3-D MHD simulation of plasmoid formation during coalescence of two current loops

We consider two force-free current loops, as proposed by Gold and Hoyle (1960), as the initial current loops, to investigate two types of the magnetic reconnection process, the partial and complete reconnections during coalescence of these loops, by using a 3-D resistive MHD code. It is shown that two plasmoids can be produced on both sides of the coalescence area by both types of the magnetic reconnection process during coalescence of two current loops. It is also shown that strong fast magnetosonic waves can be induced in the partial reconnection case of two-current-loop collision. When two current loops collide locally at two points, four plasmoids can be produced and two of these plasmoids merge into one.     

Formation of fast magnetosonic shock waves during a two-current-loop collision in solar flares

We present a numerical simulation of the fast magnetosonic shock wave formation during a two-current-loop collision by using a magnetohydrodynamical model. It is shown that the rarefaction waves are generated in the initial stage when the two current loops start to collide. After the rarefaction waves propagate away from the excited region, the fast magnetosonic waves with density enhancement can be produced for the simulation when the current strength of the loop is weak. As the current becomes strong enough, the magnetosonic shock waves can be generated in the direction perpendicular to that of the two-loop collision.     

Electric Currents at imf Sector Boundaries

Numerical simulation of magnetic field reconnection at IMF sector boundaries shows that the reconnection line may be carried by the solar wind out of the region of the anomalous resistivity. This makes it possible to observe magnetic loops at the Earth's orbit open to the Sun as well as from it. Besides, it is shown that the current sheet in the vicinity of the reconnection line has to split into two currents.Experimental data on the structure of the sector boundaries are analyzed, and it is shown that the currents at sector boundaries are indeed often splitted.The thickness of the splitted boundaries may amount to 18×106 km; taking into account this value, the heliocentric distance of the region of anomalous resistivity in the interplanetary current sheet is estimated as 0.4–0.5 AU.The probability of observing magnetic loops open towards the Sun seems to be greater than that of loops open from the Sun, which suggests an essential asymmetry of the field reversal regions.     

Recombination of small ions in the troposphere and lower stratosphere

The current practice of treating ionic recombination in the lower atmosphere is in error in two respects: firstly the Thomson formula for the ter-molecular recombination coefficient does not represent the behaviour as accurately as commonly assumed: secondly the ter-molecular recombination coefficient (expressed in binary form) and the rate coefficient for the binary recombination of an isolated ion-pair are not additive. Computer simulated experiments are performed which should give the total recombination coefficient in the region below 40 km with some precision. It is shown that the recombination rate is not appreciably affected by inhomogeneity in the cosmic ray ionization. The equilibrium small ion number density profile is calculated and found to be in good agreement with the observed profile. It is inferred that the mixing ratio of the trace gas x which reacts with proton hydrates to form non-proton hydrates has an approximately constant value of 5 × 10⁻¹³ from 20 to 42 km.     

Buoyant Magnetic Loops Generated by Global Convective Dynamo Action

Our global 3D simulations of convection and dynamo action in a Sun-like star reveal that persistent wreaths of strong magnetism can be built within the bulk of the convention zone. Here we examine the characteristics of buoyant magnetic structures that are self-consistently created by dynamo action and turbulent convective motions in a simulation with solar stratification but rotating at three times the current solar rate. These buoyant loops originate within sections of the magnetic wreaths in which turbulent flows amplify the fields to much higher values than is possible through laminar processes. These amplified portions can rise through the convective layer by a combination of magnetic buoyancy and advection by convective giant cells, forming buoyant loops. We measure statistical trends in the polarity, twist, and tilt of these loops. Loops are shown to preferentially arise in longitudinal patches somewhat reminiscent of active longitudes in the Sun, although broader in extent. We show that the strength of the axisymmetric toroidal field is not a good predictor of the production rate for buoyant loops or the amount of magnetic flux in the loops that are produced.     

Magnetic energy buildup in a quadrupole field by photospheric shear motion

Using a two-dimensional, dissipative magnetohydrodynamic model, this paper presents a numerical simulation of the magnetic energy buildup in a quadrupolar field by photospheric shear motion. When electric current density is larger than a certain critical value, an anomalous resistivity is introduced in order to account for the dissipation caused by instabilities in high current regions. It is shown that like a bipolar field, a quadrupolar field can efficiently store magnetic free energy through photospheric shear motion. Electric current formed by shear concentrates on the separatrix and magnetic loops rooted in areas where the shear velocity gradient is large. The atmosphere is heated by anomalous resistive dissipation during the shear. Both magnetic and thermal energy increases nonlinearly with shearing displacement. When the anomalous resistivity increases or the critical current density decreases, the growth rate reduces for magnetic energy but goes up for thermal energy.     

An Impulsive Heating Model for the Evolution of Coronal Loops

It was suggested by Parker that the solar corona is heated by many small energy release events generally called microflares or nanoflares. More and more observations showed flows and intensity variations in nonflaring loops. Both theories and observations have indicated that the heating of coronal loops should actually be unsteady. Using SOLFTM (Solar Flux Tube Model), we investigate the hydrodynamics of coronal loops undergoing different manners of impulsive heating with the same total energy deposition. The half length of the loops is 110 Mm, a typical length of active region loops. We divide the loops into two categories: loops that experience catastrophic cooling and loops that do not. It is found that when the nanoflare heating sources are in the coronal part, the loops are in non-catastrophic-cooling state and their evolutions are similar. When the heating is localized below the transition region, the loops evolve in quite different ways. It is shown that with increasing number of heating pulses and inter-pulse time, the catastrophic cooling is weakened, delayed, or even disappears altogether.     

3-D MHD SIMULATION OF X-TYPE COALESCENCE OF TWO CURRENT-LOOPS

We present simulation results of X-type coalescence of two current-loops, by using a 3-D resistive MHD code. The results are compared with the limb flare observed by Yohkoh on 2 August, 1993 at 08:30 UT, which is a good example of partial X-type coalescence. It is shown that the maximum temperature enhancement near the cross-point of the two loops, obtained from the simulation, agrees well with the observations when the plasma is 0.08.     

The stability of two classes of solar quiescent prominences

The stability properties of two prominence models are investigated by considering bounds on the marginal stability conditions. It is shown that Low's (1981) model is unstable to localized disturbances and the Hood and Anzer (1990) model is only stable for sufficiently low prominences. The latter result may be modified by including magnetic shear. It is shown that magnetic shear stabilizes coronal loops against Rayleigh-Taylor instabilities and may help to stabilize prominence models as well.     

Flare build-up in low-lying magnetic loops

B. C. Low's study on non-linear force-free magnetic field is extended in an effort to explain the preflare low-lying magnetic loops observed by Skylab. Using Low's method of analytical continuation, a revised boundary-value problem is solved analytically. It is shown that high magnetic loops will evolve into low-lying ones when both the shear angle between field line and the neutral line increases with time and the foot-points of the field lines close upon the neutral line. The density, temperature and electric current density are high in these lowlying loops, thus providing conditions for flare (especially proton flare) build-up.     

Acceleration and Storage of Energetic Electrons in Magnetic Loops in the Course of Electric Current Oscillations

A mechanism of electron acceleration and storage of energetic particles in solar and stellar coronal magnetic loops, based on oscillations of the electric current, is considered. The magnetic loop is presented as an electric circuit with the electric current generated by convective motions in the photosphere. Eigenoscillations of the electric current in a loop induce an electric field directed along the loop axis. It is shown that the sudden reductions that occur in the course of type IV continuum and pulsating type III observed in various frequency bands (25?–?180 MHz, 110?–?600 MHz, 0.7?–?3.0 GHz) in solar flares provide evidence for acceleration and storage of the energetic electrons in coronal magnetic loops. We estimate the energization rate and the energy of accelerated electrons and present examples of the storage of energetic electrons in loops in the course of flares on the Sun or on ultracool stars. We also discuss the efficiency of the suggested mechanism as compared with the electron acceleration during the five-minute photospheric oscillations and with the acceleration driven by the magnetic Rayleigh–Taylor instability.     

A model of solar flares triggered by interactions between force-free current loops and plasmoids

We present a model of solar flares triggered by collisions between current loops and plasmoids. We investigate a collision process between a force-free current loop and a plasmoid, by using 3-D resistive MHD code. It is shown that a current system can be induced in the front of a plasmoid, when it approaches a force-free current loop. This secondary current produced in the front of the plasmoid separates from the plasmoid and coalesces to the force-free current loop associated with the magnetic reconnection. The core of the plasmoid stays outside the reconnection region, maintaining high density. The core can be confined by the current system produced around the plasmoid. This collison process between a current loop and a plasmoid may explain the triggering of solar flares observed byYohkoh.     

Filamentation Instability of Nonlinear Alfvén Waves and Plasma Heating associated with Recombination Effect

We investigate plasma heating associated with the effect of recombination and the filamentation instability of Alfvén waves propagating along homogeneous magnetic field in low-beta plasmas, by using an MHD simulation code. The linear instability of Alfvén waves leading to the filamentation is investigated by imposing small density perturbations across a magnetic field. We show results of the nonlinear stage of the above filamentation instability and the plasma heating through a two-dimensional simulation. It is shown that the plasma heating is caused by localized heating and whole heating, which are associated with the filamentation instability and the effect of recombination, respectively. We discuss the implication of these results for plasma heating processes observed in the chromosphere of the Sun.     

The temperature structure and pressure balance of magnetic loops in active regions

EUV observations show many active region loops in lines formed at temperatures between 10⁴K and 2×l0⁶K. The brightest loops are associated with flux tubes leading to the umbrae of sunspots. It is shown that the high visibility of certain loops in transition region lines is due principallly to a sharp radial decrease of temperature to chromospheric values toward the loop axis. The plasma density of these cool loops is not significantly greater than in the hot gas immediately surrounding it. Consequently, the internal gas pressure of the cool material is clearly lower. The hot material immediately surrounding the cool loops is generally denser than the external corona by a factor 3–4. When the active region is examined in coronal lines, this hot high pressure plasma shows up as loops that are generally parallel to the cool loops but significantly displaced laterally. In general the loop phenomenon in an active region is the result of temperature variations by two orders of magnitude and density variations of around a factor five between adjacent flux tubes in the corona.     

Coronal Loops Above a Sunspot Region

By analysing the data of Yohkoh soft X-ray images, vector magnetograms and 2D spectral observations, coronal loops above a large sunspot on 16–19 May 1994 have been studied. It is shown that the loops follow generally the alignment of concentrated magnetic flux. The results indicate that the soft X-ray emission is low just above the sunspot, while some loops connecting regions with opposite magnetic polarities show strong soft X-ray emission. Especially, the part of the loops near the weaker magnetic field region tends to be brighter than the one near the stronger magnetic field. The temperature around the top of the loops is typically 3 × 10⁶ K, which is higher than that at the legs of the loops by a factor of 1.5–2.0. The density near the top of the loops is about 5 x 10⁹ cm^-3, which is higher than that of the leg parts of the loops. These loops represent probably the sites where strong magnetic flux and/or current are concentrated.     

Generation of low-frequency magnetic field disturbances in coronal loops by proton and electron beams

We consider the generation of low-frequency magnetic field disturbances in coronal loops when low density proton and electron beams propagate in them. Two mechanisms of low-frequency magnetic field perturbation generation are analyzed. The first mechanism is concerned with the longitudinal current generated by charged particles’ beams moving in the loop. It is shown that this mechanism of the Alfvén waves’ generation can lead to development of low-frequency perturbations even if the currents are very weak. It can facilitate the reconnection of magnetic fields and flare development. The second mechanism is not concerned with currents propagating in the coronal loop. It is shown that, in this case, the proton beams can cause an instability with significantly lower values of beam density. We found increments and criteria of the development of instabilities. Not only Alfvén-type perturbations can be generated as a result of development of those instabilities but also kinetic Alfvén-type perturbations can be generated.     

Aspherical accretion of cosmic strings

A simulation of accretion of a string loop has been done. It shows that aspherical accretion is essential for large-scale loops. All configurations found in the distribution of galaxies, such as filaments, pancakes, bubbles, and voids, can be formed by the accretion of cosmic strings.     

MHD equilibrium and stability properties of a bipolar current loop

A study is made of equilibrium and stability properties of a semi-toroidal current loop imbedded in a high temperature plasma. The loop carries a toroidal current density J _t and poloidal current density J _p. By explicity including the global curvature of the loop, the net Lorentz and pressure forces acting along the major radius are calculated. Requirement of equilibrium force-balance gives rise to conditions that must be satisfied by the physical parameters and geometry. On the basis of these conditions, we deduce a class of equilibrium semi-toroidal current loops satisfying c ^#X2212;1 J × B ? ▽p = 0. It is found that the averge pressure inside the loop is less than the ambient coronal pressure in equilibrium. Furthermore, this class of equilibria is shown to be stable to a number of destructive MHD modes. The theoretical results are discussed in the context of solar bipolar current loops.     

Energies of Electrons Accelerated in Turbulent Reconnecting Current Sheets in Solar Flares

Yohkoh observations strongly suggest that electron acceleration in solar flares occurs in magnetic reconnection regions in the corona above the soft X-ray flare loops. Unfortunately, models for particle acceleration in reconnecting current sheets predict electron energy gains in terms of the reconnection electric field and the thickness of the sheet, both of which are extremely difficult to measure. It can be shown, however, that application of Ohm's law in a turbulent current sheet, combined with energy and Maxwell's equations, leads to a formula for the electron energy gain in terms of the flare power output, the magnetic field strength, the plasma density and temperature in the sheet, and its area. Typical flare parameters correspond to electron energies between a few tens of keV and a few MeV. The calculation supports the viewpoint that electrons that generate the continuum gamma-ray and hard X-ray emissions in impulsive solar flares are accelerated in a large-scale turbulent current sheet above the soft X-ray flare loops.     

Thermal electrons runaway from a hot plasma during a flare in the reverse-current model and their X-ray bremsstrahlung

The behaviour of the thermal electrons escaping from a hot plasma to a cold one during a solar flare is investigated. We suppose that the direct current of fast electrons is compensated by the reverse current of the thermal electrons in ambient plasma. It is shown that the direct current strength is determined only by the regular energy losses due to Coulomb collisions. The reverse-current electric field and the distribution function of fast electrons are found in the form of an approximate analytical solution to the self-consistent kinetic problem of the dynamics of a beam of escaping thermal electrons and its associated reverse current.The reverse-current electric field in solar flares leads to a significant reduction of the convective heat flux carried by fast electrons escaping from the high-temperature plasma to the cold one. The spectrum and polarization of hard X-ray bremsstrahlung, and its spatial distribution along flare loops are calculated and can be used for diagnostics of flare plasmas and escaping electrons.Send offprint requests to B. V. Somov.