due to repeated reflections off the lower boundary, we find no evidence of oscillatory reconnection arising from the dynamics of the null itself. Wave mode conversion around the null generates a series of slow mode shocks localized near each separatrix. The shock strength is asymmetric across each separatrix, and subsequent shock damping therefore creates a tangential discontinuity across each separatrix, with long--lived current densities. A parameter study of the injected wave energy to reach the null confirms our previous WKB estimates. Finally, using current estimates of the photospheric acoustic power, we estimate that the shock and Ohmic heating we describe may account for $\approx1-10\%$ of the radiative losses from coronal bright points with similar topologies, and are similarly insufficient to account for losses from larger structures such as ephemeral regions. At the same time, the dynamics are comparable to proposed mechanisms for generating type--II spicules.

Intermediate shock sub-structures within a slow-mode shock occurring in partially ionised plasma

Context. Slow-mode shocks are important in understanding fast magnetic reconnection, jet formation and heating in the solar atmosphere, and other astrophysical systems. The atmospheric conditions in the solar chromosphere allow both ionised and neutral particles to exist and interact. Under such conditions, fine sub-structures exist within slow-mode shocks due to the decoupling and recoupling of the plasma and neutral species. Aims. We study numerically the fine sub-structure within slow-mode shocks in a partially ionised plasma, in particular, analysing the formation of an intermediate transition within the slow-mode shock. Methods. High-resolution 1D numerical simulations were performed using the (PIP) code using a two-fluid approach. Results. We discover that long-lived intermediate (Alfvén) shocks can form within the slow-mode shock, where there is a shock transition from above to below the Alfvén speed and a reversal of the magnetic field across the shock front. The collisional coupling provides frictional heating to the neutral fluid, resulting in a Sedov-Taylor-like expansion with overshoots in the neutral velocity and neutral density. The increase in density results in a decrease of the Alfvén speed and with this the plasma inflow is accelerated to above the Alfvén speed within the finite width of the shock leading to the intermediate transition. This process occurs for a wide range of physical parameters and an intermediate shock is present for all investigated values of plasma-β, neutral fraction, and magnetic angle. As time advances the magnitude of the magnetic field reversal decreases since the neutral pressure cannot balance the Lorentz force. The intermediate shock is long-lived enough to be considered a physical structure, independent of the initial conditions. Conclusions. Intermediate shocks are a physical feature that can exist as shock sub-structure for long periods of time in partially ionised plasma due to collisional coupling between species.

Intermittency in Solar Wind Turbulence From Fluid to Kinetic Scales

Solar wind is a highly turbulent medium exhibiting fluctuations ranging from the solar sidereal rotation period to proton and electron gyroperiods. Their amplitudes show remarkable scalings with frequency across more than seven decades, suggesting a self‐similar nature for these fluctuations. However, these fluctuations are not globally scale invariant and require a multifractal approach. Multifractality is closely related to intermittency, a phenomenon that has been studied in the solar wind for more than three decades. We now have a rather complete picture of the nature of the most intermittent events and the radial/latitudinal dependence of this phenomenon in the heliosphere. Parallel shocks, slow mode shocks or tangential discontinuities/current sheets identified as the border between adjacent flux tubes are the most intermittent structures within the low‐frequency turbulence. It is more complicated and fascinating to understand the nature of intermittent events at kinetic scales since they are directly related to dissipative phenomena and might be the key to understanding the dissipation mechanisms in the collisionless solar wind plasma. Unfortunately, we still do not have adequate plasma observations at kinetic scales to work on, but several studies, mostly numeric, have addressed this topic suggesting that discontinuities, small‐scale current sheets, and sites which are candidates for reconnection events might be regions where dissipative phenomena are at work with consequent plasma heating and acceleration. This review is intended to provide the reader with a quick overview on the past and most recent understanding of intermittency phenomenon in the solar wind from fluid to kinetic scales.

Multi-Scale Kinetic Simulation of Magnetic Reconnection With Dynamically Adaptive Meshes

Magnetic reconnection is essentially a multi-scale phenomenon, driven by kinetic process in microscopic region and enabling explosive energy conversion from magnetic field energy to plasma kinetic energy in large area. It has been poorly understood how the kinetic process around the x-line connects to the magnetohydrodynamics (MHD) scale process in the reconnection downstream region. The present study has investigated the energy conversion process in the region far downstream of the x-line, by means of the particle-in-cell (PIC) simulation with the adaptive mesh refinement (AMR). The AMR-PIC model enables efficient kinetic simulation of multi-scale phenomena using dynamically adaptive meshes. It is found that the ion energy gain dominates in the reconnection region and is carried out mainly in the exhaust center rather than the exhaust boundaries. The simulation results suggest that the energy conversion process in collisionless magnetic reconnection is significantly different from that in the MHD reconnection model in which most energy conversion occurs at slow mode shocks formed at the exhaust boundaries.

Surge-like Oscillations above Sunspot Light Bridges Driven by Magnetoacoustic Shocks

Abstract High-resolution observations of the solar chromosphere and transition region often reveal surge-like oscillatory activities above sunspot light bridges (LBs). These oscillations are often interpreted as intermittent plasma jets produced by quasi-periodic magnetic reconnection. We have analyzed the oscillations above an LB in a sunspot using data taken by the Interface Region Imaging Spectrograph. The chromospheric 2796 Å images show surge-like activities above the entire LB at any time, forming an oscillating wall. Within the wall we often see that the core of the Mg ii k 2796.35 Å line first experiences a large blueshift, and then gradually decreases to zero shift before increasing to a redshift of comparable magnitude. Such a behavior suggests that the oscillations are highly nonlinear and likely related to shocks. In the 1400 Å passband, which samples emission mainly from the Si iv ion, the most prominent feature is a bright oscillatory front ahead of the surges. We find a positive correlation between the acceleration and maximum velocity of the moving front, which is consistent with numerical simulations of upward propagating slow-mode shock waves. The Si iv 1402.77 Å line profile is generally enhanced and broadened in the bright front, which might be caused by turbulence generated through compression or by the shocks. These results, together with the fact that the oscillation period stays almost unchanged over a long duration, lead us to propose that the surge-like oscillations above LBs are caused by shocked p-mode waves leaked from the underlying photosphere.

A RECONNECTION-DRIVEN MODEL OF THE HARD X-RAY LOOP-TOP SOURCE FROM FLARE 2004 FEBRUARY 26

ABSTRACT A compact X-class flare on 2004 February 26 showed a concentrated source of hard X-rays at the tops of the flare’s loops. This was analyzed in previous work and interpreted as plasma heated and compressed by slow magnetosonic shocks (SMSs) generated during post-reconnection retraction of the flux. That work used analytic expressions from a thin flux tube (TFT) model, which neglected many potentially important factors such as thermal conduction and chromospheric evaporation. Here we use a numerical solution of the TFT equations to produce a more comprehensive and accurate model of the same flare, including those effects previously omitted. These simulations corroborate the prior hypothesis that slow-mode shocks persist well after the retraction has ended, thus producing a compact, loop-top source instead of an elongated jet, as steady reconnection models predict. Thermal conduction leads to densities higher than analytic estimates had predicted, and evaporation enhances the density still higher, but at lower temperatures. X-ray light curves and spectra are synthesized by convolving the results from a single TFT simulation with the rate at which flux is reconnected, as measured through motion of flare ribbons, for example. These agree well with light curves observed by RHESSI and GOES and spectra from RHESSI. An image created from a superposition of TFT model runs resembles one produced from RHESSI observations. This suggests that the HXR loop-top source, at least the one observed in this flare, could be the result of SMSs produced in fast reconnection models like Petschek’s.

HEATING MECHANISMS IN THE LOW SOLAR ATMOSPHERE THROUGH MAGNETIC RECONNECTION IN CURRENT SHEETS

ABSTRACT We simulate several magnetic reconnection processes in the low solar chromosphere/photosphere; the radiation cooling, heat conduction and ambipolar diffusion are all included. Our numerical results indicate that both the high temperature (≳8 × 104 K) and low temperature (∼104 K) magnetic reconnection events can happen in the low solar atmosphere (100–600 km above the solar surface). The plasma β controlled by plasma density and magnetic fields is one important factor to decide how much the plasma can be heated up. The low temperature event is formed in a high β magnetic reconnection process, Joule heating is the main mechanism to heat plasma and the maximum temperature increase is only several thousand Kelvin. The high temperature explosions can be generated in a low β magnetic reconnection process, slow and fast-mode shocks attached at the edges of the well developed plasmoids are the main physical mechanisms to heat the plasma from several thousand Kelvin to over 8 × 104 K. Gravity in the low chromosphere can strongly hinder the plasmoid instability and the formation of slow-mode shocks in a vertical current sheet. Only small secondary islands are formed; these islands, however, are not as well developed as those in the horizontal current sheets. This work can be applied to understand the heating mechanism in the low solar atmosphere and could possibly be extended to explain the formation of common low temperature Ellerman bombs (∼104 K) and the high temperature Interface Region Imaging Spectrograph (IRIS) bombs (≳8 × 104) in the future.

The formation and evolution of reconnection-driven, slow-mode shocks in a partially ionised plasma

The role of slow-mode MHD shocks in magnetic reconnection is one of great importance for energy conversion and transport, but in many astrophysical plasmas the plasma is not fully ionised. In this paper, we investigate, using numerical simulations, the role of collisional coupling between a proton-electron charge-neutral fluid and a neutral hydrogen fluid for the 1D Riemann problem initiated in a constant pressure and density background state by a discontinuity in the magnetic field. This system, in the MHD limit, is characterised by two waves: a fast-mode rarefaction wave that drives a flow towards a slow-mode MHD shock. The system evolves through four stage: initiation, weak coupling, intermediate coupling and a quasi steady state. The initial stages are characterised by an over-pressured neutral region that expands with characteristics of a blast wave. In the later stages, the system tends towards a self-similar solution where the main drift velocity is concentrated in the thin region of the shock front. Due to the nature of the system, the neutral fluid is overpressured by the shock when compared to a purely hydrodynamic shock which results in the neutral fluid expanding to form the shock precursor. The thickness of the shockfront once it has formed proportional to the ionisation fraction to the power -1.2, which is a smaller exponent than would be naively expected from simple scaling arguments. One interesting result is that the shock front is a continuous transition of the physical variables for sub-sonic velocity upstream of the shock front (a c-shock) to a sharp jump in the physical variables followed by a relaxation to the downstream values for supersonic upstream velocity (a j-shock). The frictional heating that results from the velocity drift across the shock front can amount to approximately two per cent of the reference magnetic energy.

Ion and electron dynamics generating the Hall current in the exhaust far downstream of the reconnection x-line

We have investigated the ion and electron dynamics generating the Hall current in the reconnection exhaust far downstream of the x-line where the exhaust width is much larger than the ion gyro-radius. A large-scale particle-in-cell simulation shows that most ions are accelerated through the Speiser-type motion in the current sheet formed at the center of the exhaust. The transition layers formed at the exhaust boundary are not identified as slow mode shocks. (The layers satisfy mostly the Rankine-Hugoniot conditions for a slow mode shock, but the energy conversion hardly occurs there.) We find that the ion drift velocity is modified around the layer due to a finite Larmor radius effect. As a result, the ions are accumulated in the downstream side of the layer, so that collimated ion jets are generated. The electrons experience two steps of acceleration in the exhaust. The first is a parallel acceleration due to the out-of-plane electric field Ey which has a parallel component in most area of the exhaust. The second is a perpendicular acceleration due to Ey at the center of the current sheet and the motion is converted to the parallel direction. Because of the second acceleration, the electron outflow velocity becomes almost uniform over the exhaust. The difference in the outflow profile between the ions and electrons results in the Hall current in large area of the exhaust. The present study demonstrates the importance of the kinetic treatments for collisionless magnetic reconnection even far downstream from the x-line.

IRISSi iv LINE PROFILES: AN INDICATION FOR THE PLASMOID INSTABILITY DURING SMALL-SCALE MAGNETIC RECONNECTION ON THE SUN

Our understanding of the process of fast reconnection has undergone a dramatic change in the last 10 years driven, in part, by the availability of high-resolution numerical simulations that have consistently demonstrated the break-up of current sheets into magnetic islands, with reconnection rates that become independent of Lundquist number, challenging the belief that fast magnetic reconnection in flares proceeds via the Petschek mechanism that invokes pairs of slow-mode shocks connected to a compact diffusion region. The reconnection sites are too small to be resolved with images but these reconnection mechanisms, Petschek and the plasmoid instability, have reconnection sites with very different density and velocity structures and so can be distinguished by high-resolution line-profiles observations. Using IRIS spectroscopic observations we obtain a survey of typical line profiles produced by small-scale events thought to be reconnection sites on the Sun. Slit-jaw images are used to investigate the plasma heating and re-configuration at the sites. A sample of 15 events from two active regions is presented. The line profiles are complex with bright cores and broad wings extending to over 300 km/s. The profiles can be reproduced with the multiple magnetic islands and acceleration sites that characterise the plasmoid instability but not by bi-directional jets that characterise the Petschek mechanism. This result suggests that if these small-scale events are reconnection sites, then fast reconnection proceeds via the plasmoid instability, rather than the Petschek mechanism during small-scale reconnection on the Sun.

Review on Current Sheets in CME Development: Theories and Observations

We introduce how the catastrophe model for solar eruptions predicted the formation and development of the long current sheet (CS) and how the observations were used to recognize the CS at the place where the CS is presumably located. Then, we discuss the direct measurement of the CS region thickness by studying the brightness distribution of the CS region at different wavelengths. The thickness ranges from to about at heights between 0.27 and from the solar surface. But the traditional theory indicates that the CS is as thin as the proton Larmor radius, which is of order tens of meters in the corona. We look into the huge difference in the thickness between observations and theoretical expectations. The possible impacts that affect measurements and results are studied, and physical causes leading to a thick CS region in which reconnection can still occur at a reasonably fast rate are analyzed. Studies in both theories and observations suggest that the difference between the true value and the apparent value of the CS thickness is not significant as long as the CS could be recognised in observations. We review observations that show complex structures and flows inside the CS region and present recent numerical modelling results on some aspects of these structures. Both observations and numerical experiments indicate that the downward reconnection outflows are usually slower than the upward ones in the same eruptive event. Numerical simulations show that the complex structure inside CS and its temporal behavior as a result of turbulence and the Petschek-type slow-mode shock could probably account for the thick CS and fast reconnection. But whether the CS itself is that thick still remains unknown since, for the time being, we cannot measure the electric current directly in that region. We also review the most recent laboratory experiments of reconnection driven by energetic laser beams, and discuss some important topics for future works.

NUMERICAL EXPERIMENTS ON THE DETAILED ENERGY CONVERSION AND SPECTRUM STUDIES IN A CORONA CURRENT SHEET

In this paper, we study the energy conversion and spectra in a corona current sheet by 2.5-dimensional MHD numerical simulations. Numerical results show that many Petschek-like fine structures with slow-mode shocks mediated by plasmoid instabilities develop during the magnetic reconnection process. The termination shocks can also be formed above the primary magnetic island and at the head of secondary islands. These shocks play important roles in generating thermal energy in a corona current sheet. For a numerical simulation with initial conditions close to the solar corona environment, the ratio of the generated thermal energy to the total dissipated magnetic energy is around $1/5$ before secondary islands appear. After secondary islands appear, the generated thermal energy starts to increase sharply and this ratio can reach a value about $3/5$. In an environment with a relatively lower plasma density and plasma $\beta$, the plasma can be heated to a much higher temperature. After secondary islands appear, the one dimensional energy spectra along the current sheet do not behave as a simple power law and the spectrum index increases with the wave number. The average spectrum index for the magnetic energy spectrum along the current sheet is about $1.8$. The two dimensional spectra intuitively show that part of the high energy is cascaded to large $kx$ and $ky$ space after secondary islands appear. The plasmoid distribution function calculated from numerical simulations behaves as a power law closer to $f(\psi) \sim \psi^{-1}$ in the intermediate $\psi$ regime. By using $\eta_{eff} = v_{inflow}\cdot L$, the effective magnetic diffusivity is estimated about $10^{11}\sim10^{12}$~m$^2$\,s$^{-1}$.