A quasi-one-dimensional velocity regime of super-thermal electron stream propagation through the solar corona

The propagation of an inhomogeneous-stream of fast electrons through the corona-the type III radio burst source - is considered. It is shown, that the angular spectrum width of plasma waves excited by the stream is defined both by Landau damping by particles of the diffuse component and by damping (in the region of large phase velocities) by particles of the stream itself having large pitch angles. The regime of quasi-one-dimensional diffusion in the velocity space is realized only in the presence of a sufficiently dense diffuse component of super-thermal particles and only for a sufficiently large inhomogeneity scale of the stream. A large scale of the stream space profile is formed, evidently, close to the region of injection of super-thermal particles. It is the result of stripping of part of the electrons from the stream front to its slower part due to essential non-one-dimensionality of the particle diffusion in velocity space.Results obtained may explain, in particular, the evolution of a stream particle angular spectrum in the generation region of type III radio bursts observed by spacecrafts (Lin et al., 1981). For the relatively low energetic part of the stream, the oblique plasma wave stabilization by a diffuse component results in a quasi-one-dimensional regime of diffusion. The latter conserves the beam-like structure of this part of the stream.     

On the relation between solar-flare gamma-ray emission and proton escape into interplanetary space

It is shown that escaping of solar flare energetic protons into interplanetary space as well as their relation to the flare gamma-ray emission depend on the parameter = 8p/B ₀ ² , where p is the pressure of hot plasma and energetic particles and B ₀ is the magnetic field in a flaring loop. If 1, the bulk of the energetic protons escape to the loss cone because of diffusion due to small-scale Alfvén-wave turbulence, and precipitate into the footpoints of the flaring loop. The flare then produces intense gamma-ray line emission and a weak flux of high energy protons in interplanetary space. If >_*0.3-1.0, then fast eruption of hot plasma and energetic particles out of the flaring loop occurs, this being due to the flute instability or magnetic-field-plasma nonequilibrium. The flare then produces a comparatively weak gamma-radiation and rather intense proton fluxes in interplanetary space. We predict a modulation of the solar flare gamma-ray line emission with a period 1 s during the impulsive phase that is due to the MHD-oscillations of the energy release volume. The time lag of the gamma-ray peaks with respect to the hard X-ray peaks during a simultaneous acceleration of electrons and protons can be understood in terms of strong diffusion.     

The spectra of extended radio sources with a nonuniform magnetic field and hard injection of particles

On the basis of an analytical solution of the diffusion-type kinetic equation for electrons, electron distributions and radiation spectra have been found which result from a hard injection of particles in sources of the core halo type, characterized by spatially nonuniform magnetic fields and diffusion parameters. Such radio sources are shown to possess nonlinear radiation spectra containing universal (=0.5) and diffusion-controlled power-law sections shaped by synchrotron losses, spatial diffusion and radiation conditions of the electrons. The diffusion-controlled sections can be described by spectral indices 0.5<1, if the magnetic field decreases towards the source edge, and by <0.5 where the magnetic field increases.     

Electron trapping in evolving coronal structures during a large gradual hard X-ray/radio burst

Gradual hard X-ray/radio bursts are characterized by their long duration, smooth time profile, time delays between peaks at different hard X-ray energies and microwaves, and radiation from extended sources in the low and middle corona. Their characteristic properties have been ascribed to the dynamic evolution of the accelerated electrons in coronal magnetic traps or to the separate acceleration of high-energy electrons in a second step process. The information available so far was drawn from qualitative considerations of time profiles or even only from the common occurrence of emissions in different spectral ranges. This paper presents model computations of the temporal evolution of hard X-ray and microwave spectra, together with a qualitative discussion of radio lightcurves over a wide spectral range, and metric imaging observations. The basic hypothesis investigated is that the peculiar gradual features can be related to the dynamical evolution of electrons injected over an extended time interval in a coronal trap, with electrons up to relativistic energies being injected simultaneously. The analyzed event (26 April, 1981) is particularly challenging to this hypothesis because of the long time delays between peaks at different X-ray energies and microwave frequencies. The observations are shown to be consistent with the hypothesis, provided that the electrons lose their energy by Coulomb collisions and possibly betatron deceleration. The access of the electrons to different coronal structures varies in the course of the event. The evolution and likely destabilisation of part of the coronal plasma-magnetic field configuration is of crucial influence in determining the access to these structures and possibly the dynamical evolution of the trapped electrons through betatron deceleration in the late phase of the event.     

Coherent propagation of non-relativistic solar electrons

An experimental study of the propagation of solar electrons with energyE _e > 30 keV was carried out. Measurements were made during the period 1972-1974 using the Prognoz satellite-borne instruments.A two-component structure of electron fluxes was found. The fast component, rather well-observed after solar flares of minor importance, consists of a compact beam of electrons propagating without scattering inside a narrow cone with an opening 10° along interplanetary magnetic field lines. Characteristics of this component are given.Peculiarities of the slow or diffusive component of electron fluxes are compared with the diffusive component of solar protons. It is shown that the diffusion coefficient for non-relativistic electrons is the function of the number of particles injected in the event. A model of coherent propagation of non-relativistic electrons is offered, which takes into account the presence of the fast and slow components and their interaction with solar wind plasma oscillations.     

Propagation of solar cosmic rays: Diffusion versus focused diffusion

This paper is designed to bring to the attention the fact that the effect of focusing of solar energetic particles is always essential as compared with scattering, no matter how small the value of the mean free path may be. That is why, an ordinary (focusing-free) diffusion approach can not be applied to the solar cosmic ray transport. In the case of high-energy solar particles, the focused diffusion is demonstrated to lead to a power law decay of energetic particle intensity much like an ordinary diffusion. However, the power law index of the decay is renormalized by the focusing.     

Energetic ions in solar γ-ray flares

Solar flares emit line and continuum -radiation as well as neutrons and charged particles. These high-energy emissions require the presence of energetic ions within the magnetic structures of the flare proper. We have already learned a great deal about the location and mode of particle acceleration. The observations have now become extensive enough so that we can begin to study the dynamics of the energetic ions within the flare structures themselves. This paper reviews the -ray and neutron observations and the theory of their emission, and discusses on this basis the presence of energetic ions deep within the flaring atmosphere.     

First Images of Impulsive Millimeter Emission and Spectral Analysis of the 1994 August 18 Solar Flare

We present here the first images of impulsive millimeter emission of a flare. The flare on 1994 August 18 was simultaneously observed at millimeter (86 GHz), microwave (1-18 GHz), and soft and hard X-ray wavelengths. Images of millimeter, soft and hard X-ray emission show the same compact ( 8) source. Both the impulsive and the gradual phases are studied in order to determine the emission mechanisms. During the impulsive phase, the radio spectrum was obtained by combining the millimeter with simultaneous microwave emission. Fitting the nonthermal radio spectra as gyrosynchrotron radiation from a homogeneous source model with constant magnetic field yields the physical properties of the flaring source, that is, total number of electrons, power-law index of the electron energy distribution, and the nonthermal source size. These results are compared to those obtained from the hard X-ray spectra. The energy distribution of the energetic electrons inferred from the hard X-ray and radio spectra is found to follow a double power-law with slope 6–8 below 50 keV and 3–4 above those energies. The temporal evolution of the electron energy spectrum and its implication for the acceleration mechanism are discussed. Comparison of millimeter and soft X-ray emissions during the gradual phase implies that the millimeter emission is free-free radiation from the same hot soft X-ray emitting plasma, and further suggests that the flare source contains multiple temperatures.     

Cyclotron wave instability in the corona and origin of solar radio emission with fine structure

The longitudinal waves (Bernstein modes and plasma waves near the hybrid frequency) in a mixture of equilibrium coronal plasma and a small group of energetic electrons are investigated. The energetic electrons have a nonequilibrium momentum distribution inherent in trapped particles. The frequency dependence of the cyclotron instability increments is studied. Attention is paid to a significant role of the relativistic effects for the cyclotron instability of longitudinal waves. For sufficiently large velocity of nonequilibrium electrons the increments are shown to increase when the hybrid frequency coincides with one of the gyrofrequency harmonics (double plasma resonance). The results obtained are used in Parts II and III to explain tadpoles and zebra-pattern in solar radio bursts.     

Coronal explosions

We searched for a new phenomenon, called coronal explosions, in three solar flares, and found them in all three. A coronal explosion is the propagation of a density wave through the flaring area. The wave emerges from one or two small areas (the sources) which are close to, but not identical with the sources of hard X-ray burst emission. In all three cases the explosion starts at the end of the impulsive phase, during or after the last hard ( 20 keV) X-ray burst. The velocities of propagation range between 1800 and a few tens of km s^-1, and tend to decrease with time. We suggest that the bursts are magneto-hydrodynamical (shock) waves moving downward into denser regions.     

Investigation of the electrostatic charging of dust particles in a Paul-trap

Dust particles (glass, tungsten, and nickel) with sizes ranging from 0.25 to 3m were levitated in a Paul-trap and charged by ions or electrons. For ions the particle potential is limited at field strength of about 1×10⁹ V m^–1 by a temperature-dependent discharge mechanism. The particles interaction with 2 to 20 keV electrons always leads to positive surface potentials which can be explained in terms of a decreased absorption of electrons by small particles. Micrometer sized agglomerates were used for the investigation of the electrostatic fragmentation. Fragmentation takes place in a twofold manner: small surface flufl can be removed or the parent particle can be disrupted into smaller agglomerates.Paper presented at the 11th European Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain.     

Type IV dm bursts: Onset and sudden reductions

The effect of collisions of suprathermal electrons with a thermal background plasma is investigated and is shown to cause flattening of a monotonically descending velocity distribution of fast particles. As a result flare-produced energetic electrons that are trapped in a coronal magnetic arch and that are initially distributed in energy according to a power-law, can give rise to an instability of Langmuir waves in the background plasma and the subsequent emission of continuum radiation as observed in type IV dm bursts.To explain the appearance of sudden reductions observed in type IV dm outbursts the effects both of magnetic compressions of the source region and of renewed injections of fast particles on the continuum source are investigated. It is found that the latter process can explain the observed reductions.     

Propagation and confinement of energetic electrons in solar flares

The propagation, cofinement and total energy of energetic (>25 keV) electrons in solar flares are examined through a brief review of the following hard X-ray measurements: (1) spatially resolved observations obtained by imaging instruments; (2) stereoscopic observations of partially occulted sources providing radial (vertical) spatial resolution; and (3) directivity of the emission measured through stereoscopic observations and the center-to-limb variation of the occurrence frequency of hard X-ray flares. The characteristics of the energetic electrons are found to be quite distinct in impulsive and gradual hard X-ray flares. In impulsive flares the non-thermal electron spectrum seems to extend down to 2 keV indicating that the total energy of non-thermal electrons is much larger than that assumed in the past.     

The emission and propagation of ∼ 40keV solar flare electrons

Observations of prompt 40 keV solar flare electron events by the IMP series of satellites in the period August, 1966 to December, 1967 are tabulated along with prompt energetic solar proton events in the period 1964–1967. The interrelationship of the various types of energetic particle emission by the sun, including relativistic energy electrons reported by Cline and McDonald (1968) are investigated. Relativistic energy electron emission is found to occur only during proton events. The solar optical, radio and X-ray emission associated with these various energetic particle emissions as well as the propagation characteristics of each particle species are examined in order to study the particle acceleration and emission mechanisms in a solar flare. Evidence is presented for two separate particle acceleration and/or emission mechanisms, one of which produces 40 keV electrons and the other of which produces solar proton and possibly relativistic energy electrons. It is found that solar flares can be divided into three categories depending on their energetic particle emission: (1) small flares with no accompanying energetic phenomena either in particles, radio or X-ray emission; (2) small flares which produce low energy electrons and which are accompanied by type III and microwave radio bursts and energetic ( 20 keV) X-ray bursts; and (3) major solar flare eruptions characterized by energetic solar proton production and type II and IV radio bursts and accompanied by intense microwave and X-ray emission and relativistic energy electrons.     

Formation of universal and diffusion regions of non-linear spectra of relativistic electrons in spatially limited sources

It is demonstrated that in the case of hard injection of relativistic electrons accompanied by the joint action of synchrotron (Compton) losses and energy-dependent spatial diffusion, a spectrum with breaks is formed containing universal (with index =2) and diffusion regions, both independent of the injection spectrum. The effect from non-linearity of the electron spectrum is considered in averaged electromagnetic spectra for various geometries of sources (sphere, disk, arm). It is shown that a universal region (with index =0.5) can occur in the radiation spectrum.     

Flaring arches

We discuss first the development of the coronal arch-shaped structure of 57000 km length which was born at or before 08:00 UT on 6 November, 1980 and became the site of 13 quasi-periodic brightenings in hard X-rays from 10:00 to 14:30 UT. The same structure became the site of a series of 17 flaring arches between 15:30 and 24:00 UT on that day. The periodicity of 19 min, defined well for the quasi-periodic variations, seems to be partly retained during the occurrence of the flaring arches.The flaring arch studied in Paper I (called SB arch) was the brightest event of this set of events. This paper presents its extended analysis and also an analysis of three other flaring arches that occurred in this configuration. All these events exhibit similar characteristics and thus demonstrate that the flaring arch is a distinct solar phenomenon with specific characteristic properties.A comparison of H, Ov, and X-ray data for the SB arch essentially confirmed, in a quantitative way, the qualitative interpretation of the flow of emitting plasma through the arch proposed in Paper I. In particular, these data show: (1) a hot conduction front producing X-rays in the least dense plasma ahead, a decelerating more dense plasma bulk seen next in Ov, and still more decelerating very dense plasma eventually visible in emission in H; (2) a gradient of densities from the primary towards the secondary footpoint, by factor 3 in X-rays, one order of magnitude in Ov, and probably more in the densest loops emitting in H; (3) the secondary footpoint with hard X-ray spectrum, predominantly excited by particle streams.Member of the Carrera del Investigador, CONICET, Argentina.     

Spontaneous and induced Čerenkov emission in a turbulent medium

It is shown that the presence of spatially random fluctuations in refractive index, about a mean exceeding unity, influences the power output of erenkov waves emitted by a charged particle in several ways.(1) The frequency spectrum of the spontaneous emission is altered by the fluctuations. (2) There is an induced erenkov emission, due to the interaction of the spontaneous field with the random refractive index variations. This induced field can, in certain frequency bands, be as large as the spontaneous field. And it also contains a backscattered component which propagates in theopposite direction to the particle. (3) The conditions for emission of the erenkov waves, be they spontaneous or induced, depend critically on both the mean refractive index, the particle velocity, the intensity and correlation length of the fluctuations. And the dependence is sensitive to the precise functional form of the two-point correlation function.Instruments detect the optical erenkov emission produced by cosmic ray particles penetrating the Earth's atmosphere (below about 5 km). Also gas erenkov counters are triggered by the passage of highly energetic particles through the gas. Since both the Earth's lower atmosphere and the gas counters contain turbulent fluctuations, the present calculation is of some interest in connection with particle energy loss mechanisms in turbulent media and the basic structure of such media.     

Multiperiodic irradiance changes caused by r-modes and g-modes

The acceleration of the influential 100 keV electrons in flares observed in hard X-rays and several radio emissions is unknown. Shock-waves and MHD turbulence, successfully applied to interprete interplanetary energetic particles, have recently been called in question concerning energetic flare electrons and ions. Other possible mechanisms are considered which are closely related to the primary flare energy release. In particular, runaway acceleration by the electric field of the reconnection current sheet, bulk heating by microturbulence, and cross-field ion currents due to bulk motion as a primary result of reconnection are reviewed. All three are likely to occur in some way. Their relative importance cannot be definitively assessed due to the lack of information on non-thermal, low energy protons.Proceedings of the Second CESRA Workshop on Particle Acceleration and Trapping in Solar Flares, held at Aubigny-sur-Nère (France), 23–26 June, 1986.     

Containment of an adiabatic plasma on magnetic lines of force by a self-generated electrostatic field

One component of a three-fluid adiabatic plasma is under certain conditions contained in a restricted region of space by a large-scale electrostatic field generated within the plasma. The containment is discussed here for plasma consisting of ions and two populations of electrons characterized by different pitch angle distribution functions.The bouncing motion of electrons along open fieldlines between a magnetic mirror and an electrostatic mirror produces a velocity distribution function similar to that generated by bouncing particles on closed fieldlines.     

19–20 May 1969, an example of type III emission during the impulsive phase of flares

I examined two multiple impulsive events in May 1969 and compared their impulsive Hex, hard X-ray and microwave components to the observed type III emission. No good correlation was observed between meter intensity and the degree of simultaneous H outflow although almost every type III burst had some associated H activity. Correspondingly, an inverse relationship existed between X-ray and type III emission, i.e., a strong meter burst accompanied weak hard X-radiation. This, along with the fact that sufficient energetic electrons were normally present to produce the X-rays, implies that the trajectory, rather than electron spectrum or supply, determines whether type III noise is observed during an impulsive event.