Solar flares through electric current interaction

The fundamental hypothesis by Alfvén and Carlqvist (1967) that solar flares are related to electrical currents in the solar chromosphere and low corona is investigated in the light of modern observations. We confirm the important role of currents in solar flares. There must be tens of such current loops (flux threads) in any flare, and this explains the hierarchy of bursts in flares. We summarize quantitative data on energies, numbers of particles involved and characteristic times. A special case is the high-energy flare: this one may originate in the same way as less energetic ones, but it occurs in regions with higher magnetic field strength. Because of the high particle energies involved their emission seats live only very briefly; hence the area of emission coincides virtually with the seat of the instability. These flares are therefore the best examples for studying the primary instability leading to the flare. Finally, we compare the merits of the original Alfvén-Carlqvist idea (that flares originate by current interruption) with the one that they are due to interaction (reconnection) between two or more fluxthreads. We conclude that a final decision cannot yet be made, although the observed extremely short time constants of flare bursts seem to demand a reconnection-type instability rather than interruption of a circuit.Paper dedicated to Professor Hannes Alfvén on the occasion of his 80th birthday, 30 May 1988.     

Excitation of high-m tearing modes at the solar flare site

It is shown that high-m drift tearing modes can be excited under the conditions prevalent at the solar flare sites. Since the growth rate of the high-m tearing modes is larger than that for low-m macroscopic tearing modes and smaller than that of microscopic ion-acoustic instability, these modes warrant accommodation in the scheme of instabilities possibly operating in the hybrid model of solar flares suggested by Spicer.     

An unstable arch model of a solar flare

The theoretical consequences of assuming that a current flows along flaring arches consistent with a twist in the field lines of these arches are examined. It is found that a sequence of magneto-hydrodynamic (MHD) and resistive MHD instabilities driven by the assumed current (which we refer to as the toroidal current) can naturally explain most manifestations of a solar flare.The principal flare instability in the proposed model is the resistive kink (or tearing mode in arch geometry) which plays the role of thermalizing some of the field energy in the arch and generating X-configured neutral points needed for particle acceleration. The difference between thermal and nonthermal flares is elucidated and explained, in part, by amplitude-dependent instabilities, generally referred to as overlapping resonances. We show that the criteria for the generation of flare shocks strongly depend on the magnitude and gradient steepness of the toroidal current, which also are found to determine the volume and rate of energy release. The resulting model is in excellent agreement with present observations and has successfully predicted several flare phenomena.     

A new numerical method for simulating the solar wind Alfvén waves: Development of the Vlasov-MHD model

A novel scheme of plasma simulation particularly suited for computing the one-dimensional nonlinear evolution of parallel propagating solar wind Alfvén waves is presented. The scheme is based on the Vlasov and the MHD models, for solving the longitudinal and the transverse components, respectively. As long as the nonlinearity is not very large (so that the longitudinal and transverse components are well separated), our Vlasov-MHD model can correctly describe evolution of finite amplitude parallel Alfvén waves, which are typical in the solar wind, both in the linear and nonlinear stages. The present model can be applied to discussions of phenomena where the parallel Alfvén waves play major roles, for example, the solar coronal heating and solar wind acceleration by the Alfvén waves propagating from the photosphere.     

The role of eruption in solar flares

This article focuses on two problems involved in the development of models of solar flares. The first concerns the mechanism responsible for eruptions, such as erupting filaments or coronal mass ejections, that are sometimes involved in the flare process. The concept of loss of equilibrium is considered and it is argued that the concept typically arises in thought-experiments that do not represent acceptable physical behavior of the solar atmosphere. It is proposed instead that such eruptions are probably caused by an instability of a plasma configuration. The instability may be purely MHD, or it may combine both MHD and resistive processes. The second problem concerns the mechanism of energy release of the impulsive (or gradual) phase. It is proposed that this phase of flares may be due to current interruption, as was originally proposed by Alfvén and Carlqvist. However, in order for this process to be viable, it seems necessary to change one's ideas about the heating and structure of the corona in ways that are outlined briefly.     

Resonant Absorption of Alfvén Waves in Steady Coronal Loops

The effect of equilibrium flow on linear Alfvén resonances in coronal loops is studied in the compressible viscous MHD model. By means of a finite element code, the full set of linearised driven MHD equations are solved for a one-dimensional equilibrium model in which the equilibrium quantities depend only on the radial coordinate. Computations of resonant absorption of Alfvén waves for two classes of coronal loop models show that the efficiency of the process of resonant absorption strongly depends on both the equilibrium parameters and the characteristics of the resonant wave. We find that a steady equilibrium shear flow can also significantly influence the resonant absorption of Alfvén waves in coronal magnetic flux tubes. The presence of an equilibrium flow may therefore be important for resonant Alfvén waves and coronal heating. A parametric analysis also shows that the resonant absorption can be strongly enhanced by the equilibrium flow, even up to total dissipation of the incoming wave.     

Kelvin-Helmholtz instability in an Alfvén resonant layer of a solar coronal loop

A Kelvin-Helmholtz instability has been identified numerically on an azimuthally symmetric Alfvén resonant layer in an axially bounded, straight cylindrical coronal loop. The physical model employed is an incompressible, reduced magnetohydrodynamic (MHD) model including resistivity, viscosity, and density variation. The set of equations is solved numerically as an initial value problem. The linear growth rate of this instability is shown to be approximately proportional to the Alfvén driving amplitude and inversely proportional to the width of the Alfvén resonant layer. It is also shown that the linear growth rate increases linearly with m - 1 up to a certain m, reaches its maximum value for the mode whose half wavelength is comparable to the Alfvén resonant layer width, and decreases at higher m's. (m is the azimuthal mode number.)     

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.     

The study of magnetic reconnection in solar spicules

This work is devoted to study the magnetic reconnection instability under solar spicule conditions. Numerical study of the resistive tearing instability in a current sheet is presented by considering the magnetohydrodynamic (MHD) framework. To investigate the effect of this instability in a stratified atmosphere of solar spicules, we solve linear and non-ideal MHD equations in the x?z plane. In the linear analysis it is assumed that resistivity is only important within the current sheet, and the exponential growth of energies takes place faster as plasma resistivity increases. We are interested to see the occurrence of magnetic reconnection during the lifetime of a typical solar spicule.     

Alfvén waves and the sunspot phenomenon

Parker's explanation of the sunspot phenomenon in terms of the enhanced emission of Alfvén waves (solar vulcanology) is shown to be compatible with observation only if 90% of the waves propagate downwards. Further difficulties arise if the region of cooling by Alfvén wave generation is restricted to a depth of 2 Mm. However, it is shown that, if Alfvén wave generation is included in a recent model proposed by Meyer, Schmidt, Weiss and Wilson, these difficulties may be resolved. The problem of the sharp umbra and penumbra boundaries is discussed and it is shown that features of this combined model are relevant to the flare phenomenon.     

Coronal loop heating by discrete Alfvén waves

We have modeled the solar coronal active loop heating by discrete Alfvén waves. Discrete Alfvén waves (DAW) are a new class of Alfvén waves which can be described by the two-fluid model with finite ion-cyclotron frequency, or the MHD model with plasma current along the magnetic field line as shown by Appert, Vaclavik, and Villar (1984). We have modeled the coronal loop as a semi-toroidal plasma with the major toroidal radius much larger than the plasma radius. We have shown that the absorption of discrete Alfvén waves by the plasma through viscosity can account for at least 30% of the coronal heating rate density of 10^–4 J m^–3 s^–1.     

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.     

Dual pulsations in solar radio bursts at short centimeter wavelengths

It is well known that the oscillating MHD waves drive periodic variations in the magnetic field. But how the MHD waves can be triggered in the flaring loops is not yet well known. It seems to us that this problem should be connected with the physical processes occurring in the flare loop during a solar flare. A peculiar solar flare event at 04:00–04:51 UT on May 23, 1990 was observed simultaneously with time resolutions 1 s and 10 ms by Nanjing University Observatory and Beijing Normal University Observatory, which are about 1000 km apart, at 3.2 cm and 2 cm wavelengths, respectively. Two kinds of pulsations with quasi-periods 1.5 s and 40 s were found in radio bursts at the two short centimeter waves; however, the shorter quasi-periodic pulsations were superimposed upon the longer ones. From the data analysis of the above-mentioned quasi-periodic pulsations and associated phenomena in radio and soft X-ray emissions during this flare event published in Solar Geophysical Data (SGD), the authors suggest that the sudden increase in plasma pressure inside (or underlying) the flare kernel due to the upward moving chromospheric evaporated gas, which is caused by the explosive collision heating of strong non-thermal electrons injected downwards from the microwave burst source, plays the important role of triggering agents for MHD oscillations (fast magneto-acoustic mode and Alfvén mode) of the flare loop. These physical processes occurring in the flare loop during the impulsive phase of the solar flare may be used to account for the origin and observational characteristics of quasi-periodic pulsations in solar radio bursts at the two short centimeter wavelengths during the flare event of 1990 May 23. In addition, the average physical parameters N, T, B inside or underlying the flare kernel can be also evaluated.     

Nonlinear Alfvén wave modulation in the solar atmosphere

Nonlinear interaction of finite-amplitude Alfvén waves with non-resonant finite-frequency electrostatic and stationary electromagnetic perturbations is considered. This interaction is governed by a pair of coupled equations consisting of nonlinear Schrödinger equation for the Alfvén wave envelope and an equation for the plasma slow response that is driven by the ponderomotive force of the Alfvén wave packets. The modulational instability of a constant amplitude Alfvén pump is investigated and some new results for the growth rate of the instability are presented. It is found that a possible stationary state of the modulated Alfvén wave packets could lead to localized structures. The relevance of our investigation to the solar atmosphere is discussed.     

Non-adiabatic discrete Alfvén waves in coronal loops and prominences

Discrete Alfvén waves in coronal loops and prominences are investigated in non-ideal magnetohydrodynamics. The non-ideal effects included are anisotropic, thermal conduction, and optically thin radiation. The classic ideal Alfvén continuum is not altered by these non-ideal effects, but the discrete Alfvén modes, which exist under certain conditions above or below the Alfvén continuum in ideal MHD, are shown to be influenced by non-adiabatic effects.The existence of discrete, non-adiabatic Alfvén waves, and their damping and overstability are examined for 1D cylindrical equilibrium states with twisted magnetic fields. First, analytic results are obtained for modes of high radial order by means of a WKB-analysis. The subspectrum of discrete Alfvén modes is computed with a numerical code, with particular emphasis on the modes of low radial order. The results show that discrete Alfvén waves are of potential importance for solar applications and also that the information obtained with the WKB-analysis is of limited use in this context.Research Assistant of the Belgian National for Scientific Research.     

Low-frequency plasma turbulence during solar wind-comet interaction

The pick up cometary ion distributions are shown to excite Alfvénic mode instabilities, slow ion-acoustic mode instability and a lower hybrid instability during solar wind-comet interaction. The growth rates of all these instabilities become larger as the comet is approached. The lower hybrid instability is shown to account for the low-frequency 0–300 Hz electrostatic turbulence observed near comet Halley. The Alfvén modes can grow to large amplitudes and become modulationally unstable, in the presence of low-frequency density fluctuations, going over to envelope Alfvén solitons. A model consisting of a gas of Alfvén solitons is suggested to explain the hydromagnetic turbulence observed near comet Halley and comet Giacobini-Zinner.     

剪切流动和电阻撕裂模的相互作用

本文在细长柱位形下数值研究了具有剪切流动的电流片中电阻撕裂模不稳定性的非线性演化。结果表明，电流片附近Ｓｅｃｈ形式的剪切流动，将导致电阻撕裂模不稳定性的发展，且不稳定性增长率随着剪切参数Ｒｒ的增加而增长，导致磁岛的形成和快速的磁能释放。这种剪切流动和撕裂模的耦合过程以及超热不稳定性的相互作用，改变了磁拱中的磁场剪切强度或者说电流密度梯度，从而驱动电阻撕裂模不稳定性的发展，这种过程对于等离子体电流密     

Waves and Oscillations in the Corona – (Invited Review)

It has long been suggested on theoretical grounds that MHD waves must occur in the solar corona, and have important implications for coronal physics. An unequivocal identification of such waves has however proved elusive, though a number of events were consistent with an interpretation in terms of MHD waves. Recent detailed observations of waves in events observed by SOHO and TRACE removes that uncertainty, and raises the importance of MHD waves in the corona to a higher level. Here we review theoretical aspects of how MHD waves and oscillations may occur in a coronal medium. Detailed observations of waves and oscillations in coronal loops, plumes and prominences make feasible the development of coronal seismology, whereby parameters of the coronal plasma (notably the Alfvén speed and through this the magnetic field strength) may be determined from properties of the oscillations. MHD fast waves are refracted by regions of low Alfvén speed and slow waves are closely field-guided, making regions of dense coronal plasma (such as coronal loops and plumes) natural wave guides for MHD waves. There are analogies with sound waves in ocean layers and with elastic waves in the Earth's crust. Recent observations also indicate that coronal oscillations are damped. We consider the various ways this may be brought about, and its implications for coronal heating.     

Alfvén wave plasma turbulence during solar wind-comet interaction

The large differences in drift velocities between the solar wind protons and the picked-up ions of cometary origin cause the Alfvén waves (among others) to become unstable and generate turbulence. A self-consistent treatment of such instabilities has to take into account that these cometary ions affect the solar wind plasma in a decisive way. With the help of a previously developed formalism one finds the correct Alfvén instability criterion, which is here nondispersive, in contrast to recent calculations where the cometary ions are treated as a low-density, high-speed, and non-neutral beam through an otherwise undisturbed solar wind. The true bulk speed of the combined solar wind plus cometary ion plasma clearly shows the mass-loading and deceleration of the solar wind near the cometary nucleus, indicating a bow shock. The instability criterion is also used to determine the region upstream where the Alfvén waves can be unstable, based upon recent observations near comet Halley.     

On the mean free path of solar cosmic rays – I. Protons

The spatial transport of charged particles in the presence of pure slab Alfvén waves, pure isotropic magnetosonic waves and their mixture is considered using Monte Carlo particle simulations. We show that the mean free path of solar cosmic ray protons strongly depends on the assumed spectrum and amplitude of MHD turbulence but much less on the type of the considered waves. It is demonstrated that, for realistic solar wind parameters, the presented wide range wave spectrum models can reproduce the observed mean free path in a particular SEP event but not in a wide range of rigidity characterized by the Palmer's `consensus'.