Evolution of a flaring loop after injection of energetic electrons

For the November 5, 1980 flare it is investigated how the plasma in a large flaring loop responds to the injection of energetic electrons. Observations are compared with the results of a one-dimensional numerical simulation. For the simulation it is assumed that at the time the injection is started, the plasma is in an equilibrium state with a constant pressure along the loop and conductive heating compensated by radiative losses. Especially important for the evolution of the impulsively heated plasma is the penetration depth of the fast electrons compared to the depth of the transition layer. Both parameters are known from the observations. The injected energy is 2.6 × 10¹¹ ergs cm ^?2 in 30 s (as derived from the hard X-ray observations) and computations show that the high temperature plasma of the loop responds to it with upward motions of about 50 km s^?1, i.e. with velocities much smaller than the ion sound speed (≈ 500km s^?1). The heating of the plasma due to the absorption of beam energy can be understood using a constant density approximation. After the heating phase the plasma returns in about 5 min to its initial state by conductive cooling. The downward conducted energy is radiated away in the transition zone. The numerical simulation shows that impulsive heating by non-thermal electrons only does not explain the observed large increase in the density of the loop during the flare. It is therefore required that continuous energy and/or mass input occur after the impulsive phase.     

Angular distributions of solar protons and electrons

High angular-resolution measurements of directional fluxes of solar particles in space have been obtained with detectors aboard OGO-5 during the cosmic ray event of 18 November 1968. This is the only case on record for which sharply-defined directional observations of protons and electrons covering a wide rigidity range (0.3 MV to 1.5 GV) are available.The satellite experiment provided data for determining pitch-angle distributions with respect to the direction of the local interplanetary magnetic field lines during the lengthy highly anisotropic phase of the event. It was found that the unidirectional differential intensities j(θ) of 3- to 25-MeV protons varied in accordance with the relationship j(θ) = b₀ + b₁cosθ + b₂cos²θ, where b₀ and b₁ ? 0, and b₂, is positive, zero or negative. Soon after onset, 79–266-keV electrons arriving from the direction of the Sun displayed an anisotropic component with the intensity varying as cos θ. Later, a double-peaked distribution appeared at the lower energies, whereas the flux at the upper end of the range covered by the experiment became isotropic. These results have been interpreted in the light of the temporal flux profiles and the state of the interplanetary medium.The observation of the unusually large and long-lasting anisotropies lead to several conclusions including: (1) If injection of the solar particles was instantaneous, the diffusion coefficient was either constant or increasing with distance from the Sun. (2) If the solar source emitted particles over an extended period, and there is evidence to that effect, there was weak scattering in the region between the Sun and the Earth and a strong scattering region beyond the Earth's orbit. (3) Solar electrons were stored near the Sun. (4) The observed angular distribution of 200-MV protons in the magnetosheath was in good agreement with that deduced in an earlier analysis of polar orbiting satellite observations and trajectory calculations.     

Topology and current ribbons: A model for current,reconnection and flaring in a complex,evolving corona

Magnetic field enters the corona from the interior of the Sun through isolated magnetic features on the solar surface. These features correspond to the tops of submerged magnetic flux tubes, and coronal field lines often connect one flux tube to another, defining a pattern of inter-linkage. Using a model field, in which flux tubes are represented as point magnetic charges, it is possible to quantify this inter-linkage. If the coronal field were current-free then motions of the magnetic features would change the inter-linkage through implicit (vacuum) magnetic reconnection. Without reconnection the conductive corona develops currents to avoid changing the flux linkage. This current forms singular layers (ribbons) flowing along topologically significant field lines called separators. Current ribbons store magnetic energy as internal stress in the field: the amount of energy stored is a function of the flux tube displacement. To explore this process we develop a model called the minimum-current corona (MCC) which approximates the current arising on a separator in response to displacement of photospheric flux. This permits a model of the quasi-static evolution of the corona above a complex active region. We also introduce flaring to rapidly change the flux inter-linkage between magnetic features when the internal stress on a separator becomes too large. This eliminates the separator current and releases the energy stored by it. Implementation of the MCC in two examples reveals repeated flaring during the evolution of simple active regions, releasing anywhere from 10²⁷–10²⁹ ergs, at intervals of hours. Combining the energy and frequency gives a general expression for heat deposition due to flaring (i.e., reconnection).     

Weakly relativistic solitary waves in multicomponent plasmas with electron inertia

Existence of compressive relativistic solitons is established in an arbitrary ξ-direction, inclining at an angle to the direction of the weak magnetic field (ω _pi ≫ω _Bi ) in this plasma compound with ions, relativistic electrons and relativistic electron beams. It is observed that the absolute linear growth of amplitudes of compressive solitons is due to inactive role of the weak magnetic field and the initial streaming speeds of relativistic electrons, electron beams, and Q _b (ion mass to electron beam mass). Besides, the small initial streaming of electrons is found to be responsible to generate relatively high amplitude compressive solitons. The non-relativistic ions in the background plasma, but in absence of electron-beam drift and in presence of weak magnetic field are the causing effect of interest for the smooth growth of soliton amplitudes in this model of plasma.     

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.     

Polar 5—an electron accelerator experiment within an aurora. 4. Measurements of the 391.4 nm light produced by an artificial electron beam in the upper atmosphere

The POLAR 5 sounding rocket, launched from Andøya, Norway, on February 1, 1976, was of the “mother-daughter” configuration.A rocket-borne electron accelerator, mounted on the “daughter,” produced a pulsed electron beam with a maximum current of 130 mA and electron energies up to 10 kev.Using a photometer the luminescence at 391.4nm produced by electrons colliding with ambient nitrogen molecules was studied. The observed light at 391.4 nm consisted of low background, with occasional flashes due to the natural auroral excitations, and intense sparkles when the electron beam was emitted.Below 130 km the light observed during beam injection can be explained by excitations of ambient N₂ due to high energy beam electrons.In the altitude range from 150 km to apogee at 220 km, the observed light level during beam emission is fairly constant and much larger than that produced by the high energy beam electrons. A possible source of this light is the excitation of ambient N₂ by an enhanced population of low energy electrons, created by the presence of a beam plasma discharge in the vicinity of the “daughter” payload.     

Dissipation and stability of return currents in solar flares

The dynamics of an electron beam, under the effects of Coulomb collisions and classical Ohmic dissipation of the return current, is analysed for a background plasma with a temperature which is time dependent due to the heating effect of beam dissipation offset by thermal conductive cooling. It is shown that the plasma is heated toward a steady state, in time scales short compared to typical flare beam switch on times, and that in this steady state only two regimes of beam dynamics arise.For moderate values of the ratio of beam flux to plasma density (F ₀/n), beam dynamics is dominated by direct Coulomb collisions as in the usual thick target treatment. With increase of F ₀/n, before return current (classical) Ohmic losses can exceed collisions, the return current becomes unstable. In this latter regime beam dynamics is presumably dominated by wave generation and anomalous Ohmic dissipation of the return current, but no detailed treatment is attempted here.     

Instability of Electrons Trapped by the Coronal Magnetic Field and Its Evidence in the Fine Structure (Zebra Pattern) of Solar Radio Spectra

Solar radio emission is a significant source of information regarding coronal plasma parameters and the processes occurring in the solar atmosphere. High resolution frequency, space, and time observations together with the developed theory make it possible to retrieve physical conditions in the radiation source and recognize the radiation mechanisms responsible for various kinds of solar radio emission. In particular, the high brightness temperature of many bursts testifies to coherent radiation mechanisms, that is, to plasma instabilities in the corona. As an example, the fine structure of solar radio spectra looking like a set of quasi-harmonic stripes of enhanced and lowered radiation, which is observed against the type IV continuum at the post-flare phase of activity, is considered. It is shown that such emission arises from a trap-like source filled with a weakly anisotropic equilibrium plasma and a small addition of electrons which have a shortage of small velocities perpendicular to the magnetic field. For many recorded events with the mentioned fine spectral structure the instability processes responsible for the observed features are recognized. Namely, the background type IV continuum is due to the loss-cone instability of hot non-equilibrium electrons, and the enhanced striped radiation results from the double-plasma-resonance effect in the regions where the plasma frequency f _p coincides with the harmonics of electron gyrofrequency f _B ; f _p=sf _B . Estimations of the electron number density and magnetic field in the coronal magnetic traps, as well as the electron number density and velocities of hot electrons necessary to excite the radiation with the observed fine structure, are given. It is also shown that in some cases several ensembles of non-equilibrium electrons can coexist in magnetic traps during solar flares and that its radio signature sensitively depends on the parameters of the distribution functions of the various ensembles.     

Temperature anisotropy instabilities in a plasma containing cold and hot species in the magnetosphere

The nature of convective instability has been investigated for an electromagnetic wave, either right circularly polarised or left circularly polarised, propagating along a magnetic line of force in a plasma whose distribution function exhibits a temperature anisotropy in the hot species, a loss cone structure and a beam of cold electrons or ions travelling along the line of force with velocity V₁. Detailed numerical calculations have been made using a computer for the growth and decay of the wave for different values of the anisotropy ratio T_⊥/T_∥ = δ of the perpendicular and parallel temperatures, the McIlwain parameter L, the loss cone index j, velocity V₁ of the streaming particle and the particle density ratio ε. The ranges of values of ε and δ for which the wave becomes unstable have been studied in detail. It is found that wave propagation shows no dependence on the loss cone index but shows very strong dependence on the temperature anisotropy δ.     

The analytic properties of the flapping current sheets in the earth magnetotail

The current sheet in Earth’s magnetotail often flaps, and the flapping waves could be induced propagating towards the dawn and dusk flanks, which could make the current sheet dynamic. To explore the dynamic characteristics of current sheet associated with the flapping motion holistically and provide reasonable physical interpretations, detailed direct calculation and analysis have been applied to one approximate analytic model of magnetic field in the flapping current sheet. The main results from the model demonstrate: (1) the magnetic fluctuation amplitude is attenuated from the center of current sheet to the lobe regions; The larger wave amplitude would induce the larger magnetic amplitude; (2) the curvature of magnetic field lines (MFLs), with maximum at the center of current sheet, is only dependent on the displacement Z along the south-north direction from the center of current sheet, regardless of the tilt of current sheet; (3) the half-thickness of neutral sheet, h, the minimum curvature radius of MFLs, R_cmin, and the tilt angle of current sheet, δ, satisfies h=R_cmin cos δ; (4) the gradient of magnetic strength forms a double-peak profile, and the peak value would be more intense if the local current sheet is more tilted; (5) current density j and its j_y, j_z components reach the extremum at the center of CS. j and j_z would be more intense if the local current sheet is more tilted, but it is not the case for j_y; and (6) the field-aligned component of current density mainly appears in the neutral sheet, and the sign of it would change alternatively as the flapping waves passing by. To check the validity of the model, one simulation on the virtual measurements has been made, and the results are in well consistence with actual observations of Cluster.     

Radial oscillations of coronal loops and microwave radiation from solar flares

We consider the damping mechanisms for the radial oscillations of solar coronal loops in the approximation of a thin magnetic flux tube. We show that the free tube oscillations can have a high Q if the plasma density inside the magnetic flux tube is much higher than the density outside. We analyze the effect of radial coronal-loop magnetic-field oscillations on the modulation of the microwave radiation from solar flares. In the case of a nonthermal gyrosynchrotron mechanism, the fluxes from optically thin and optically thick sources are modulated in antiphase. Based on our model, we diagnose the flare plasma. For the event of May 23, 1990, we estimate the spectral index for accelerated electrons, α≈4.4, and the magnetic-field strength in the region of energy release, B≈190 G.     

Non-equilibrium of Magnetic Flux Tubes emerging into the Solar Corona

A lack of equilibrium of twisted magnetic flux tubes emerging from the photosphere into the corona is considered. Assuming mass and flux conservation in the tube and an isothermal tube that is in thermal equilibrium with the surrounding plasma, it is shown that a sufficently rapid temperature increase through the transition zone may lead to the loss of magnetohydrostatic equilibrium of the emerging flux tube due to the enhancement of the plasma pressure inside the tube. The non-equilibrium leads to a rapid expansion of the tube to reach a new equilibrium state. The rise and expansion of the tube before and after the non-equilibrium are accompanied by an increase in the twist of the magnetic field. This may lead to the field exceeding the threshold for the onset of the kink instability and a subsequent explosive release of magnetic energy.     

The propagation of a dense quasi-neutral ion beam across a magnetized plasma

Propagation of a quasi-neutral narrow ion beam across a magnetised cold plasma is investigated in slab geometry. This problem is of interest in connection with artificial beam injection experiments and with naturally appearing plasma injections into magnetic fields as astrophysical jets. Several different cases are discussed briefly where the beam is assumed either slow or fast. For fast beams it is shown that they propagate due to generation of a polarisation electric field even in the case of presence of a background plasma. Slow beams can depolarise by currents flowing into the beam along the field lines and providing the required electrons for charge neutralisation. Some implications of the model are discussed in the context of recent active beam injection experiments into space plasma.     

Field-aligned electric field caused by the decay of force-free magnetic field and particle acceleration

Numerical simulation for the dynamics of a coronal filamentary magnetic loop has been made under the assumption that the field is initially force-free and an electric resistivity suddenly increases at a given moment due to an appearance of ion sound waves, which can be excited due to a high current density if a characteristic radius r ₀ of the magnetic loop is about 3 km or less in a magnetic field B ₀ of 1000 G. During the resistive decay of the magnetic field a strong field-aligned electric field is created and maintained for a sufficient time to acceleratie both electrons and protons to a high energy, which is proportional to B ₀/r ₀ and can be 100 MeV if r ₀ = 10 km and B ₀ = 1000 G. If the coronal magnetic tube is composed of many such filamentary loops, the total number of accelerated electrons is consistent with the observations.     

Plasma flow in a curved magnetic field

A beam of collisionless plasma is injected along a longitudinal magnetic field into a region of curved magnetic field. Two unpredicted phenomena are observed: The beam becomes deflected in the directionopposite to that in which the field is curved, and itcontracts to a flat slab in the plane of curvature of the magnetic field.The plasma is produced by a conical theta-pinch gun and studied by means of high speed photography, electric and magnetic probes, ion analyser, and spectroscopy.The plasma beam is collisionless and its behaviour is, in principle, understood on the basis of gyro-centre drift theory. A fraction of the transverse electric fieldE=–v×B, which is induced when the beam enters the curved magnetic field, is propagated upstream and causes the reverse deflection byE×B drift. The upstream propagation of the transverse electric field is due to electron currents.The circuit aspect on the plasma is important. The transverse polarization current in the region with the curved field connects to a loop of depolarization currents upstream. The loop has limited ability to carry current because of the collisionless character of the plasma; curlE is almost zero and electric field components arise parallel to the magnetic field. These play an essential role, producing runaway electrons, which have been detected. An increased electron temperature is observed when the plasma is shot into the curved field. Runaway electrons alone might propagate the electric field upstream in case the electron thermal velocity is insufficient.The phenomenon is of a general character and can be expected to occur in a very wide range of ensities. The lower density limit is set by the condition for self-polarization,nm _i / ₀ B ² 1 or, which is equivalent,c ²/v _A ² ;1, wherec is the velocity of light, andv _A the Alfvén velocity. The upper limit is presumably set by the requirement _{e e} 1.The phenomenon is likely to be of importance, for example, for the injection of plasma into magnetic bottles and in space and solar physics. The paper illustrates the complexity of plasma flow phenomena and the importance of close contact between experimental and theoretical work.Paper dedicated to Professor Hannes Alfvén on the occasion of his 70th birthday, 30 May, 1978     

The Evolution of Sunspot Magnetic Fields Associated with a Solar Flare

Solar flares occur due to the sudden release of energy stored in active-region magnetic fields. To date, the precursors to flaring are still not fully understood, although there is evidence that flaring is related to changes in the topology or complexity of an active-region’s magnetic field. Here, the evolution of the magnetic field in active region NOAA 10953 was examined using Hinode/SOT-SP data over a period of 12 hours leading up to and after a GOES B1.0 flare. A number of magnetic-field properties and low-order aspects of magnetic-field topology were extracted from two flux regions that exhibited increased Ca ii H emission during the flare. Pre-flare increases in vertical field strength, vertical current density, and inclination angle of ≈ 8° toward the vertical were observed in flux elements surrounding the primary sunspot. The vertical field strength and current density subsequently decreased in the post-flare state, with the inclination becoming more horizontal by ≈ 7°. This behavior of the field vector may provide a physical basis for future flare-forecasting efforts.     

Interpreting Yohkoh hard and soft X-ray flare observations

A simple model is presented to account for theYohkoh flare observations of Feldmanet al. (1994), and Masuda (1994). Electrons accelerated by the flare are assumed to encounter the dense, small regions observed by Feldmanet al. at the tops of impulsively flaring coronal magnetic loops. The values of electron density and volume inferred by Feldmanet al. imply that these dense regions present an intermediate thick-thin target to the energised electrons. Specifically, they present a thick (thin) target to electrons with energy much less (greater) thanE _c , where 15 keV <E _c < 40 keV. The electrons are either stopped at the loop top or precipitate down the field lines of the loop to the footpoints. Collisional losses of the electrons at the loop top produce the heating observed by Feldmanet al. and also some hard X-rays. It is argued that this is the mechanism for the loop-top hard X-ray sources observed in limb flares by Masuda. Adopting a simple model for the energy losses of electrons traversing the dense region and the ambient loop plasma, hard X-ray spectra are derived for the loop-top source, the footpoint sources and the region between the loop top and footpoints. These spectra are compared with the observations of Masuda. The model spectra are found to qualitatively agree with the data, and in particular account for the observed steepening of the loop-top and footpoint spectra between 14 and 53 keV and the relative brightnesses of the loop-top and footpoint sources.     

On the origin of time delays in hard X-ray and gamma-ray emission of solar flares

The possibility of a strong pitch-angle diffusion regime as well as of turbulent propagation of energetic ions and electrons in flaring loops has been shown. The strong diffusion regime suggests that two regions with a high level of small-scale turbulence are formed in the magnetic trap. Such additional turbulent mirrors scatter energetic particles and, therefore, the flux of precipitating particles decreases and the mean lifetime of electrons and protons in a flaring loop grows. We cannot rule out that the turbulent propagation of the particles can be responsible for the energy dependence of hard X-ray delays as well as the time lag of the gamma-ray line peaks with respect to the hard X-ray peaks as the electrons and ions are accelerated simultaneously. The trap plus turbulent propagation model may also explain the lack of abundant population of 10–100 keV electrons in interplanetary space in proton-rich events and offers new possibilities for flare plasma diagnostics.     

A Special Radio Spectral Fine Structure Used for Plasma Diagnostics in Coronal Magnetic Traps

A specific combination of spectral fine structures in meter –  decimeter dynamic spectra of solar radio burst emission is reported in observations carried out at the Astrophysical Institute Potsdam. We describe and interpret the occurrence of zebra patterns in fast drifting (type III burst-like) envelopes of absorbed continuum emission. A possible mechanism of the origin of such an involved spectral pattern is put forward, leading to a necessarily multinonequlibrium component coronal plasma. The suggested mechanism is based on the fact that during the passage of a fast electron beam through the corona the loss cone instability (which is caused by electrons captured in a magnetic trap generating the continuum) is quenched. As result, a fast drift burst appears in absorption, and the zebra pattern becomes visible on the low background emission. This zebra pattern is generated by a group of electrons with a nonequilibrium distribution over transverse velocities. In the absence of the beam the pattern is invisible against the background of the stronger continuum. It is shown that the mechanism is sensitive to the distribution parameters of the different electron ensembles. Therefore the effect in dynamic radio spectra is comparatively rare but its proper existence underlines that the simultaneous presence of different ensembles of electrons in the flaring corona can be quite a frequent situation. This can explain some problems in deconvolving X-ray photon spectra to electron energy spectra.     

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.