Beam-return current systems in nonthermal solar flare models

Previous investigations of return currents driven by suprathermal electron beams in solar flares have been based both conceptually and mathematically on analyses of electron beams in the laboratory environment. However, the physics of laboratory electron beams is fundamentally different from the physics of solar flare electron beams. Consider first the laboratory beam, which is injected into the plasma from an external source and is, therefore, modeled as a semi-infinite charged rigid rod. The longitudinal electrostatic field of such a charged rod has no preferred direction and therefore cannot drive a return current. Consequently, in the laboratory the return current is established inductively through the appearance of the changing magnetic field associated with the rising beam current, there being no offsetting displacement current term in such a geometry. It subsequently decays on the resistive time-scale; because of this decay, the net current of the system increases, and the lifetime of the electron beam becomes limited by self-pinching effects. Therefore, in the laboratory, the beam/return current system cannot reach a steady state.By contrast, the electron beam in the solar flare forms in situ and the longitudinal electrostatic field is produced by charge separation. Such an electrostatic field does have a preferred direction and so can drive a cospatial return current. Further, the magnetic field generated by the beam current is always close to being offset by either the magnetic field associated with the displacement current (E/t) or the electrostatically-driven return current; hence, inductive fields are never important. Thus, in the solar flare the return current is principally established by electrostatic fields; the return current is continuously driven and does not decay resistively. Thus, if the acceleration mechanism drives a steady beam current, then the beam/return current system rapidly achieves a steady state. We present in this paper analytic expressions for the approach to this state.Presidential Young Investigator.     

Collisional and return current heating functions for beam-heated models of solar flares

In beam-heated models of solar flares, the bulk of the energy deposited in the flare atmosphere resides in the low-energy end of the electron spectrum. Since the shape of the spectrum at low energy is not well determined observationally, various forms of low-energy cut-off have been assumed in theoretical modelling. Certain results of such modelling may depend strongly on the assumed spectrum. We derive the heating distributions for various spectra, both for collisional energy loss and for Ohmic dissipation of the return current, and show that none of the spectra are fully satisfactory, according to the criteria that for both collisional and Ohmic heating, the heating rate should be bounded, continuous, and smooth, and have a tractable functional form. A simple form of electron spectrum is suggested, which satisfies these criteria.     

A solar flare model including the formation and destruction of the current sheet in the corona

A numerical simulation method is used to show the possibility of forming a current sheet in the solar corona in an active region with four magnetic poles. The evolution of the quasi-stationary current sheet can lead to its transfer to an unsteady state. The MHD instability of this sheet causes its decay, accompanied by a set of events which characterizes the solar flare. The electrodynamical model of a solar flare includes a system of field-aligned currents typical of a magnetospheric substorm. Several events in substorms and solar flares are explained by the generation of field-aligned currents.     

Modulation of Jovian middle magnetosphere currents and auroral precipitation by solar wind-induced compressions and expansions of the magnetosphere: initial response and steady state

We present results from a theoretical model which has been used to investigate the modulation of the magnetosphere-ionosphere coupling currents in the Jovian middle magnetosphere by solar wind-induced compressions and expansions of the magnetosphere. We consider an initial system in which the current sheet field lines extend to 50R_J in the equatorial plane, and where the iogenic plasma in the current sheet undergoes steady outward radial diffusion under the influence of the ionospheric torque which tends to maintain corotation with the planet. We show using typical Jovian parameters that the upward-directed field-aligned currents flowing throughout the middle magnetosphere region in this system peak at values requiring the existence of significant field-aligned voltages to drive them, resulting in large precipitating energy fluxes of accelerated electrons and bright ‘main oval’ UV auroras. We then consider the changes in these parameters which take place due to sudden expansions or compressions of the magnetosphere, resulting from changes in the solar wind dynamic pressure. Two cases are considered and compared, these being first the initial response of the system to the change, determined approximately from conservation of angular momentum of the radially displaced plasma and frozen-in field lines, and second the subsequent steady state of steady outward radial diffusion applied to the compressed or expanded system. We show that moderate inward compressions of the outer boundary of the current sheet field lines, e.g. from 50 to 40R_J, are effective in significantly reducing the coupling currents and precipitation in the initial state, the latter then recovering, but only partly so, during the evolution to the steady state. Strong inward compressions, e.g. to 30R_J cause significant super-corotation of the plasma and a reversal in sense of the current system in the initial state, such that bright auroras may then be formed poleward of the usual ‘main auroral oval’ due to the ‘return’ currents. The sense of the currents subsequently reverts back to the usual direction as steady-state conditions are restored, but they are weak, and so is the consequent electron precipitation. For outward expansions of the current sheet, however, the field-aligned currents and electron precipitation are strongly enhanced, particularly at the poleward border mapping to the outer weak field region of the current sheet. In this case there is little evolution of the parameters between the initial expansion and the subsequent steady state. Overall, the results suggest that the Jovian middle magnetosphere coupling currents and resulting ‘main oval’ auroral acceleration and precipitation will be strongly modulated by the solar wind dynamic pressure in the sense of anti-correlation, through the resulting compressions and expansions in the size of the magnetosphere.     

On the magnetic reconnection of electric currents in solar flares

The role of the electric currents distributed over the volume of an active region on the Sun is considered from the standpoint of solar flare physics. We suggest including the electric currents in a topological model of the magnetic field in an active region. Typical values of the mutual inductance and the interaction energy of the coronal electric currents flowing along magnetic loops have been estimated for the M7/1N flare on April 27, 2006. We show that if these currents actually make a significant contribution to the flare energetics, then they must manifest themselves in the photosphericmagnetic fields. Depending on their orientation, the distributed currents can both help and hinder reconnection in the current layer at the separator during the flare. Asymmetric reconnection of the currents is accompanied by their interruption and an inductive change in energy. The reconnection of currents in flares differs significantly from the ordinary coalescence instability of magnetic islands in current layers. Highly accurate measurements of the magnetic fields in active regions are needed for a quantitative analysis of the role of distributed currents in solar flares.     

Stochastic acceleration of electrons in solar flares

The generation of lower-hybrid waves by cross-field currents is applied to reconnection processes proposed for solar flares. Recent observations on fragmentation of energy release and acceleration, and on hard X-ray (HXR) spectra are taken into account to develop a model for electron acceleration by resonant stochastic interactions with lower-hybrid turbulence. The continuity of the velocity distribution is solved including collisions and escape from the turbulence region. It describes acceleration as a diffusion process in velocity space. The result indicates two regimes that are determined by the energy of the accelerating electrons which may explain the double power-law often observed in HXR spectra. The model further predicts an anticorrelation between HXR flux and spectral index in agreement with observations.     

Have the electric currents produced by plasma and magnetic field gradients been discovered in the solar photosphere?

We check whether the currents of inhomogeneities (diffusion, thermodiffusion, and gradient ones) can exist at the photospheric level. For this purpose, the vertical currents are compared with the theoretically estimated currents of inhomogeneities; our comparison shows them to be of the same order of magnitude. Therefore, the currents of inhomogeneities actually exist in the solar photosphere; their exact values are determined by the (electron density, temperature, and magnetic field) gradients, which are not known very well at present. This paper continues the current tendency in describing the atmospheric magnetic field (in particular, its fine structure) that consists in allowing for the Hall, diffusion, and thermodiffusion currents.     

Particle beams in the solar atmosphere: General overview

An overview of particle beams in the solar atmosphere is separated into discussions of (i) current-carrying beams, (ii) current-neutralized electron beams, and (iii) ion beams. The Alfvén-Lawson limit on an electric current implies some severe limitations including the following: the current flowing into the corona cannot exceed about 10¹² A; if the current density is near threshold for a current instability then the current must flow in thin layers; and, the primary electrons and ions cannot be accelerated simply by the particles falling down a parallel potential drop. Considerable progress has been made in understanding how electron beams in type III solar radio events propagate in a way that is consistent with the generation of Langmuir waves, but a completely consistent picture has not yet emerged. Such beams, and more importantly the electron beams that generate hard X-ray bursts require current neutralization; how the required return current is set up is still not entirely clear. There is direct evidence for ion beams with energies 10 MeV per nucleon from -ray line emission; there is no unambiguous evidence for ion beams of lower energy. A mechanism is suggested for bulk energization of electrons due to dissipation of a parallel current in solar flares. Some outstanding problems concerning particle beams are identified.     

Rocket-borne and groundbased observations of coincident field-aligned currents,electron beams,and plasma density enhancements in the afternoon auroral oval

Results are reported from a rocket experiment conducted at Søndre Strømfjord, Greenland, on 22 August 1976, at 16.00 M.L.T. A series of plasma, particles, and fields and wave experiments were carried on board the payload, and the venture was supported by data from the AE-C satellite and by groundbased ionosondes and magnetometers at the launch site and at Godhavn. Two regions of field-aligned electron precipitation, electron density and temperature enhancements, and field-aligned upflowing current sheets were intercepted by the rocket. The density enhancements were also observed by groundbased ionosondes. Significant discrepancies were found between the currents carried by the streaming electrons in the 0.15–10 keV range and the upflowing currents seen by the on board magnetometer, suggesting that the upflowing current could not be the primary driver of the electron acceleration mechanism. The E-region was unstable to the combined Gradient-Drift and Farley-Buneman instability, and plasma turbulence was observed in situ, but the absolute density fluctuations were too small to return detectable HF-radar power to the ground.     

On the influence of solar wind turbulent flows on decameter wavelength scintillations

Expressions for cross-correlation functions and spectra of weak interplanetary scintillations are deduced taking into account the solar wind flow structure. The paper discusses the influence of large-scale currents and small-scale velocity fluctuations distributed under the normal and lognormal laws.     

Power transmission from the solar wind-magnetosphere dynamo to the magnetosphere and to the ionosphere: Analysis of the IMS Alaska meridian chain data

It is shown that the power ε generated by the solar wind-magnetosphere dynamo is transmitted to the convective motion of magnetospheric plasma. This convective motion generates what we may call the “Pedersen counterpart currents” in the magnetosphere and drives a large part of the “region 1 and 2” field-aligned currents which are closed by the Pedersen currents in the ionosphere. These results are based on a self-consistent set of the ionospheric current and potential distribution patterns obtained from a study of the International Magnetosphere Study Alaska meridian chain data.     

Generalized Regularization Techniques with Constraints for the Analysis of Solar Bremsstrahlung X-ray Spectra

Hard X-ray spectra in solar flares provide knowledge of the electron spectrum that results from acceleration and propagation in the solar atmosphere. However, the inference of the electron spectra from solar X-ray spectra is an ill-posed inverse problem. Here, we develop and apply an enhanced regularization algorithm for this process making use of physical constraints on the form of the electron spectrum. The algorithm incorporates various features not heretofore employed in the solar flare context: Generalized Singular Value Decomposition (GSVD) to deal with different orders of constraints; rectangular form of the cross-section matrix to extend the solution energy range; regularization with various forms of the smoothing operator; and preconditioning of the problem. We show by simulations that this technique yields electron spectra with considerably more information and higher quality than previous algorithms.     

Effect of Collisions and Magnetic Convergence on Electron Acceleration and Transport in Reconnecting Twisted Solar Flare Loops

We study a model of particle acceleration coupled with an MHD model of magnetic reconnection in unstable twisted coronal loops. The kink instability leads to the formation of helical currents with strong parallel electric fields resulting in electron acceleration. The motion of electrons in the electric and magnetic fields of the reconnecting loop is investigated using a test-particle approach taking into account collisional scattering. We discuss the effects of Coulomb collisions and magnetic convergence near loop footpoints on the spatial distribution and energy spectra of high-energy electron populations and possible implications on the hard X-ray emission in solar flares.     

Variations of magnetic fields and electric currents associated with a solar flare

The high-resolution vector magnetograms obtained with the solar telescope magnetograph of the Beijing Astronomical Observatory of the active region AR 4862 on 7 October, 1987, close before and after a solar flare, were used to calculate the electric current densities in the region. Then the relations between the flare and the magnetic fields as well as the electric currents were studied. The results are: (i) the transverse magnetic fields, and hence the longitudinal electric currents in the region before and after the flare, are evidently different, while the longitudinal magnetic fields remain unchanged; (ii) this confirms the result obtained previously that the flare kernels coincide with the peaks of longitudinal electric density in active regions; (iii) the close relation between the flare kernels and the electric currents indicates that the variations of the transverse magnetic fields and the longitudinal electric currents arise not from the general global evolution of the active region, but from the flare. These results tend to the conclusion that the triggering of a solar flare might be related with the plasma instability caused by the surplus longitudinal electric currents at some local regions in the solar atmosphere.     

The Effects of Streamers on the Shape of the K-Coronal Spectrum

We conducted an experiment in conjunction with the total solar eclipse of 21 June 2001 in Lusaka, Zambia, to obtain the K-coronal spectrum simultaneously from multiple locations on the solar corona. Then we matched the observed K-coronal spectra with the modeled K-coronal spectra to determine the coronal electron temperature and its bulk flow speed. Here the models assumed a symmetric and isothermal corona with the coronal electron flowing away from the Sun at a constant flow speed. We were able to make remarkable matches between the observations and the models. In this paper we will try to explain how the anomalies in the matches could be accounted for with the introduction of streamers in the K-coronal spectral models.     

Distributions of tangential discontinuity in the corotating solar wind structure

Distributions of the tangential discontinuity (TD) in the solar wind sector structure are investigated on the basis of the magnetic field data and the ion plasma parameters from the Explorer 33 satellite from 23 January to 23 March 1968. The TD is separated from the observed field fluctuations by calculating the direction of the plasma flow and also the direction of the minimum field fluctuation with respect to the ambient magnetic field direction.It is found that the TD is formed by the thin layered field-aligned currents (the current sheets), and that the TD is predominantly built up in the leading edge of the solar wind where the compression of the plasma and the magnetic field takes place.It is suggested that the current sheets might be locally generated in the leading edge in the turbulent conditions arising from collisions between the fast- and the slow-stream of the solar sector structure.     

Three-dimensional computer modeling of dynamic reconnection in the magnetotail

Magnetospheric substorm in the magnetotail region is studied numerically by means of a three-dimensional MHD code. The analytic solution for the quiet magnetotail is emloyed as an initial configuration. The localized solar wind is modeled to enter the simulation domain through the boundaries located in the magnetotail lobe region. As a result of the interaction between the solar wind and the magnetosphere, the magnetic field lines are stretched, and the plasma sheet becomes thinner and thinner. When the current-driven resistivity is generated, magnetic reconnection is triggered by this resistivity. The resulting plasma jetting is found to be super-magnetosonic. Although the plasmoid formation and its tailward motion is not quite clear as in the two-dimensional simulation, which is mainly because of the numerical model chosen for the present simulation, the rarification of the plasmas near thex-point is observed. Field-aligned currents are observed in the late expansive stage of the magnetospheric substorm. These field-aligned currents flow from the tail toward the ionosphere on the dawn side and from the ionosphere toward the tail on the dusk side, namely in the same sence of the region 1 current. As the field-aligned currents develop, it is found that the cross-tail current in the Earthside midnight section of the magneticx-point is reduced.     

Distribution of ionospheric currents induced by the solar wind interaction with Venus

The electric currents induced in the atmosphere of a non-magnetic planet such as Venus by the interaction of the solar wind satisfy a generalized Ohm's Law relationship with tensor conductivity. The distribution of these currents within the planetary ionosphere may be calculated by a variational technique which minimizes the Joule heating over the ionospheric volume. In this paper, we present the development of the variational technique, and apply it to a model of the solar wind interaction with Venus.Potential and current distributions are shown, and the use of these distributions in determining convective transport patterns of planetary ions is discussed.