Evolution of electron and proton temperatures in a flaring loop

We have investigated numerically how a temperature difference between electrons and protons is produced in a flaring loop by adopting a one-fluid, two-temperature model instead of a single-temperature model. We have treated a case in which flare energy is released in the form of heating of electrons located in the top part of the loop.In this case, a large temperature difference (T _e/T _p 10) appears in the corona in the energy-input phase of the flare. When the material evaporated from the chromosphere fills the corona, the temperature difference in the loop begins to shrink rapidly from below. Eventually, in the loop apex, the proton temperature exceeds the electron temperature mainly due to cooling of the electrons by conduction down the loop and heating of the protons by compression of the ascending material. In the late phase of the flare (t 15 min from the flare onset), the temperature difference becomes less than 2% of the mean temperature of electrons and protons at every point in the loop.     

Energy release in a prominence-loaded flaring loop

Zaitsev and Stepanov (1991, 1992) proposed a mechanism for energy release in solar flares that involves the intrusion of dense prominence material into a coronal loop. The resulting non-steady state conditions are claimed to increase the resistance of the loop by 8–10 orders of magnitude. It is shown here that the dramatic increase in resistance calculated by Zaitsev and Stepanov depends on a gross overestimate of the of the magnitude of the magnetic force in the loop prior to the flare trigger. A more realistic estimate of the increase due to the mechanism suggests that it is by no more than about four orders of magnitude. As a consequence, the prominence-loading mechanism does not provide a tenable flare model.     

The resistances of the photosphere and of a flaring coronal loop

Solar Physics - We consider two aspects of solar flares from the point of view of circuit theory. First, we show that the so-called “dynamo models”, which invoke an analogy between the...     

The resistances of the photosphere and of a flaring coronal loop

We consider two aspects of solar flares from the point of view of circuit theory. First, we show that the so-called dynamo models, which invoke an analogy between the Earth's magnetosphere-ionosphere circuit and the solar corona-photosphere circuit, are illfounded. Second, we consider the rate of coronal energy release in the impulsive phase of a modest flare, and show that, if the energy going into mass motion can be neglected, the corona must present a resistance of about 10^–3 . Classical resistivity, even in a highly filamented circuit, cannot provide so high a resistance. Anomalous resistivity due to ion sound turbulence can provide the required resistance in this case, but is insufficient to explain the very high power levels inferred in some fast spikes.     

Microwave diagnostics of energetic electrons in flares

Electrons accelerated during solar flares are revealed by their electromagnetic radiation in different spectral ranges, emitted at different heights in the solar atmosphere. The observational analysis points to a common and continuous injection of particles. Based on this result, a quantitative investigation of the hard X-ray and microwave emissions observed during the 29 June, 1980 flare at 11: 40 UT has been performed. This is the first modelisation that takes into account both the inhomogeneity of the microwave source region and the dynamical evolution of the electron population. First results of our model computations demonstrate that during the most energetic phase of the event both hard X-rays and microwaves are described by electron populations resulting from the same injection function, and that the total numbers of electrons required for both emissions are compatible. Account for the inhomogeneity of the microwave source is shown to be a necessary condition for the interpretation of observed spectra.Proceedings of the Workshop on Radio Continua during Solar Flares, held at Duino (Trieste), Italy, 27–31 May, 1985.     

The spatial distribution of 6 centimeter gyroresonance emission from a flaring X-ray loop

We compare simultaneous high resolution soft X-ray and 6 cm images of the decay phase of an M3 X-ray flare in Hale Region 16413. The photographic X-ray images were obtained on an AS & E sounding rocket flown 7 November, 1979, and the 6 cm observations were made with the VLA. The X-ray images were converted to arrays of line-of-sight emission integrals and average temperature throughout the region. The X-ray flare structure consisted of a large loop system of length 1.3 arc min and average temperature 8 × 10⁶ K. The peak 6 cm emission appeared to come from a region below the X-ray loop. The predicted 6 cm flux due to thermal bremsstrahlung calculated on the basis of the X-ray parameters along the loop was about an order of magnitude less than observed. We model the loop geometry to examine the expected gyroresonance absorption along the loop. We find that thermal gyroresonance emission requiring rather large azimuthal or radial field components, or nonthermal gyrosynchrotron emission involving continual acceleration of electrons can explain the observations. However, we cannot choose between these possibilities because of our poor knowledge of the loop magnetic field.     

The absorption of energetic electrons by argon gas

The processes by which energetic electrons lose energy in a weakly ionized gas of argon are analysed and calculations are carried out taking into account the discrete nature of the excitation processes. The excitation, ionization and heating efficiences are computed for energies up to 200 eV absorbed in a gas with fractional ionizations varying up to 10^?2.     

Effect of low energy electron injection on storm-time evolution of radiation belt energetic electrons: three-dimensional modeling

Using the STEERB (storm-time evolution of electron radiation belt) code, we simulate the evolution of radiation belt energetic electrons during geomagnetic storms in the case of low energy electron injection. The STEERB code is used to solve the three-dimensional Fokker–Planck diffusion equation which incorporates wave-particle interaction, Coulomb collisions and radial diffusion. Numerical simulations show that under the short time (～1 h) injection of low energy (0.1 MeV≤E _k ≤0.2 MeV) fluxes of radiation belt energetic electrons can increase during the entire storm period. During the main and recovery phases, such injection efficiently enhances chorus-driven acceleration of radiation belt energetic electrons, allowing fluxes of energetic electrons by a factor of 1–2 orders higher than those in the absence of injection. The current results indicate that substorm-induced electron injection must be incorporated to investigate the evolution of radiation belt energetic electrons.     

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 absorption of energetic electrons by molecular hydrogen gas

The processes by which energetic electrons lose energy in a weakly ionized gas of molecular hydrogen are analysed and calculations are carried out taking into account the discrete nature of the excitation processes. The excitation, ionization and heating efficiencies are computed for electrons with energies up to 100 eV absorbed in a gas with fractional ionizations up to 10^?2 and the mean energy per neutral hydrogen atom pair is calculated.     

Propagation and confinement of energetic electrons in solar flares

Solar Physics - 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:...     

Collisional heating by nonthermal electrons in a tapered magnetic loop

We examine the behavior of non-thermal electrons injected into a tapered magnetic loop, under the action of both Coulomb collisional and magnetic field gradient forces. An approximate analytic formula for the heating rate as a function of distance along the loop is developed, and found to be in good agreement with exact numerical solutions of the relevant equations. Such a formula is useful as a source term in many situations, such as hydrodynamic simulations of atmospheric response to flare energy input.Presidential Young Investigator.     

Incoherent radiation from relativistic electrons with power energetic spectrum

It is shown that an incoherent high-frequency radiation from an ensemble of relativistic particles with the power energy distribution is described by a certain general expression which covers practically all the cases of particle radiation in random electromagnetic fields of cosmic radiation sources.     

Atmospheric loss of energetic electrons in the Jovian synchrotron zone

For decades, ground-based radio observations of Jovian synchrotron radiation have shown emission originating predominantly from the equatorial region and from high-latitude regions (lobes) near L∼2.5. The observations show a longitudinally asymmetric gap between the emission peaks of the lobes and the atmosphere of Jupiter. One possible explanation for these gaps is the loss of electrons through collisions with atmospheric neutrals as the electrons bounce along magnetic field lines and drift longitudinally in the presence of asymmetric magnetic fields. To assess this hypothesis, we applied the recently developed O6 and VIP4 magnetic field models to calculate the trajectories of electrons as they drift longitudinally in Jupiter's magnetic field, and derive the sizes of their equatorial drift loss cones. We then identified the shells on which electrons would be lost due to collisions with the atmosphere. The calculated drift loss cone sizes could be applied in future to the modeling of electron distribution functions in this region and could also be applied to the study of Jovian auroral zone. This method also allowed us to compute the shell-splitting effects for these drifting electrons and we find the shell-splitting to be small (?0.05R_J). This justifies a recent modeling assumption that particles drift on the same shells in a three-dimensional distribution model of electrons. We also compared the computed gaps with the observed gaps, and found that the atmospheric loss mechanism alone is not able to sufficiently explain the observed gap asymmetry.     

Coronal and interplanetary transport of solar energetic protons and electrons

We present a new method to separate interplanetary and coronal propagation, starting from intensity variations observed by spaceprobes at different heliolongitudes. In general, a decrease in absolute intensities is observed simultaneously with an increase in temporal delays. The coupling of these two effects can be described by Reid's model of coronal diffusion and can in principle be used to determine the two coronal time constants, diffusion time t _c and escape time A. In addition, a least-squares fit method is used to determine the parameters of interplanetary transport, assuming a radial dependence as (r) = ₀(r/1 AU)^b. The method is applied to the two solar events of 27 December, 1977 and 1 January, 1978 which were observed by the spaceprobes Helios 1, Helios 2, and Prognoz 6. Energetic particle data are analysed for 13–27 MeV protons and -0.5 MeV electrons. For the regions in space encountered during these events the mean free path of electrons is smaller than that of protons. Straight interpolation between the two rigidities leads to a rather flat rigidity dependence (P) P ⁿ with n = 0.17–0.25. This contradicts the prediction of a constant mean free path or of the transition to scatter-free propagation below about 100 MV rigidity. In three of the four cases the mean free path of 13–27 MeV protons is of the order 0.17 AU, the mean free path of electrons of the order 0.06 AU. For protons we find b - 0.7 for the exponent of the radial variation.The concept of two different coronal propagation regimes is confirmed. It is remarkable that in both regimes electrons are transported more efficiently than protons. This holds for the temporal delay as well as for the amplitude decrease. This is in contrast with the long existing concept of rigidity independent transport and puts severe limits to any model of coronal transport. For the December event all three spaceprobes are in the fast propagation regime up to an angular distance of 62°. For protons we find a finite delay even in the fast propagation region, corresponding to a coronal delay rate of about 0.8 hr rad^-1 up to 60° angular distance. In contrast, relativistic electrons may reach this distance within a few minutes.The fast transport of electrons and the different behaviour of electrons and protons is in contradiction to the expanding bottle concept. An explanation of coronal transport by shock acceleration directly on open field lines could in principle work in case of protons in the fast propagation region, but would fail in case of the electrons. The fast and efficient transport of electrons is most likely due to a region of field lines extending over a wide range of longitudes directly from the active region into interplanetary space. The much slower transport of both particle types at large azimuthal distances can neither be explained by direct access to open field lines not by the direct shock acceleration concept. A possible explanation is the loop reconnection model in a modified version, allowing for a faster lateral transport of electrons.Now at AEG, 2000 Wedel, F.R.G.     

The possible role of energetic electrons in the production of surges

Energetic electrons, which play a major role in the explosive phases of flares, are proposed as the energy source for the production of surges. Flare data from a two-year interval are analyzed to show that the probability of having surges associated with flares is greater when there are accompanying decimeter type III bursts or impulsive 8800 MHz bursts. The model of chromospheric heating by impulsive electrons proposed by Hudson is examined and shown to provide an adequate explanation for the origin of flare surges. The proposed surge model is consistent with the temporal evolution of the flare-surge event and the required surge energy. Surges not accompanied by flares can also probably be explained by the model.     

The spatial distribution of energetic ions and electrons in the magnetotail

The spatial distributions of energetic ion and electron bursts observed on the IMP 7 and 8 satellites in the Earth's magnetotail were studied. It was found that the ion bursts were more frequently detected in the dusk than in the dawn quarter of the neutral sheet whereas the electron bursts, more frequently in the dawn than the dusk quarter. The degree of dawn-dusk asymmetry is however energy dependent; the distribution for higher energy particle bursts exhibits higher degree of asymmetry. The morphologies of the distributions manifest themselves as seasonal variations of the most probable solar ecliptic latitudes at which the ion and electron bursts were observed. The amplitudes of the variations are about 25° with the seasonal variation for ions leading that for electrons by about 2 months.     

Comparison of flare bremsstrahlung resulting from energetic thermal and nonthermal electrons

We have investigated the behavior of the X-ray bremsstrahlung spectra resulting from two distinct types of electron distribution functions impinging on a target atmosphere during flare activity. A power-law distribution function is compared with two double-peaked Maxwellians. The results of these calculations show that it would be difficult to rule out multithermal interpretations for the emitted high-energy X-rays.