Beam-driven return current instability and anomalous plasma heating in solar flares

We consider the problem of ion-acoustic wave generation, and resultant anomalous Joule heating, by a return current driven unstable by a small-area thick-target electron beam in solar flares. With a prescribed beam current evolution, j _b (t) (and, therefore, a prescribed return current j _p (t) = –j _b (t)), and using an approximate local treatment with a two component Maxwellian plasma, and neglecting energy losses, we demonstrate the existence of two quite distinct types of ion-acoustic unstable heating regimes. First, marginally stable heating occurs when the onset of instability occurs at electron-ion temperature ratios T _e /T _i > 4.8. Secondly, there exists a catastrophic heating regime for which marginally stable evolution is impossible, when the onset of instability occurs at T _e /T _i < 4.8.For the marginally stable case, we solve the electron and ion heating equations numerically and find that rapid anomalous Ohmic heating occurs in a substantial plasma volume. This large hot plasma emits thermal bremsstrahlung hard X-rays ( 20 keV) comparable to, or exceeding, the nonthermal bremsstrahlung which would have been emitted by the beam in a conventional thick target, large area, collisional scenario without anomalous effects. This means that, contrary to the usual assumption, onset of return current instability need not turn off hard X-ray production by a beam, though changing its source from direct to indirect. Indeed with small beam areas, this indirect mechanism can result in a higher hard X-ray bremsstrahlung efficiency than in a conventional collisional thick target.The catastrophic heating regime, for which we expect much larger wave levels, is discussed qualitatively, and preliminary results cited of an alternative approach, incorporating an equation directly describing the electrostatic wave energy level. Which of these two regimes will pertain in any particular case depends (discontinuously) on the beam and atmospheric parameters and we suggest that this effect may manifest itself in the distinctive temporal behaviour of X-ray flares.     

The heating of the solar plasma due to microwave phenomena correlated with type II meter bursts

The heating of the solar plasma of those layers is considered where the microwave bursts are emitted. In a first step, we restrict ourselves to phenomena correlated with the so-called type II m bursts. Bursts of this kind are excited by shock-waves initiated near the optical flare region. These shock-waves spread out into the higher corona, and if the shock strength is sufficiently high, the microwave region is heated to 10⁷ K. But this temperature is too low to explain the burst radiation. In this paper, it is shown that at plasma temperatures about 10⁷ K a fairly high number of electrons is accelerated by Alfvén waves to equivalent kinetic temperatures of about 10⁸ K. We assume that the Alfvén waves are generated near the sunspots, and, therefore, the accelerated electrons run along the magnetic-field lines into the microwave source lying between the two spots of an assumed dipole field. Within this source, the considered electrons thermalize and, after a short time, the source reaches temperatures of 5 × 10⁷ K to 10⁸ K.A plasma of this temperature with an electron density about 5 × 10⁹ cm^–3 and a magnetic induction of 300 G is optically thick even at frequencies about 10 GHz, because the gyromagnetic absorption is very high.     

Thermal instability of the reconnecting current layer in solar flares

To interpret the present-day satellite observations of the sequential brightening of coronal loops in solar flares, we have solved the problem of the stability of small longitudinal perturbations of a homogeneous reconnecting current layer (CL). Within the magnetohydrodynamic approximation we show that an efficient suppression of plasma heat conduction by amagnetic field perturbation inside the CL serves as an instability condition. The instability in the linear phase grows in the characteristic radiative plasma cooling time. A periodic structure of cold and hot filaments located across the direction of the electric current can be formed as a result of the instability in the CL. The proposed mechanism of the thermal instability of a reconnecting CL can be useful for explaining the sequential brightening (“ignition”) of flare loops in solar flares.     

Nonlinear stage of instability due to local Joule-overheating in the solar active regions

The numerical solution by a computer of the system of magnetohydrodynamics equations in the one-dimensional approximation serves as the basis for studying the non-linear stage of the instability due to local Joule-overheating of zones with large values of magnetic field gradients in the active regions of the Sun. We have demonstrated the formation of a system of current layers responsible for efficient transformation of magnetic energy into Joule heat and kinetic energy of the macroscopic motion. The specific features of quasi-stationary skinning of magnetic field with gravitation have been noted.     

Radio model of the transition layer in solar active regions

A model of the transition layer of an active region of the Sun is presented based on radio observations. The model is deduced by using the Laplace transform of the brightness temperature and the hydrostatic equilibrium equation. A rational function, well-behaved in the coronal region, has been used to represent the observed brightness temperature. The model indicates the existence of a very steep temperature gradient and suggests the presence of a constant conductive flux from the corona into the chromosphere. Both these conclusions are quantitatively in a very good agreement with those deduced from the UV emission lines observations, thus removing a previous discrepancy between radio and optical based models. It is also shown that the presence of a weak magnetic field does not alter the above conclusions.     

Modulational instability of fast magnetosonic waves in a solar plasma

Transverse amplitude modulations of fast magnetosonic waves propagating perpendicular to the background magnetic field are shown to be unstable on a time scale τ ～- λ_∥/V _aφ, if the wave amplitude φ exceeds a critical value, φ _c = C _s/V _a. The slow modes generated by the modulational instability under gravity can propagate along the magnetic field with the characteristic velocity, V _ph = g/2k _∥ V _aφ. The applications of this modulational instability and slow-mode generation mechanism to a solar plasma are discussed.     

On Kelvin–Helmholtz instability due to the solar wind interaction with unmagnetized planets

In this paper, the Kelvin–Helmholtz instability is studied by solving the ideal MHD equations for a compressible plasma. A transition layer of finite thickness between two plasmas, across which the magnitude of the velocity and the density change, is assumed. Growth rates are presented for the transverse case, i.e., the flow velocity is perpendicular to the magnetic field. If only the velocity changes across the boundary layer and the density is kept constant, an important quantity affecting the growth of the Kelvin–Helmholtz instability is the magnetosonic Mach number, which characterizes compressibility. The growth rates for the case when both, the velocity and the density, change are very sensitive to the ratio of the upper plasma density to the lower plasma density: a decrease of the density ratio yields a decrease of the growth rate. Including a density profile is very important for the application of the Kelvin–Helmholtz instability to the solar wind flow around unmagnetized planets, e.g., Venus, where the plasma density increases from the magnetosheath to the ionosphere.     

Ion acoustic instability in the presence of plasma turbulence in the solar wind

The adiabatic theory of interaction between high and low frequency waves has been studied for the case of electron plasma oscillations and ion acoustic waves and the results are applied to the solar wind. The modified dispersion relation for ion acoustic waves has been derived, taking a Gaussian distribution for plasmons. Two limiting cases of the spectrum are studied. For a broad spectrum, the plasma turbulence has a destabilising effect by introducing a growth rate denoted by turbulence, which is positive for k ₀ > (m _e/ m _i )^1/2 _De ^–1 , k ₀ being the central wave numger of the spectrum, _De the electron Debye length. Also, even for v _d(drift velocity between electrons and ions) < c _s, we arrive at unstable ion acoustic modes. For narrow spectrum, the plasma turbulence has a stabilising effect.     

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.)     

Vertical and horizontal heating in solar chromosphere

Anisotropy of the stress tensor of turbulent waves is used in this paper to explain the effects of Alfven waves in a magnetic tube. Under the conditions of a force-free field with negligible thermal conduction and convection, the equations governing the behaviour of a one-dimensional steady flow are derived. The calculated results give a reasonable explanation of the observations that the density in a plage is of the same order as, and slightly higher than the density in the surroundings while the temperature is higher by a few hundred degrees. The model of horizontal heating explains the temperature excess in “plage bridges”. The fact that, in the quiet regions, bright patches are often where the vertical field is strong while dark filaments correspond to locations with predominent horizontal field can be attributed to the different amounts of absorption of the turbulent waves by magnetic field of different strengths.     

Alfvén wave heating and acceleration of plasmas in the solar transition region producing jet-like eruptive activity

We present an analysis of observations and theory of selected transition-region phenomena, concentrating on small scale jet-like structures known as spicules and macrospicules. We examine a number of mechanisms that may be responsible for their formation and conclude that Alfvén waves could provide the necessary acceleration through the ponderomotive force and dissipation for heating forming a beam or jet like structure. In applying the Alfvén wave model we make no fundamental distinction between spicules and macrospicules. In this respect we consider them to be manifestations of the same phenomenon on different scales. We predict that the most effective Alfvén waves have frequencies around 1 Hz and amplitudes of 1 V m^–1. The resulting plasma jet sets up plasma conditions suitable for creating rotating structures which are also observed.     

Observations of the December 6, 2006 solar flare: Electron acceleration and plasma heating

The flare plasma temperature calculated from GOES-11 (1.5–12.4 and 3.1–24.8 keV) data is compared with the solar nonthermal fluxes in various energy ranges in the December 6, 2006 event. Particle acceleration and plasma heating episodes took place in the pre-flare and impulsive phases; a hard (ACS SPI > 150 keV) X-ray emission was observed 5 min before the onset of the GOES X-ray flare and was not accompanied by a temperature rise. A close correlation has been found between the flare plasma temperature and the hard X-ray intensity. The temperature delayed by 0.4 min turned out to be directly proportional to the logarithm of the ACS SPI count rate within the first 3 min of the impulsive phase. This shows that the accelerated electrons responsible for the X-ray emission were the main plasma heating source in the pre-flare and impulsive phases. The correlation between the temperature and the hard X-ray intensity disappears after the observation of a resonance peak at a frequency of 245 MHz. Significant electron fluxes may no longer be able to effectively heat the expanding plasma when its density in the interaction region reaches ∼10⁹ cm⁻³. The observations of the July 23, 2002 and December 5, 2006 events confirm the trends found.     

Microscopic spectral features in solar decametric bursts and coronal irregularities

A crossed Yagi antenna array at 35 MHz was employed in conjunction with a polarization switch so as to enable spectral observations of solar noise storm activity in R and L polarizations. Intense decametric solar noise storms were recorded during the third week of November 1975 and fourth week of March 1976 with the help of a high resolution spectroscope operating near 35 MHz.The paper describes some of the new microscopic spectral features observed during these two noise storms. Three sets of high resolution dynamic spectra of decametric solar bursts, two of which are explained in terms of induced scattering of Langmuir waves by thermal ions and the third in terms of additional propagation effects through dense coronal irregularities, are presented. The microscopic bursts, classified as inverted U U and dots, represent small-scale (10⁴ km) phenomena with durations of less than a second.Some burst spectra appear as chain of dots with individual bandwidths 40 kHz and durations 0.3 sec. It is suggested that the bandwidth of such dot emissions (40 kHz) provides an evidence that they might indeed be generated by the process of induced scattering of plasma waves which predicts emission bandwidth f × 10^–3, where f is the center frequency.Some bursts are observed as a chain of striations showing curvature along the frequency axis which is attributed to dispersion in propagation delays through the dense coronal irregularities.     

MHD waves and instabilities of a temperature-anisotropic plasma in the solar corona as a source of its heating

The MHD instabilities of a temperature-anisotropic coronal plasma are considered. We show that aperiodic mirror instabilities of slow MHD waves can develop under solar coronal conditions for weak magnetic fields (B < 1 G) and periodic ion-acoustic instabilities can develop for strong magnetic fields (B > 10 G). We have found the instability growth rates and estimated the temporal and spatial scales of development and decay of the periodic instability. We show that the instabilities under consideration can play a prominent role in the energy balance of the corona and may be considered as a large-scale energy source of the wave coronal heating mechanism.     

MHD effects triggered by beams of fast particles in magnetic tubes and their possible relation to plasma heating and dynamics during solar flares

We study the magnetohydrodynamic response of a plasma in the low solar atmosphere to a changing current system of a flaring magnetictube, which contains a beam of fast non-thermal electrons. The local disturbances of a current system of a magnetic tube when the beam is injected into it are estimated using the classical idea of a return current. According to this idea, after injection of abeam, the total current density in a magnetic tube, which includes as well the current density of the beam j_b, should not change compared to the current density in the tube before the injection. In order to keep constant the total current density j=j'+ j_b, the current density of the magnetic tube j'in fact changes. This change is due to a return current j_r.c.= –j_b, which compensates the current density of the injected beam of fast electrons. At the same time, any changes of the current density in the magnetic tube change the Joule heating and disturb the thermodynamic equilibrium of the system. Changing of the plasma temperature destroys also the force balance and starts the process of complex dynamics of the whole plasma-magnetic structure. The impulsive character of a beam injection causes two stages in the dynamic behavior of the tube. During the first stage, characterized by the presence of a beam, the preliminary equilibrium state of a magnetic tube is disturbed and complex dynamics of the plasma start in the region of the beam propagation. During the second stage, when the injection of the beam is already over, the plasma and magnetic field continue to evolve from the disturbed state and gradually relax to an equilibrium state. Various types of magnetic tube response onto injection of a beam of energetic electrons are studied using the dynamic models of the magnetic tube (Khodachenko, 1996a; 1996b) built on the basis of known self-similar solutions of plasma MHD. The model results are applied to the interpretation of observed flaring and burst phenomena.     

Nonlinear excitation of small-scale Alfvén waves by fast waves and plasma heating in the solar atmosphere

We study a nonlinear mechanism for the excitation of kinetic Alfvén waves (KAWs) by fast magneto-acoustic waves (FWs) in the solar atmosphere. Our focus is on the excitation of KAWs that have very small wavelengths in the direction perpendicular to the background magnetic field. Because of their small perpendicular length scales, these waves are very efficient in the energy exchange with plasmas and other waves. We show that the nonlinear coupling of the energy of the finite-amplitude FWs to the small-scale KAWs can be much faster than other dissipation mechanisms for fast wave, such as electron viscous damping, Landau damping, and modulational instability. The nonlinear damping of the FWs due to decay FW = KAW + KAW places a limit on the amplitude of the magnetic field in the fast waves in the solar corona and solar-wind at the level B/B ₀∼10⁻². In turn, the nonlinearly excited small-scale KAWs undergo strong dissipation due to resistive or Landau damping and can provide coronal and solar-wind heating. The transient coronal heating observed by Yohkoh and SOHO may be produced by the kinetic Alfvén waves that are excited by parametric decay of fast waves propagating from the reconnection sites.     

On the role of plasma parameters and the Kelvin-Helmholtz instability in a viscous interaction of solar wind streams

We examine a mechanism for breaking down solar wind (SW) speed shears within 1 astronomical unit (a.u.), initiated by the development of the Kelvin-Helmholtz (K-H) instability for typical parameters of the plasma and magnetic field in the interplanetary medium. A semi-empirical SW model has been invoked to derive a distribution of the plasma parameters β = 8πP/B² and M_A² = (ρν²/2)/(B²/8π) between the Sun and 1 a.u. It is shown that in the vicinity of the Sun, up to heliocentric distances r ≈ 0.1 a.u., the parameters β ? 1, and M²_A ? 1 and therefore the magnetic field here may be considered a very strong one. Because of the stabilizing effect of the magnetic field the K-H instability in this region does not develop and a presence of great shears in SW speed with large velocity gradients is possible here.At distances r > 0.1 a.u. the parameters β ? 1, and M²_A > 1. Examination of a variety of SW speed profiles showed that the presence of plasma flow velocity shears in this region leads to an excitation of the K-H instability. Numerical analysis results indicate that a principal role in the excitation of this instability is played by oblique waves that propagate at an angle α ≈ 45° to the stream velocity vector.The question of the evolution of the leading front of a high speed SW streams within 1 a.u. is discussed, with a proper account of the influence of competing effects of kinematic steepening and turbulent viscosity, the latter being due to the development of the K-H instability. It is shown that the turbulent viscosity effect in this region is substantial and is capable of ensuring an expansion of the leading front of the high speed SW stream as this moves from 0.3 to 1 a.u., in agreement with experimental evidence reported by Rosenbauer et al. (1977).     

Radiation loss and mechanical heating in the solar chromosphere

The raditation loss of the solar chromosphere is evaluated on the basis of the Harvard Smithsonian Reference Atmosphere. The total radiative flux is found to be between 2.5 and 3.3 E6 erg cm^?2 s^?1. A discussion of possible heating mechanisms shows that the short period acoustic wave theory is the only one able to balance the chromospheric radiation loss and is consistent with observation.