Generalized analytical models of Syrovatskii’s current sheet

Two-dimensional stationary magnetic reconnection models that include a thin Syrovatskii-type current sheet and four discontinuous magnetohydrodynamic flows of finite length attached to its endpoints are considered. The flow pattern is not specified but is determined from a self-consistent solution of the problem in the approximation of a strong magnetic field. Generalized analytical solutions that take into account the possibility of a current sheet discontinuity in the region of anomalous plasma resistivity have been found. The global structure of the magnetic field in the reconnection region and its local properties near the current sheet and attached discontinuities are studied. In the reconnection regime in which reverse currents are present in the current sheet, the attached discontinuities are trans-Alfvénic shock waves near the current sheet endpoints. Two types of transitions from nonevolutionary shocks to evolutionary ones along discontinuous flows are shown to be possible, depending on the geometrical model parameters. The relationship between the results obtained and numerical magnetic reconnection experiments is discussed.     

A coronal magnetic field model with horizontal volume and sheet currents

When globally mapping the observed photospheric magnetic field into the corona, the interaction of the solar wind and magnetic field has been treated either by imposing source surface boundary conditions that tacitly require volume currents outside the source surface (Schatten, Wilcox, and Ness, 1969) or by limiting the interaction to thin current sheets between oppositely directed field regions (Wolfson, 1985). Yet observations and numerical MHD calculations suggest the presence of non-force-free volume currents throughout the corona as well as thin current sheets in the neighborhoods of the interfaces between closed and open field lines or between oppositely directed open field lines surrounding coronal helmet-streamer structures. This work presents a model including both horizontal volume currents and streamer sheet currents. The present model builds on the magnetostatic equilibria developed by Bogdan and Low (1986) and the current-sheet modeling technique developed by Schatten (1971). The calculation uses synoptic charts of the line-of-sight component of the photospheric magnetic field measured at the Wilcox Solar Observatory. Comparison of an MHD model with the calculated model results for the case of a dipole field and comparison of eclipse observations with calculations for CR 1647 (near solar minimum) show that this horizontal current-current-sheet model reproduces polar plumes and axes of corona streamers better than the source-surface model and reproduces coronal helmet structures better than the current-sheet model.     

Sudden commencement associated discontinuities in the interplanetary magnetic field observed by IMP 3

The magnetic field measurements made by the magnetic field experiment on the IMP 3 (Explorer 28) spacecraft have been examined at the time of geomagnetic s.s.c. events. Thirty-six such events occurred while IMP 3 was in the interplanetary medium during 1965, 1966 and 1967 and have been analysed. Of these events 8 must have been tangential discontinuities, 2 are either tangential discontinuities or rotational discontinuities and 26 are possible shock waves. (Two of these 26 events have been shown by other authors to be shocks.) These 26 possible shocks have similar magnetic signatures: an increase of 20 % or more in the magnetic field magnitude and a relatively small (always less than 90°) change in direction. The larger s.s.c. events were more likely to be caused by possible shocks while the smaller events were often associated with tangential discontinuities. The orientation of the discontinuity surfaces of the 26 possible shocks shows a preference to be aligned somewhere between a direction perpendicular to the sun-earth line and a direction tangent to the local spiral angle of the magnetic field. It was possible to associate solar flares with 14 of the 26 possible shock events. Of these 14, a reliable orientation was deduced for 8 events. By considering the orientation of these 8 events in relation to the position of the parent flares on the solar disk it is suggested that a typical shock front propagating out from the sun has a radius of curvature less than but of the order of 1 AU.NAS/NRC Postdoctoral Resident Research Associate.     

Non-evolutionarity of a reconnecting current sheet as a cause of its splitting into MHD shocks

Numerical simulations of the magnetic reconnection process in a current sheet show that, in some cases, MHD shocks appear to be attached to edges of the sheet. The appearance of the shocks may be considered to be a result of splitting of the sheet. In the present paper we suppose that this splitting takes place in consequence of non-evolutionarity of the reconnecting current sheet as a discontinuity. The problem of time evolution of small perturbations does not have a unique solution for a non-evolutionary discontinuity, and it splits into other (evolutionary) discontinuities. Such an approach allows us to determine conditions under which the splitting of the-sheet occurs. The main difficulty of this approach is that a current sheet is not reduced to a classified 1D discontinuity, because inhomogeneity of flow velocity inside the sheet is two-dimensional. To formulate the non-evolutionarity problem, we solve the linear MHD equations inside and outside the sheet and deduce linearized 1D boundary conditions at its surface. We show that for large enough conductivity, small perturbations exist which interact with the sheet as with a discontinuity. Then we obtain a non-evolutionarity criterion, with respect to these perturbations, in the form of a restriction on the flow velocity across the surface of the sheet.     

Interplanetary disturbances produced by a simulated solar flare and equatorially-fluctuating heliospheric current sheet

A recently developed nonplanar, time-dependent magnetohydrodynamic (MHD) model (Wuet al., 1983) was used to study the interplanetary disturbances produced by a compound event in the heliosphere. That is, a steady-state interplanetary medium is first disturbed by a simulated equatorially-fluctuating current sheet. After a few days (100 hr), the disturbed interplanetary medium is again perturbed by a solar-flare-generated shock wave. Attention is directed toward the differences that are caused by the presence of the equatorially-fluctuating (warped) current sheet.     

A numerical experiment relevant to line-tied reconnection in two-ribbon flares

The nonlinear evolution of a reconnecting magnetic field configuration similar to that occurring just before the onset of ‘post’-flare loops in two-ribbon flares is determined. The evolution, which is obtained by numerically solving the resistive MHD equations, shows two new features that have not yet been incorporated into contemporary models of ‘post’-flare loops. The first of these new features is the formation of a nearly stationary fast-mode shock above the region corresponding to the top of the loops. This fast-mode shock occurs just below the magnetic neutral line and between the slow-mode shocks associated with fast magnetic reconnection at the neutral line. The second new feature is the creation and annihilation of large-scale magnetic islands in the current sheet above the loops. The annihilation of the islands occurs very rapidly and appears to be a manifestation of the coalescence instability. The creation and annihilation of magnetic islands could be important in understanding the energetics of ‘post’-flare loops since the coalescence instability can produce an intermittent energy release more than an order of magnitude faster than that predicted by steady-state reconnection theories.     

Long-wavelength MHD instability in the prefront of collisionless shocks with accelerated particles

Collisionless shocks in turbulent space plasmas accelerate particles by the Fermi mechanism to ultrarelativistic energies. The interaction of accelerated particles with the plasma inflow produces extended supersonic MHD flows of multicomponent plasma. We investigate the instabilities of a flow of three-component turbulent plasma with relativistic particles against long-wavelength perturbations with scales larger than the accelerated particle transport mean free path and the initial turbulence scales. The presence of turbulence allows us to formulate the system of single-fluid equations, the equation of motion for the medium as a whole, and the induction equation for the magnetic field with turbulent magnetic and kinematic viscosities. The current of accelerated particles enters into the induction equation with an effective magnetic diffusion coefficient. We have calculated the local growth rates of the perturbations related to the nonresonant long-wavelength instability of the current of accelerated particles for MHD perturbations in the WKB approximation. The amplification of long-wavelength magnetic field perturbations in the flow upstream of the shock front can affect significantly the maximum energies of the particles accelerated by a collisionless shock and can lead to the observed peculiarities of the synchrotron X-ray radiation in supernova remnants.     

Interaction of interplanetary shocks with the bow shock

Fast forward interplanetary (IP) shocks have been identified as a source of large geomagnetic disturbances. However, the shocks can evolve in the solar wind, they are modified by interaction with the bow shock and during their propagation through the magnetosheath. A few previous papers refer the inclination and deceleration of the IP shock front in this region. Our contribution continues this effort and presents the study of an IP shock interaction with the bow shock. Since the bow shock is a reversed fast shock, the interaction of the IP shock and bow shock is a problem of interaction of two fast MHD shocks.

We compare profiles of magnetic field and plasma parameters observed by several spacecraft in the solar wind and magnetosheath with the profiles of the same parameters resulting from the MHD numerical model. The MHD model suggests that the interaction of an IP shock with the bow shock results in an inward bow shock displacement that is followed by its outward motion. Such motion will result in an indentation propagating along the bow shock surface. This scenario is confirmed by multipoint observations. Moreover, the model confirms also previous suggestions on the IP shock deceleration in the magnetosheath.     

Numerical simulation of slow shocks in the solar wind

The evolutionary state of slow forward shock waves is examined with the use of two MHD numerical codes. Our study is intended to be exploratory rather than a detailed parametric one. The first code is one-dimensional (with three components of velocity and magnetic field) which is used to follow a slow shock that propagates into a positive gradient of density versus distance. It is found that the slow shock evolves into an extraneous (intermediate) shock wave. The second code has a spherical, one-dimensional, planar geometry (with two velocity and magnetic field components) which is used to follow a spiral interplanetary magnetic field. It is found that a slow shock type perturbation can generate a forward slow shock; a fast forward shock is generated in the front of the slow shock; a contact discontinuity is formed behind the slow shock, and a compound nonlinear MHD wave is formed behind the contact discontinuity with a fast reverse shock formed further behind. Thus, we demonstrate that the evolution of a slow shock into (solely) a fast shock, as suggested by Whang (1987), is much more complicated.     

Analytical model of magnetic reconnection in the presence of shock waves attached to a current sheet

We consider a stationary two-dimensional model of magnetic reconnection in plasma. The model includes a current sheet and four MHD shock waves attached to its endpoints. The solution to the problem has been found in an analytical form that admits of efficient numerical implementation. We analyze in detail the structure of the magnetic field in the reconnection region and its variation with model parameters.     

On discontinuous plasma flows in the vicinity of reconnecting current sheets in solar flares

The question about the interpretation of numerical experiments on magnetic reconnection in solar flares is considered. A correspondence between the standard classification of magnetohydrodynamic discontinuities and the parameters characterizing the mass flux through a discontinuity and the magnetic field configuration has been established within a classical formulation of the problem on discontinuous magnetohydrodynamic flows. A pictorial graphical representation of the relationship between the angles of the magnetic field vector relative to the normal to the discontinuity plane on both its sides has also been found. The relations between the parameters of a two-dimensional discontinuous flow have the simplest form in a frame of reference where the magnetic field lines (B) are parallel to the matter velocity (u)—the deHoffmann-Teller frame. The question about the transformation of the magnetic field configuration when passing to a “laboratory” frame of reference where (v · B) ≠ 0, i.e., an electric field is present, is considered in this connection. The result is applied to the analytical solution of the problem on the magnetic field structure in the vicinity of a reconnecting current sheet obtained previously by Bezrodnykh et al. The regions of nonevolutionary shocks are shown to appear near the endpoints of a current sheet with reverse currents.     

Magnetic reconnection and coronal transients

Every two-ribbon flare observed during the Skylab period produced an observable coronal transient, provided the flare occurred close enough to the limb. The model presented here treats these two events as a combined process. Transients that occur without flares are believed to involve magnetic fields that are too weak to produce significant chromospheric emission. Adopting the hypothesis that the rising flare loop systems observed during two-ribbon flares are exhibiting magnetic reconnection, a model of a coronal transient is proposed which incorporates this reconnection process as the driving force. When two oppositely directed field lines reconnect a lower loop is created rooted to the solar surface (the flare loop) and an upper disconnected loop is produced which is free to rise. The magnetic flux of these upper loops is proposed as the driver for the transient. The force is produced by the increase in magnetic pressure under the filament and transient.A quantitative model is developed which treats the transient configuration in terms of four distinct parts- the transient itself with its magnetic field and material, the region just below the transient but above the filament, the filament with its magnetic field, and the reconnected flux beneath the filament. Two cases are considered - one in which all the prominence material rises with the transient and one in which the material is allowed to fall out of the transient. The rate of rise of the neutral line during the reconnection process is taken from the observations of the rising X-ray flare loop system during the 29 July, 1973 flare. The MHD equations for the system are reduced to four non-linear ordinary coupled differential equations which are solved using parameters believed to be realistic for solar conditions. The calculated velocity profiles, widths, etc., agree quite well with the observed properties of coronal transients as seen in white light. Since major flares are usually associated with a filament eruption about 10–15 min before the flare and since this model associates the transient with the filament eruption, we suspect that the transient is actually initiated some time before the actual flare itself.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Magnetohydrodynamic study of shock waves in the current sheet of a solar coronal magnetic loop

A Lagrangian Remap (LareXd) Code is employed to investigate the shock wave formation in the current sheet of a solar coronal magnetic loop and its effect on the magnetic reconnection. We constructed the slow shock structure in the presence of viscosity and heat conduction parallel and perpendicular to the magnetic field and pairs of slow shocks propagate away from the central current sheet, the so-called diffusion region. Significant jumps in plasma density, pressure, velocity and magnetic field occur across the main shock while the temperature appears in the foreshock. In the presence of dissipative effects, the distinct jumps disappear and the shock profiles show smooth transition between the downstream and the upstream regions while the plasma density and the pressure show very narrow and a sharp decrease with time. These results can be applied to the heating of the solar corona, the structure of the magnetic reconnection and the solar wind.     

Field-aligned currents and auroral acceleration by non-linear MHD waves

This paper examines the consequences of the assumption that substorm-associated growth of magnetosphere-ionosphere current systems is triggered by the incidence, on the ionosphere, of a large amplitude Alfvén wave generated in the distant magnetotail. It is pointed out that there is a large body of evidence suggesting that, in the acceleration region near 1 R_E, one is likely to find a major discontinuity in mass density. Following the approach of Cohen and Kulsrud (1974) who studied the steepening of large amplitude hydromagnetic waves into shocks, we demonstrate that the character of the background plasma and magnetic field in the auroral acceleration region near 1 R_E can be ideal for the generation of MHD shocks and that these shocks can lead to the acceleration of ions and electrons as reported by investigators using S3-3 satellite data.     

Turbulence in fast-mode shocks as a triggering mechanism in a solar flare

If a solar flare originates from the dissipation of magnetic energy, available in abundance in a larger region, this dissipation must take place very rapidly. A local topological change in the magnetic field structure may be sufficient to start the dissipation process. Such a change in topology might be obtained by fast reconnection in a smaller region, such as e.g. in the Sweet-Parker model, as a result of current-driven microinstabilities.Among the candidates satisfying the requirements to obtain large enough currents, such as magnetically neutral or current sheets and MHD shocks, the latter are shown to be most probable. In a fast MHD shock the (thermal) results of turbulence do in fact destroy the conditions for turbulence. However, in this work we show numerically that the nonlinear steepening mechanism of such a shock is able to restore the driving current for a large range of parameters and over a long time. This is still true if the most difficult threshold for turbulence, being that for Langmuir turbulence, is to be achieved. The critical parameter, not only for the occurrence of turbulence but also for the restoration of the driving current, is the shock thickness.     

Effects of the passage of an IMF discontinuity on the polar cap geometry and the formation of a polar cap arc

Changes of the geometry of the open field line region (namely, the polar cap) caused by the passage of a tangential IMF discontinuity are simulated using the model constructed by Akasofu and Roederer (1983). A singly-bounded open field line region tends to split into two, forming a narrow closed field line region and thus allowing the formations of a plasma sheet and of an auroral arc across the highest latitude region of the Earth. The three-dimensional geometry of some of the closed field lines in the narrow closed region is examined. In this connection, an interesting observation of the formation of an auroral arc over Thule, Greenland, is reported.     

The Hall effect as the producer of current sheets in astrophysical plasmas

Our solution of the MHD equations with the Hall effect shows that this effect can produce thin current sheets in stellar atmospheres at heights where the plasma is tenuous and the Hall effect can profoundly influence the magnetic field variations. The current in the sheets is directed oppositely to the local plasma density gradient. In partiuclar, such a phenomenon is possible on the Sun near the base of the corona.     

Re-connexion of magnetic lines of force: Evolution in incompressible MHD fluids

Time-dependent incompressible MHD solutions in two dimensions are obtained numerically to study the evolutionary process involving a re-connexion of magnetic lines of force. Given an initial antiparallel magnetic field, or a current sheet, to which there is an injection of fluid in a transverse direction, we seek to see how the process of re-connexion builds up. In this numerical experiment, special considerations are given to the confirmation of reconnexion, the formation of X-type magnetic field, the speed of growth, conditions that control the evolution, acceleration of particles, the structure of the diffusion region and so forth. The findings are: magnetic lines of force can re-connect and grow to the X-type configuration in fluids of any finitely large hydromagnetic and hydrodynamic Reynolds numbers; the conditions local to the neutral point are less important than the boundary conditions that set up global flow patterns; acceleration of fluid in bulk only concerns whether the X-type configuration grows to the comparably large extent or not; the electric field at the neutral point due to the rapidly changing magnetic field is less efficient in accelerating charged particles.     

Self-similar dynamics of a magnetized polytropic gas

In broad astrophysical contexts of large-scale gravitational collapses and outflows and as a basis for various further astrophysical applications, we formulate and investigate a theoretical problem of self-similar magnetohydrodynamics (MHD) for a non-rotating polytropic gas of quasi-spherical symmetry permeated by a completely random magnetic field. Within this framework, we derive two coupled nonlinear MHD ordinary differential equations (ODEs), examine properties of the magnetosonic critical curve, obtain various asymptotic and global semi-complete similarity MHD solutions, and qualify the applicability of our results. Unique to a magnetized gas cloud, a novel asymptotic MHD solution for a collapsing core is established. Physically, the similarity MHD inflow towards the central dense core proceeds in characteristic manners before the gas material eventually encounters a strong radiating MHD shock upon impact onto the central compact object. Sufficiently far away from the central core region enshrouded by such an MHD shock, we derive regular asymptotic behaviours. We study asymptotic solution behaviours in the vicinity of the magnetosonic critical curve and determine smooth MHD eigensolutions across this curve. Numerically, we construct global semi-complete similarity MHD solutions that cross the magnetosonic critical curve zero, one, and two times. For comparison, counterpart solutions in the case of an isothermal unmagnetized and magnetized gas flows are demonstrated in the present MHD framework at nearly isothermal and weakly magnetized conditions. For a polytropic index γ=1.25 or a strong magnetic field, different solution behaviours emerge. With a strong magnetic field, there exist semi-complete similarity solutions crossing the magnetosonic critical curve only once, and the MHD counterpart of expansion-wave collapse solution disappears. Also in the polytropic case of γ=1.25, we no longer observe the trend in the speed-density phase diagram of finding infinitely many matches to establish global MHD solutions that cross the magnetosonic critical curve twice.      

Energetic protons associated with a forward-reverse interplanetary shock pair at 1 A.U.

A forward-reverse interplanetary shock was observed on 25 March 1969 by the magnetometer and plasma detector on the HEOS-1 satellite. This relatively rare event was described by Chao et al (1972) who concluded that the shock pair was formed at a distance 0.10–0.13 A.U. upstream of the Earth as a result of the interaction between a fast and a slow solar wind streams. Simultaneous observations of 1 MeV solar proton fluxes were also performed on HEOS-1. A characteristic intensity peak was observed as the forward shock passed by the spacecraft. The evolution of the proton intensity, together with a detailed analysis of anisotropies and pitch angle distributions show a complex dynamic picture of the effect of the forward shock on the ambient proton population. Significant changes in particle fluxes are seen to be correlated with fluctuations in the magnetic field. It is suggested that simple geometrical models of shock-associated acceleration should be expanded to include the effect of magnetic fluctuations on particle fluxes. The interaction region limited by the forward and reverse shocks contained a large variety of magnetic fluctuations. Following the tangential discontinuity separating the fast solar wind stream from the preceding slow stream, a sunward flow was observed in the proton data, followed by a small but significant drop in intensity prior to the reverse shock.