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The primary scientific goal of ICARUS (Investigation of Coronal AcceleRation and heating of solar wind Up to the Sun), a mother-daughter satellite mission, proposed in response to the ESA “Voyage 2050” Call, will be to determine how the magnetic field and plasma dynamics in the outer solar atmosphere give rise to the corona, the solar wind, and the entire heliosphere. Reaching this goal will be a Rosetta Stone step, with results that are broadly applicable within the fields of space plasma physics and astrophysics. Within ESA’s Cosmic Vision roadmap, these science goals address Theme 2: “How does the Solar System work?” by investigating basic processes occurring “From the Sun to the edge of the Solar System”. ICARUS will not only advance our understanding of the plasma environment around our Sun, but also of the numerous magnetically active stars with hot plasma coronae. ICARUS I will perform the first direct in situ measurements of electromagnetic fields, particle acceleration, wave activity, energy distribution, and flows directly in the regions in which the solar wind emerges from the coronal plasma. ICARUS I will have a perihelion altitude of 1 solar radius and will cross the region where the major energy deposition occurs. The polar orbit of ICARUS I will enable crossing the regions where both the fast and slow winds are generated. It will probe the local characteristics of the plasma and provide unique information about the physical processes involved in the creation of the solar wind. ICARUS II will observe this region using remote-sensing instruments, providing simultaneous, contextual information about regions crossed by ICARUS I and the solar atmosphere below as observed by solar telescopes. It will thus provide bridges for understanding the magnetic links between the heliosphere and the solar atmosphere. Such information is crucial to our understanding of the plasma physics and electrodynamics of the solar atmosphere. ICARUS II will also play a very important relay role, enabling the radio-link with ICARUS I. It will receive, collect, and store information transmitted from ICARUS I during its closest approach to the Sun. It will also perform preliminary data processing before transmitting it to Earth. Performing such unique in situ observations in the area where presumably hazardous solar energetic particles are energized, ICARUS will provide fundamental advances in our capabilities to monitor and forecast the space radiation environment. Therefore, the results from the ICARUS mission will be extremely crucial for future space explorations, especially for long-term crewed space missions.

We consider weakly ionized plasma where frequent elastic scattering of electrons on neutrals changes the individual acts and the rate of electron–electron collisions significantly. In this case, the kinetics of electron thermalization is very different from that in fully ionized plasma. The colliding electrons do not move freely. They, instead, diffuse because of fast scattering on neutrals. We demonstrate how a proper account of this diffusion enables one to estimate the characteristic time of electron thermalization. We also present a rigorous derivation of the kinetic equation for electrons by using Bogolyubov's method based on Liouville equations for multi-particle distribution functions.

The aim of this study is to generate maps of the hard X-ray emission produced by energetic electrons in a solar flare and compare them with observations. The ultimate goal is to test the viability of the combined MHD/test-particle approach for data-driven modelling of active events in the solar corona and their impact on the heliosphere. Based on an MHD model of X-class solar flare observed on the 8th of September 2017, we calculate trajectories of a large number of electrons and protons using the relativistic guiding-centre approach. Using the obtained particle trajectories, we deduce the spatial and energy distributions of energetic electrons and protons, and calculate bremsstrahlung hard X-ray emission using the 'thin target' approximation. Our approach predicts some key characteristics of energetic particles in the considered flare, including the size and location of the acceleration region, energetic particle trajectories and energy spectra. Most importantly, the hard X-ray bremsstrahlung intensity maps predicted by the model are in a good agreement with those observed by RHESSI. Furthermore, the locations of proton and electron precipitation appear to be close to the sources of helioseismic response detected in this flare. Therefore, the adopted approach can be used for observationally-driven modelling of individual solar flares, including manifestations of energetic particles in the corona, as well as inner heliosphere., Comment: Accepted for publication in the Astrophysical Journal (on 19 Aug 2020)

This is a tutorial-style selective review explaining basic concepts of forced magnetic reconnection. It is based on a celebrated model of forced reconnection suggested by J. B. Taylor. The standard magnetohydrodynamic (MHD) theory of this process has been pioneered by Hahm & Kulsrud (Phys. Fluids, vol. 28, 1985, p. 2412). Here we also discuss several more recent developments related to this problem. These include energetics of forced reconnection, its Hall-mediated regime, and nonlinear effects with the associated onset of the secondary tearing (plasmoid) instability.

The present paper provides a comprehensive description of various regimes involved in the two-fluid model of resistive tearing instability. These include two novel regimes of this instability, which correspond to the long-wave modes that can develop in a highly elongated current sheet. This issue is relevant to the study of fast magnetic reconnection and magnetic turbulence in magnetohydrodynamic objects with a large value of the Lundquist number.

This article presents a mini-tutorial aimed at a wide readership not familiar with the field of solar plasma physics. The exposition is centred around the issue of excess/free magnetic energy stored in the solar corona. A general consideration is followed with a particular example of coronal magnetic arcade, where free magnetic energy builds up by photospheric convective flows. In the context of solar physics the major task is to explain how this free energy can be released quickly enough to match what is observed in coronal explosive events such as solar flares. Therefore, in the last section of the paper we discuss briefly a possible role of magnetic reconnection in these processes. This is done in quite simple qualitative physical terms, so that an interested reader can follow it up in more detail with help of the provided references.

We consider the generation of electric currents in the solar chromosphere where the ionization level is typically low. We show that ambient electrons become magnetized even for weak magnetic fields (30 G); that is, their gyrofrequency becomes larger than the collision frequency while ion motions continue to be dominated by ion-neutral collisions. Under such conditions, ions are dragged by neutrals, and the magnetic field acts as if it is frozen-in to the dynamics of the neutral gas. However, magnetized electrons drift under the action of the electric and magnetic fields induced in the reference frame of ions moving with the neutral gas. We find that this relative motion of electrons and ions results in the generation of quite intense electric currents. The dissipation of these currents leads to resistive electron heating and efficient gas ionization. Ionization by electron-neutral impact does not alter the dynamics of the heavy particles; thus, the gas turbulent motions continue even when the plasma becomes fully ionized, and resistive dissipation continues to heat electrons and ions. This heating process is so efficient that it can result in typical temperature increases with altitude as large as 0.1-0.3 eV/km. We conclude that this process can play a major role in the heating of the chromosphere and corona, Comment: 13 pages, two figures

Proton and electron acceleration in a fragmenting periodic current sheet (CS) is investigated, based on the forced magnetic reconnection scenario. The aim is to understand the role of CS fragmentation in high-energy beam generation in solar flares. We combine magnetohydrodynamics and test-particle models to consider particle trajectories consistent with a time-dependent reconnection model. It is shown that accelerated particles in such a model form two distinct populations. Protons and electrons moving in open magnetic field have energy spectra that are a combination of the initial Maxwellian distribution and a power-law high-energy (E > 20 keV) part. The second population contains particles moving in a closed magnetic field around O-points. These particles move predominantly along the guiding field and their energies fall within quite a narrow range between similar to 1 MeV and similar to 10 MeV. It is also found that particles moving in an open magnetic field have a considerably wider pitch-angle distribution.

A nanoflare-heated coronal loop model is developed based on the model of Vekstein & Katsukawa. We performed numerical simulations based on the model, and then compared the results with the Yohkoh/Soft X-ray Telescope (SXT) and Transition Region and Coronal Explorer (TRACE) observations. We found that the most significant difference between hot (>2 MK) SXT loops and cool (~1 MK) TRACE loops is the energy of nanoflares and the magnetic field strength. Energy of individual nanoflares is 1024-25 erg for SXT loops, and 1023 erg for TRACE loops. This is derived from the observed intensity fluctuations. To observed mean intensities, we require the model SXT loops to have a stronger magnetic field than the TRACE loops, 40 G and 8 G, respectively. The model predicts two characteristic properties of nanoflare-heated coronal loops: (1) the SXT and TRACE light curves of a coronal loop show weak cross-correlation with a lag time corresponding to the cooling timescale. (2) SXT loops have a smaller volumetric filling factor than TRACE loops. We consider that this difference in the filling factor makes SXT loops look more diffuse than TRACE loops.

Context. Recent analysis of the EUV emission of the solar Active Region observed with TRACE (Sakamoto et al. 2008, ApJ, 689, 1421) revealed fluctuations which are significantly larger than the estimated photon noise and other instrumental effects. This was considered as a signature of a multiple-strand structure of coronal loops that originates from numerous sporadic coronal heating events (nanoflares). Aims. The present Letter aims to put these findings into a broader context of the nanoflare heating scenario. Methods. Simultaneous TRACE and Yohkoh/SXT observations were interpreted by using theoretical predictions of the forward modelling of the nanoflare heating. Results. It is estimated that in the coronal active region impulsive heating events have a typical energy of $10^{24} ~\rm erg$ with the average occurrence rate of $10^{-17} ~\rm events/cm^2 \, s$. These could result in the hot corona with the filling factor as large as $10\%$. Conclusions. It is demonstrated that analysis of small fluctuations of the coronal emission can provide a useful tool for probing the mechanism of solar coronal heating.

We quantitatively investigate intensity fluctuations observed with the Yohkoh SXT, which is sensitive to hot (>2 MK) plasma, and TRACE, which is sensitive to cool (~1 MK) plasma. We find that the TRACE light curves contain fluctuations that are significantly larger than the photon noise and that TRACE is more sensitive to the emission from nanoflare heating than is the SXT. We discover that the standard deviation of the fluctuation (the photon noise is removed) is proportional to the mean intensity for both the SXT and TRACE loops. We also analyze the autocorrelation functions in order to obtain the duration of the intensity fluctuations. While the duration of the intensity fluctuations for the SXT loops is relatively short because of the significant photon noise, that for the TRACE loops agrees well with the characteristic cooling timescale. This is evidence that coronal loops are continuously heated by impulsive nanoflares. We estimate the energy of nanoflares to be 1025 ergs for SXT loops and 1023 ergs for TRACE loops. The occurrence rate of nanoflares is about 0.4 and 30 nanoflares s−1 in a typical SXT loop and a typical TRACE loop, respectively.

The response of a two-dimensional X-type neutral point magnetic field to a quasi-static perturbation is considered. The latter is specified by a redistribution of the magnetic flux at a circular boundary centered on the neutral point. A special role of the dipole (m = 1) azimuthal perturbation component is revealed as the only one that results in the formation of a current sheet and subsequent magnetic reconnection. The excess magnetic energy released by such reconnective relaxation is also derived.

The equilibrium and stability of a sheared force-free magnetic field in a collisionless plasma are investigated, and the main features of charged particle motion in such a field are analyzed. A steady solution is derived to the Vlasov-Maxwell equations for the charged particle distribution function that describes different equilibrium configurations. The tearing instability of the magnetic field configurations is studied both analytically and by particle-in-cell simulations.

If the mechanism responsible for creating the high-temperature solar corona is a magnetic one, the resulting coronal heating events are likely to be highly sporadic and fragmented. Therefore, nanoflare heating, where both these features are present, by the very meaning of the concept, is a strong candidate. The major problem is how to test this theory while individual nanoflares remain beyond observational recognition. Here, we discuss a possibility of probing the nanoflare heating scenario by considering statistical characteristics of coronal active regions, which presumably originate from a large number of random impulsive heating events. This approach allows one to derive various parameters of x-ray coronal loops (temperature, emission measure, filling factor, etc) without specifying particular details of the heating events. How the energy of individual nanoflares can be estimated from observed fluctuations in the coronal x-ray emission is also discussed. Comparison of our results with recently reported analysis of small fluctuations of coronal x-ray intensity observed with Yohkoh SXT telescope yields an estimate of (1022–1023) erg for the energy of nanoflares in the active region.

This paper considers single-particle trajectories in a planar sheared force-free magnetic field. A specific feature of this magnetic configuration is the absence of both gradient and curvature magnetic drifts, as well as a diamagnetic force along field lines. Therefore, in the framework of the drift approximation, the motion of the particle guiding centre does not feel the magnetic field's non-uniformity. Here we discuss how the latter affects actual particle trajectories, making them quite different from simple circular gyromotion even when the Larmor radius is small. It is also shown how magnetic confinement ceases to work when the Larmor radius becomes comparable to the spatial scale of the field variation.

A well-known Taylor problem in the theory of forced magnetic reconnection is investigated in the framework of the Hall-Magnetohydrodynamics. In the first part of the paper, we deal with the linear theory of the Hall-mediated forced reconnection. Then, in the second part, these results are used for demonstrating how the secondary tearing (plasmoid) instability can develop in the course of this process.

Two-dimensional numerical simulations are used to investigate nonlinear aspects of forced magnetic reconnection in a zero β highly conducting plasma. This is representative of the solar corona, where reconnection may be induced by external perturbations, e.g., at the photospheric boundary of the corona. The aim is to investigate the energy dissipation by the reconnection, which may provide a mechanism for heating the coronal plasma. The field is taken to be initially a sheared force-free equilibrium in a slab, and the effects of applying a slow deformation to the boundaries are investigated. Previous analytical studies assuming small departures from the initial equilibrium have found that a current sheet forms during an initial ideal phase of evolution, which subsequently relaxes to a reconnected equilibrium, releasing some magnetic energy. The linear theory predicts that the energy release has a singularity when the field is marginally stable to the tearing mode. The nonlinear evolution of the field is c...

The concept that the solar corona is heated by numerous small flarelike events dubbed "nanoflares" is considered. The hot corona is viewed as an ensemble of high-temperature elemental magnetic filaments created within the coronal magnetic field by randomly distributed impulsive heating events. It is shown that such an approach allows us to predict various signatures of X-ray coronal loops without specifying the details of the heating process. In particular, the dependence of the temperature, filling factor, and emission measure on the length of the loop and strength of the coronal magnetic field is derived. The obtained scaling laws fit reasonably with observational data.

A self-consistent derivation of magnetic energy dissipation provided by ongoing external driving and internal current sheet reconnection in a force-free magnetic field is reported. The resulting plasma heating rate shows characteristic relaxation-type dependence on the driving frequency, being most efficient when the time scales of the driving and reconnection are comparable.

A simple model of forced magnetic reconnection in a force-free magnetic field is considered, which allows the calculation of the magnetic energy release during the current sheet reconnection. The dependence of this energy on characteristics of the magnetic configuration has been studied, and it was found that the released energy becomes very large when the field is near the marginal tearing stability. A persistent plasma heating provided by ongoing external driving and internal reconnection is most efficient when the time-scales of these processes are comparable. Possible implications of the obtained results for the problem of solar coronal heating are briefly discussed.

A model of forced magnetic reconnection in a force-free magnetic field is considered, which allows calculation of the magnetic energy release during the current sheet reconnection. The dependence of this energy on characteristics of the magnetic configuration has been studied, and it was found that the released energy becomes very large when the field is near the marginal tearing stability. A persistent plasma heating provided by ongoing external driving and internal reconnection is also derived. It shows a typical relaxation-type dependence on the driving frequency, with dissipation becoming most efficient when the time-scales of the driving and reconnection are comparable. Possible implications of the obtained results for the problem of solar coronal heating are discussed.

Forced magnetic reconnection in a sheared force-free magnetic field brings about relaxation of the system to a state of lower magnetic energy. The resulting energy release becomes strongly amplified when the field is close to the tearing instability threshold, which makes the linear theory [Vekstein and Jain, Phys. Plasmas 5, 1506 (1998)] not applicable in this case. In the present Brief Communication the reconnective energy release in the marginally stable magnetic field is derived by exploring the quasilinear theory of tearing modes.

We study Taylor's model of forced magnetic reconnection mediated by plasma hyper-resistivity. This includes both linear and nonlinear regimes of the process. It is shown how the onset of plasmoid instability occurs in the strongly nonlinear regime of forced reconnection.

International audience; We consider the generation of electric currents in the solar chromosphere. The ionization level in this region is generally supposed to be low. We show that the ambient electrons are magnetized even for weak magnetic fields (30 G), i.e. their gyrofrequency is larger than the collision frequency; ion motions continue to be dominated by ion-neutral collisions in this region. Under such conditions the ions are dragged by neutrals. As a result, the dynamics of magnetic field resembles frozen-in motion of the field with the neutral gas. On the other hand magnetized electrons drift under the action of the electric and magnetic fields induced in the reference frame of ions moving with the neutral gas. This relative motion of electrons and ions results in the generation of quite intense electric currents. The dissipation of these currents leads to the resistive electron heating and efficient gas ionization. Ionization by electron-neutral impact does not alter the dynamics of the heavy particles; thus the gas turbulent motions persist even when the plasma becomes fully ionized and the resistive current dissipation continues to heat electrons and ions. This heating process is so efficient that it can result in typical temperature increases with altitude as large as 0.1–0.3 eV/km. We conclude that this process can play a major role in the heating of the chromosphere and corona. We show that the physical conditions in the solar chromosphere, in particular the neutral and ion density dependencies upon altitude, are very similar to those in the lower ionosphere of the Earth. A very similar process of current generation occurs in the ionosphere after strong earthquakes, resulting in the generation of strong perturbations in the ionosphere. We then present well-known results of the observations of such perturbations, which allow an evaluation of the increment of the growth of the perturbations with altitude, making use of ionospheric sounding. These results are in perfect agreement with estimates obtained making use a model similar to ours. We consider that these observations clearly show the efficiency of the physical mechanisms discussed, and thus provide strong support for our ideas.

This note aims to clarify the correspondence between forced magnetic reconnection and Alfven resonances in a plasma with a sheared magnetic field subjected to continuous external driving. It is shown how a transition from one regime to another occurs, and what implications this has on the magnetic energy dissipation rate.

Standard magnetohydrodynamic (MHD) theory predicts reconnection rate that is far too slow to account for a wide variety of reconnection events observed in space and laboratory plasmas. Therefore, it was commonly accepted that some non-MHD (kinetic) effects play a crucial role in fast reconnection. A recently renewed interest in simple MHD models is associated with the so-called plasmoid instability of reconnecting current sheets. Although it is now evident that this effect can significantly enhance the rate of reconnection, many details of the underlying multiple-plasmoid process still remain controversial. Here, we report results of a high-resolution computer simulation which demonstrate that fast albeit intermittent magnetic reconnection is sustained by numerous small-scale Petschek-type shocks spontaneously formed in the current sheet due to its plasmoid instability.

This letter presents a self-consistent description of nonlinear forced magnetic reconnection in Taylor's model of this process. If external boundary perturbation is strong enough, nonlinearity in the current sheet evolution becomes important before resistive effects come into play. This terminates the current sheet shrinking that takes place at the linear stage and brings about its nonlinear equilibrium with a finite thickness. Then, in theory, this equilibrium is destroyed by a finite plasma resistivity during the skin-time, and further reconnection proceeds in the Rutherford regime. However, realization of such a scenario is unlikely because of the plasmoid instability, which is fast enough to develop before the transition to the Rutherford phase occurs. The suggested analytical theory is entirely different from all previous studies and provides proper interpretation of the presently available numerical simulations of nonlinear forced magnetic reconnection.

Context. In the present paper, we investigate particle acceleration by direct electric field in solar flares. Aims. Proton and electron kinetics are considered based on MHD simulations of magnetic reconnection, with the aim of determining the properties of accelerated particles in a time-dependent reconnecting event model. Methods. At first, we considered several two-dimensional numerical models of forced reconnection in the initially force-free Harris current sheet. The electric and magnetic fields from these models were then used to study proton and electron motion with the guiding centre, test particle approach. Results. It is shown that protons and electrons can be accelerated to very high energies up to tens of MeV in the present model. The energy spectra for both particle species are combinations of exponential and rather hard power-law shapes. Also, protons and electrons are ejected from the CS in different directions.

Collisionless forced magnetic reconnection in an electron-positron plasma, where the mechanism of the magnetic field breaking is inertia of plasma particles, is considered. The model under analytical investigation is the so-called Taylor problem: a tearing stable slab plasma equilibrium with a magnetic field reversal is subjected to a small-amplitude boundary perturbation that drives magnetic reconnection at the neutral surface within the plasma. It is shown that forced collisionless reconnection has a direct analogy with its collisional (resistive) counterpart investigated by T. S. Hahm and R. M. Kulsrud [Phys. Fluids 28, 2412 (1985)], with the role of the inverse Lundquist number S−1≪1 of the resistive magnetohydrodynamics now being played by the normalized inertia skin depth d≡cωpa≪1 (ωp is the electron-positron plasma frequency, and a is a width of the plasma slab). The transition between the collisionless and resistive regimes of forced reconnection is also considered.

The role of the Hall effect in forced magnetic reconnection is investigated analytically for the so-called Taylor problem. In the latter, a tearing stable slab plasma equilibrium, which is chosen here to be a simple magnetic field reversal, is subjected to a small-amplitude boundary deformation that drives magnetic reconnection (hence the adjective “forced” ) at the neutral surface within the plasma. It is shown that such reconnection becomes substantially accelerated by the Hall effect when the nondimensional parameter di=(c∕ωpi)∕a exceeds S−1∕5. Here, c∕ωpi is the ion inertial skin depth, a is the width of the plasma slab, and S≫1 is the Lundquist number of a highly conducting plasma. Two different types of external perturbation are considered. In the case of continuous quasistatic driving, with a frequency ω such that ωτA≪1, τA being the Alfven transit time, various reconnection regimes are identified. The corresponding heating rates, which are determined by the parameters di, S, and ωτA, are derived. ...

The rate of energy dissipation provided by the ongoing magnetic reconnection in a force-free magnetic field is investigated in the framework of visco-resistive magnetohydrodynamics (MHD). It is shown that viscous effects are important even under small magnetic Prandtl number Pm≡ν∕η, namely for Pm>S−2∕5, where ν and η are the plasma viscosity and resistivity, respectively, and S⪢1 is the Lundquist number of a highly conducting plasma. Various regimes of plasma heating, which are determined by the nondimensional parameters Pm, S, and ωτA, are identified, where τA is the Alfven transit time of the magnetic configuration and ω is the frequency of an external driver.