Small-scale Langmuir wave instability in preflare chromosphere of solar active region

Necessary conditions have been investigated for the appearance of instability of high-frequency electron Langmuir waves in plasma of solar chromosphere near the foot-point of loop structure. We have considered the earliest stage of a flare process in solar active region. At the chromospheric part of current circuit of a flare loop such instability can appear and develop as the result of combined action of large-scale electric field, Landau damping and collisional processes in preflare plasma. We have investigated the process of instability development for two possible scenarios: (a) when preflare loop plasma has a classical Coulomb conductivity and (b) when anomalous resistance appears due to saturation of Bernstein turbulence. The growth rates of instability have been obtained and analyzed in detail. It has been assumed in the process of calculation that preflare plasma can be described by the FAL model of the solar atmosphere, which takes into account the process of helium diffusion. It has been shown that Langmuir wave instability can appear in its marginal form in the area under investigation either in the presence of Coulomb conductivity or in the presence of saturated Bernstein turbulence. Existence of instability with the growth rate, which changes its sign, proves the principal possibility of generation of nondamping Langmuir waves with small amplitudes.     

Excitation of Langmuir waves by the lower energy cutoff behavior of power-law electrons

Langmuir waves (LWs), which are believed to play a crucial role in the plasma emission of solar radio bursts, can be excited by streaming instability of energetic electron beams. However, solar hard X-ray observations imply that the energetic flare electrons usually have a power-law energy distribution with a lower energy cutoff. In this paper, we investigate LWs driven by the power-law electrons. The results show that power-law electrons with the steepness cutoff behavior can excite LWs effectively because of the population inversion distribution below the cutoff energy (E _c ). The growth rate of LWs increases with the steepness index (δ) and decreases with the power-law index (α). The wave number of the fastest growing LWs (kλ _D ), decreases with the characteristic velocity of the power-law electrons ( \(v_{c}=\sqrt{2E_{c}/m_{e}}\) ) and increases with the thermal velocity of ambient electrons (v _T ). This can be helpful for us to understand better the physics of LWs and the dynamics of energetic electron beams in space and astrophysical plasmas.     

Collective plasma effects and the electron number problem in solar hard X-ray bursts

Due to the relatively high stream densities involved, collective interactions with the ambient plasma are likely to be important for the electrons producing solar hard X-ray bursts. In thick- and thin-target bremsstrahlung models the most relevant process is limitation of the invoked electron beams by ion sound wave generation in the neutralizing reverse current established in the atmosphere. For the thick target model it is shown that typical electron fluxes are near the maximum permitted by stability of the reverse current so that ion-sound wave generation may be the process which limits the electron injection rate. On the other hand the chromospheric reverse current is sufficient to supply the large total number of electrons which have to be accelerated in the corona. For the thin target the low density of the corona severely limits the possible reverse current so that the maximum upward flux of fast electrons is probably much too small to explain X-ray bursts but compatible with observations of interplanetary electrons.A distinct class of model postulates a small number of electrons confined by resonant scattering in a dense coronal slab surrounding a current sheet with continuous stochastic acceleration offsetting collisional losses. The energetic aspects of such a situation described by Hoyng (1975) are developed here by addition of equations describing the slab geometry in terms of electron diffusion by whistler scattering and of the collisional damping of the accelerating Langmuir waves. Solution of these equations results in values for the fieldB(70–350 G), densityn ₀(2–5 × 10¹² cm ^–3), slab dimensions (10¹⁸ km² × 0.3–3 km) and relative Langmuir energy density (10^–3 – 10^–2) required to produce the observed range of bursts. It is pointed out, however, that there may be no real gain in electron number requirements since the fast electrons in the emitting slab would be constantly swept out along with the frozen-in plasma as dissipation proceeds so that a large total number of electrons is still required. It could in fact be that just such a coronal region is the injection mechanism for the thick-target model.On leave from Department of Astronomy, University of Glasgow, Scotland.     

空间尘埃等离子体Maser效应以及所导致的Langmuir辐射

本文从弱湍动等离子体理论出发,由Ｖｌａｓｏｖ方程导出了Ｍａｓｅｒ效应作用机制下共振波的演化规律;并且讨论了尘埃等离子体电子束入射情况下,共振Ｌａｎｇｍｕｉｒ波的增长率．研究结果表明,Ｍａｓｅｒ效应比其它不稳定性（如本文中论及的束流不稳定性等）能更好地解释空间中的反常Ｌａｎｇｍｕｉｒ辐射现象．     

Ion-temperature-gradient driven modes in dust-contaminated plasma with nonthermal electron distribution and dust charge fluctuations

The effect of nonthermal electrons on ion-temperature-gradient (ITG) driven modes is investigated in the presence of variable dust charge and ion shear flow. The dust charge fluctuating expression is obtained in the presence of kappa distributed electrons. A dispersion relation is derived and analyzed numerically by choosing space plasma parameters of Jupiter/Saturn magnetospheres. It is found that the presence of nonthermal electrons population reduces the growth rate of ITG mode driven instability. The effects of ion temperature, electron density and magnetic field variation on the growth rate of ITG instability are presented numerically. It is also pointed out that the present results will be useful to understand the ITG driven modes with variable dust charge and kappa distributed electrons, present in most of the space plasma environments.     

The brightness temperatures of solar type III bursts

There is a characteristic maximum brightness temperature T _B 10¹⁵K for type III solar radio bursts in the solar wind. The suggestion is explored that the maximum observed values of T _Bmay be attributed to saturation of the processes involved in the plasma emission. The processes leading to fundamental and second harmonic emission saturate when T _Bis approximately equal to the effective temperature T _Lof the Langmuir waves. The expected maximum value of T _Bis estimated for this saturation model in two ways: from the growth rate for the beam instability, and from the maximum amplitude of the observed Langmuir turbulence. The agreement with the observed values is satisfactory in view of the uncertainties in the estimates (a) of the intrinsic brightness temperature from the observed brightness temperature, (b) of the actual growth rate of the beam instability, which must be driven by local, transient features (that are unobservable using available instruments) in the electron distribution, and (c) in the k-space volume filled by the Langmuir waves, and this is consistent with the observational data on two well-studied events at the orbit of the Earth and with statistical data for events over a range of radial distances from the Sun.     

Nonthermal Electron Energy Deposition in the Chromosphere and the Accompanying Soft x-ray Flare Emission

We analyse four solar flares which have energetic hard X-ray emissions, but unusually low soft X-ray flux and GOES class (C1.0–C5.5). These are compared with two other flares that have soft and hard X-ray emission consistent with a generally observed correlation that shows increasing hard X-ray accompanied by increasing soft X-ray flux. We find that in the four small flares only a small percentage of the nonthermal electron beam energy is deposited in a location where the heating rate of the electron beam exceeds the radiative cooling rate of the ambient plasma. Most of the beam energy is subsequently radiated away into the cool chromosphere and so cannot power chromospheric evaporation thus reducing the soft X-ray emission. We also demonstrate that in the four small flares the nonthermal electron beam energy is insufficient to power the soft X-ray emitting plasma. We deduce that an additional energy source is required, and this could be provided by a DC-electric field (where quasi-static electric field channels in the coronal loops accelerate electrons, and those electrons with velocity below a critical velocity will heat the ambient plasma via Joule heating) in preference to a loop-top thermal source (where heat flux deposited in the corona is conducted along magnetic field lines to the chromosphere, heating the coronal plasma and giving rise to further chromospheric evaporation).     

Quenching of the beam-plasma instability by large-scale density fluctuations in 3 dimensions

A model is presented to explain the highly variable yet low level of Langmuir waves measured in situ by spacecraft when electron beams associated with type III solar bursts are passing by; the low level of excited waves allows the propagation of such streams from the Sun to well past 1 AU without catastrophic energy losses. The model is based, first, on the existence of large-scale density fluctuations that are able to efficiently diffuse small-k beam-unstable Langmuir waves in phase space, and, second, on the presence of a significant isotropic non-thermal tail in the distribution function of the background electron population, which is capable of stabilizing larger k modes. The strength of the model lies in its ability to predict various levels of Langmuir waves depending on the parameters. This feature is consistent with the high variability actually observed in the measurements. The calculations indicate that, for realistic parameters, the most unstable, small k modes are fully stabilized while some oblique mode with higher k and lower growth rate might remain unstable; thus a very broad range of levels of Langmuir waves is possible from levels of the order of enhanced spontaneous emission to the threshold level for nonlinear processes. On the other hand, from in situ measurements of the density fluctuations spectrum by ISEE-1 and 2 in the vicinity of the Earth, it is shown that measured 100 km scale fluctuations may be too effective in quenching the instability. If such strong density fluctuations are common in the solar wind, we show they must be highly anisotropic in order to allow the build-up of Langmuir waves to the observed mV m^–1 range. Moreover, the anisotropy must be such that the strongest variations of density occur in a plane perpendicular to the magnetic field.     

Spatial structure and stability of coupled Alfvén and drift compressional modes in non-uniform magnetosphere: Gyrokinetic treatment

The spatial structure and stability properties of the coupled Alfvén and drift compressional modes in a space plasma are studied in a gyrokinetic framework in a model taking into account field-line curvature and plasma and magnetic field inhomogeneity across the magnetic shells. The perturbation is found to be localized in two transparent regions, the Alfvén and drift compressional transparent regions, where the wave vector radial component squared is positive. Both regions are bounded by the resonance and cut-off surfaces, where the wave vector radial component turns into infinity and zero, respectively. An existence of the drift compressional resonance is one of the most important results of this work. It is argued that on the surface of this resonance the longitudinal and azimuthal components of the wave's magnetic field have a pole and logarithmic singularities, respectively. The instability conditions and expressions for the growth rate of the coupled modes have been obtained. In the Alfvénic transparent region, an instability occurs in the presence of the negative plasma temperature gradient. This instability does not lead to a non-stationary wave behavior: all the energy gained from the resonance particles was finally absorbed owing to any dissipation process. In a drift compressional transparent region, a necessary condition for the instability is the growth of the temperature with the radial coordinate. The growth rate is almost independent of the radial coordinate, which means that the wave energy gained from the particles cannot disappear. It will lead to an ever increasing wave amplitude, and no stationary picture for the unstable drift compressional mode is possible.     

Nonlinear generation of ion loss-cone waves by electrostatic turbulence in the magnetosphere

Effects of plasma turbulence on the stability of electrostatic ion loss-cone waves are examined. The turbulence is assumed to be electrostatic with frequencies near 1.5 times the electron gyrofrequency and the frequencies of the generated waves are below the ion plasma frequency ω_pi>. A nonlinear growth rate of the order of 10^?2ω_pi may be obtained, when the amplitude of the turbulence is 20 mV/m. This is comparable to previously found growth rates of the linear ion loss-cone instability, in a plasma with large pitch angle anisotropy. Bounce averaged pitch angle diffusion coefficients are also presented for different models of the ion loss-cone wave spectrum.     

Vlasov – Maxwell,Self-consistent Electromagnetic Wave Emission Simulations in the Solar Corona

1.5D Vlasov – Maxwell simulations are employed to model electromagnetic emission generation in a fully self-consistent plasma kinetic model for the first time in the context of solar physics. The simulations mimic the plasma emission mechanism and Larmor-drift instability in a plasma thread that connects the Sun to Earth with the spatial scales compressed appropriately. The effects of spatial density gradients on the generation of electromagnetic radiation are investigated. It is shown that a 1.5D inhomogeneous plasma with a uniform background magnetic field directed transverse to the density gradient is aperiodically unstable to the Larmor-drift instability. The latter results in a novel effect of generation of electromagnetic emission at plasma frequency. The generated perturbations consist of two parts: i) non-escaping (trapped) Langmuir type oscillations, which are localised in the regions of density inhomogeneity, and are highly filamentary, with the period of appearance of the filaments close to electron plasma frequency in the dense regions; and ii) escaping electromagnetic radiation with phase speeds close to the speed of light. When the density gradient is removed (i.e. when plasma becomes stable to the Larmor-drift instability) and a low density super-thermal, hot beam is injected along the domain, in the direction perpendicular to the magnetic field, the plasma emission mechanism generates non-escaping Langmuir type oscillations, which in turn generate escaping electromagnetic radiation. It is found that in the spatial location where the beam is injected, standing waves, oscillating at the plasma frequency, are excited. These can be used to interpret the horizontal strips (the narrow-band line emission) observed in some dynamical spectra. Predictions of quasilinear theory are: i) the electron free streaming and ii) the long relaxation time of the beam, in accord with the analytic expressions. These are corroborated via direct, fully-kinetic simulation. Finally, the interplay of the Larmor-drift instability and plasma emission mechanism is studied by considering a dense electron beam in the Larmor-drift unstable (inhomogeneous) plasma. The latter case enables one to study the deviations from the quasilinear theory.     

Origin of power-law X-ray emission in the steep power-law state of X-ray binaries

We present a new explanation for the origin of the steep power-law(SPL) state of X-ray binaries.The power-law component of X-ray emission is the synchrotron radiation of relativistic electrons in highly magnetized compact spots orbiting near the inner stable circular orbit of a black hole.It has a hard spectrum that extends to above MeV energies,which is determined by the electron acceleration rate.These photons are then down-scattered by the surrounding plasma to form an observed steep spectrum.We discuss ...     

Stability of Electrostatic Electron Cyclotron Waves in a Multi-Ion Plasma

We have studied the stability of the electrostatic electron cyclotron wave in a plasma composed of hydrogen, oxygen and electrons. To conform to satellite observations in the low latitude boundary layer we model both the ionic components as drifting perpendicular to the magnetic field. Expressions for the frequency and the growth rate of the wave have been derived. We find that the plasma can support electron cyclotron waves with a frequency slightly greater than the electron cyclotron frequency ω _ce ; these waves can be driven unstable when the drift velocities of both the ions are greater than the phase velocity of the wave. We thus introduce another source of instability for these waves namely multiple ion beams drifting perpendicular to the magnetic field.     

Stability analysis of magnetosheath lion roars

Whistler mode wave emissions in the magnetosheath, known as lion roars, are thought to be generated by an electron cyclotron instability. Using reported satellite data we model a magnetosheath medium where lion roars emissions occurred and we study the character, absolute or convective, of the associated electron cyclotron instability. We use a linear hot plasma dispersion equation for parallel and oblique propagation to the static magnetic field and apply Derfler's frequency cusp criterion to discriminate between absolute and convective instability. Our results show that an absolute instability is compatible with experimental data. From the linear temporal growth rate we extrapolate the saturated wave magnetic field and find a good agreement with the measurements.     

Comparison of mm-wave and X-ray diagnostics of flare plasma

To compare mm-wave and X-ray diagnostics of solar flare plasma, five flares observed in 1980–1991 in Metsähovi at 22 and 37 GHz and with GOES, SMM, and GRO are studied. The first impulsive peak of the mm-wave bursts under investigation coincides in time with hard X-ray emission. The second gradual component in mm-wave emission coincides with the maximum of the soft X-ray emission measure. The bremsstrahlung mm-wave radiation from hot chromospheric plasma and gyrosynchrotron radiation driven by common population of superthermal electrons are calculated. It is shown that for mm-wave events with the first peak intensity 100 s.f.u., the thermal bremsstrahlung is more important than the gyrosynchrotron emission. The total energy of fast electrons deduced from the first peak of mm-wave bursts is one to two orders of magnitude less than that determined from the hard X-ray emission in the approximation of a thick-target nonthermal model. That can testify in favour of the hybrid thermal/nonthermal model proposed by Holman and Benka (1992). The emission measure and the energy of evaporated plasma using both mm-wave and soft X-ray data are also determined. For events investigated here the energy of evaporated chromospheric plasma is larger than the total energy of fast electron beams. We have concluded that, for evaporation, additional energy release in the chromosphere is needed. The possibility of such energy release in the framework of an advanced circuit model for solar flares is discussed.     

Turbulent spectrum of Alfvén waves excited by a kinetic instability for explaining the modulations with multi-timescales in solar flares

A low-frequency wave is treated as a local oscillation to modulate the guiding center of electrons beam, which is considered as free energy to excite Alfvén waves by a kinetic plasma instability under low-frequency approximation. The nonlinearity of the model is shown by a critical value of the amplitude of the low-frequency wave, and Alfvén waves are growing in a broad turbulent spectrum with fractional harmonics, which strongly depend on the criterion. The instability is limited in the direction nearly perpendicular to the ambient magnetic field. The growth rates are very sensitive to the beam speed that perpendicular to the magnetic field, the propagational angle, and the magnetic field strength, but not sensitive to the beam speed parallel to the magnetic field. This model is used to explain the modulations with multiple timescales in the flare light curves at radio, hard X-ray and H-alpha bands.     

Reverse-current effect in present-day models of solar flares: Theory and high-accuracy observations

We propose an accurate analytical model for the source of hard X-ray emission from a flare in the form of a “thick target” with a reverse current to explain the results of present-day observations of solar flares onboard the GOES, Hinode, RHESSI, and TRACE satellites. The model, one-dimensional in coordinate space and two-dimensional in velocity space, self-consistently takes into account the fact that the beam electrons lose the kinetic energy of their motion along the magnetic field almost without any collisions under the action of the reverse-current electric field. Some of the electrons return from the emission source to the acceleration region without losing the kinetic energy of their transverse motion. Based on the observed hard X-ray bremsstrahlung spectrum, the model allows the injection spectrum of accelerated electrons to be reconstructed with a high accuracy. As an example, we consider the white-light flare of December 6, 2006, which was observed with a high spatial resolution in the optical wavelength range at the main maximum of hard X-ray emission. Within the framework of our model, we show that to explain the hard X-ray spectrum, the flux density of the energy transferred by electrons with energies above 18 keV was ～3 × 10¹³ erg cm^?2 s^?1. This exceeds the habitual values typical of the classical model of a thick target without a reverse current by two orders of magnitude. The electron density in the beam is also very high: ～10¹¹ cm^?3. A more careful consideration of plasma processes in such dense electron beams is needed when the physical parameters of a flare are calculated.     

Thermal evolution of flare plasma

The evolution of hot thermal plasma in solar flares is analyzed by a single-temperature model applied to continuum emission in the 5 keV < E ? 13 keV spectral range. The general trend that the thermal plasma observed in soft X-rays is heated by the non-thermal electrons that emit as the hard X-ray bursts is confirmed by the observation of an electron temperature increase at the time interval of hard X-ray spikes and a quantitative comparison between thermal energy content and hard X-ray energy input. Non-thermal electrons of 10 keV < E < 30 keV energy may play an important role in pre- and post-burst phases.     

First phase acceleration mechanisms and implications for hard X-ray burst models in solar flares

Requirements for the number of nonthermal electrons which must be accelerated in the impulsive phase of a flare are reviewed. These are uncertain by two orders of magnitude depending on whether hard X-rays above 25 keV are produced primarily by hot thermal electrons which contain a small fraction of the flare energy or by nonthermal streaming electrons which contain > 50% of the flare energy. Possible acceleration mechanisms are considered to see to what extent either X-ray production scenario can be considered viable. Direct electric field acceleration is shown to involve significant heating. In addition, candidate primary energy release mechanisms to convert stored magnetic energy into flare energy, steady reconnection and the tearing mode instability, transfer at least half of the stored energy into heat and most of the remaining energy to ions. Acceleration by electron plasma waves requires that the waves be driven to large amplitude by electrons with large streaming velocities or by anisotropic ion-acoustic waves which also require streaming electrons for their production. These in turn can only come from direct electric field acceleration since it is shown that ion-acoustic waves excited by the primary current cannot amplify electron plasma waves. Thus, wave acceleration is subject to the same limitations as direct electric field acceleration. It is concluded that at most 0.1% of the flare energy can be deposited into nonthermal streaming electrons with the energy conversion mechanisms as they have been proposed and known acceleration mechanisms. Thus, hard X-ray production above 10 keV primarily by hot thermal electrons is the only choice compatible with models for the primary energy release as they presently exist.     

Statistical properties of small-amplitude Langmuir waves in the Earth''s electron foreshock

We present the results of a statistical study of Langmuir waves observed by the Cluster spacecraft in the Earth's electron foreshock. To classify the probability density distributions of the logarithms of the wave energies, a Pearson technique is used. We show that experimental distributions can be better approximated, in a statistical sense, by Beta distribution or Pearson Type IV distribution rather than by a normal distribution predicted by the stochastic growth theory. This conclusion agrees with the results of numerical simulations that were previously performed with the use of a model for Langmuir wave propagation in unstable plasma with random inhomogeneities. The main reason for deviations of empirical distributions from a normal distribution is probably related to the effective number of regions, where the waves grow, which is not sufficiently large for the central limit theorem to be applicable under typical conditions in the Earth's electron foreshock. For two of seven events such deviations may be partially attributed to the effects of thermal Langmuir waves.