Comparison of the Fermi and betatron acceleration efficiencies in collapsing magnetic traps

The acceleration of charged particles in the solar corona during flares is investigated in terms of a model in which the electrons and ions preaccelerated in the magnetic reconnection region are injected into a collapsing magnetic trap. Here, the particle energy increases rapidly simultaneously through the Fermi and betatron mechanisms. Comparison of the efficiencies of the two mechanisms shows that the accelerated electrons in such a trap produce more intense hard X-ray (HXR) bursts than those in a trap where only the Fermi acceleration mechanism would be at work. This effect explains the Yohkoh and RHESSI satellite observations in which HXR sources more intense than the HXR emission from the chromosphere were detected in the corona.     

Formation of power-law electron spectra in collapsing magnetic traps

The energy distribution of the fast electrons captured into a collapsing magnetic trap in the solar corona is calculated as a function of the trap length and diameter. It is shown that if the electrons injected into the trap have a power-law spectrum, then their spectrum remains a power-law one with the same slope throughout the acceleration process for both the Fermi and betatron acceleration mechanisms. For electrons with a thermal injection spectrum, the model predicts two types of hard X-ray sources, thermal and nonthermal. Thermal sources are formed in traps dominated by the betatron mechanism. Nonthermal sources with a power-law spectrum are formed when electrons are accelerated by the Fermi mechanism.     

Particle propagation effects on solar flare X- and γ-ray time profiles

Much of the evidence for second stage particle acceleration in solar flares lies in the temporal variation of solar X- and -ray emissions. However, the solar flare X- and -ray burst time-intensity profiles are governed not only by the production or acceleration of electrons and protons but by the propagation of these particles in the solar atmosphere. The effects of particle propagation on X-ray and -ray time profiles are illustrated and compared through the use of three models with the result that a variety of particle propagation schemes reproduce effects commonly associated with second stage acceleration. The first model is that of a closed uniform density trap. The other two models employ particle diffusion from a trap to denser regions of the solar atmosphere to produce the high energy radiation. These calculations show that delayed peaking of the photon flux with respect to particle production and reduction in the impulsiveness of the high energy emission is to be expected, effects commonly associated with second stage acceleration. Thus, well understood physical processes are capable of producing so-called time delays in the high energy emission independent of any delays produced by additional particle acceleration processes. Diagnostic differences between these models are also discussed.     

The role of collisions in the particle acceleration in solar-flare magnetic traps

We investigate the particle acceleration in a magnetic trap with converging mirrors, which is a constituent part of the magnetic reconnection mechanism in solar flares. We take into account the effect of Coulomb collisions on the formation of the accelerated-electron distribution function. The solution of the kinetic equation shows that the Coulomb scattering of anisotropic accelerated electrons leads to their isotropization. As a result, the fraction of trapped particles increases and the acceleration efficiency significantly rises.     

Role of anisotropy of the initial particle distribution in the acceleration in collapsing solar-flare traps

We consider the behavior of charged particles with an anisotropic initial velocity distribution in a magnetic trap with approaching mirrors in connection with the problem of particle acceleration in solar flares. We show that, irrespective of the charge sign, the efficiency of confinement and acceleration increases with increasing anisotropy factor of the initial distribution α = (T_⊥/T_∥)^1/2. For a positive electric potential of the trap plasma relative to the mirrors, the emerging additional effect of ion expulsion form the trap increases with α_i. The derived estimate of the electric potential suggests an amplification of the initial perturbation and the development of instability.     

Electron acceleration in solar-flare magnetic traps: Model properties and their observational confirmations

Using an analytical solution of the kinetic equation, we have investigated the model properties of the coronal and chromospheric hard X-ray sources in the limb flare of July 19, 2012. We calculated the emission spectrum at the flare loop footpoints in the thick-target approximation with a reverse current and showed it to be consistent with the observed one. The spectrum of the coronal source located above the flare loop was calculated in the thin-target approximation. In this case, the slope of the hard X-ray spectrum is reproduced very accurately, but the intensity of the coronal emission is lower than the observed one by several times. Previously, we showed that this contradiction is completely removed if the additional (relative to the primary acceleration in the reconnecting current layer) electron acceleration in the coronal magnetic trap that contracts in the transverse direction and decreases in length during the impulsive flare phase is taken into account. In this paper we study in detail this effect in the context of a more realistic flare scenario, where a whole ensemble of traps existed in the hard X-ray burst time, each of which was at different stages of its evolution: formation, collapse, destruction. Our results point not only to the existence of first-order Fermi acceleration and betatron electron heating in solar flares but also to their high efficiency. Highly accurate observations of a specific flare are used as an example to show that the previously predicted theoretical features of the model find convincing confirmations.     

Investigation of Quasi-periodic Variations in Hard X-rays of Solar Flares

The aim of the present paper is to use quasi-periodic oscillations in hard X-rays (HXRs) of solar flares as a diagnostic tool for the investigation of impulsive electron acceleration. We have selected a number of flares which showed quasi-periodic oscillations in hard X-rays and their loop-top sources could be easily recognized in HXR images. We have considered MHD standing waves to explain the observed HXR oscillations. We interpret these HXR oscillations as being due to oscillations of magnetic traps within cusp-like magnetic structures. This is confirmed by the good correlation between periods of the oscillations and the sizes of the loop-top sources. We argue that a model of oscillating magnetic traps is adequate to explain the observations. During the compressions of a trap, particles are accelerated, but during its expansions plasma, coming from chromospheric evaporation, fills the trap, which explains the large number of electrons being accelerated during a sequence of strong pulses. The advantage of our model of oscillating magnetic traps is that it can explain both the pulses of electron acceleration and quasi-periodicity of their distribution in time.     

Effect of Coulomb collisions on the particle acceleration in collapsing magnetic traps

The problem of particle acceleration in collapsing magnetic traps in the solar corona has been solved by taking into account the particle scattering and braking in the high-temperature plasma of solar flares. The Coulomb collisions are shown to be weak in traps with lifetimes t _l < 10 s and strong for t _l > 100 s. In the approximation of strong collisions, collapsing magnetic traps are capable of confining up to 20% of the injected particles in the corona for a long time. In the collisionless approximation, this value exceeds 90%. The question about the observational manifestations of collisions is examined. For collision times comparable to t _l , the electron spectrumat energies above 10 keV is shown to be a double-power-law one. Such spectra were found by the RHESSI satellite in flares.     

Particle acceleration in impulsive solar flares

A model for second-step electron acceleration in impulsive solar flares is presented. We have extended the theory of stochastic particle acceleration to include Coulomb energy losses which become important at low coronal heights. This inclusion successfully explains the observed steepening of interplanetary electron spectra below 3 MeV following impulsive solar flares taking place at low coronal heights. It also explains the observed spectral differences of relativistic electrons in long-duration and impulsive flares.     

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.     

Multiple acceleration of protons on the Sun and their free propagation to the Earth on January 20, 2005

We analyze the observations of solar protons with energies >80 MeV near the Earth and the January 20, 2005, solar flare in various ranges of the electromagnetic spectrum. Within approximately the first 30 min after their escape into interplanetary space, the solar protons with energies above 80 MeV propagated without scattering to the Earth and their time profiles were determined only by the time profile of the source on the Sun and its energy spectrum. The 80–165 MeV proton injection function was nonzero beginning at 06:43:80 UT and can be represented as the product of the temporal part, the ACS (Anticoincidence System) SPI (Spectrometer on INTEGRAL) count rate, and the energy part, a power-law proton spectrum ～E ^?4.7±0.1. Protons with energies above 165 MeV and relativistic electrons were injected, respectively, 4 and 9 min later than this time. The close correlation between high-energy solar electromagnetic emission and solar proton fluxes near the Earth is evidence for prolonged and multiple proton acceleration in solar flares. The formation of a posteruptive loop system was most likely accompanied by successive energy releases and acceleration of charged particles with various energies. Our results are in conflict with the ideas of cosmic-ray acceleration in gradual solar particle events at the shock wave driven by a coronal mass ejection.     

Proton activity of the Sun in current solar cycle 24

We present a study of seven large solar proton events in the current solar cycle 24(from 2009 January up to the current date). They were recorded by the GOES spacecraft with the highest proton fluxes being over 200 pfu for energies 10 Me V. In situ particle measurements show that:(1) The profiles of the proton fluxes are highly dependent on the locations of their solar sources, namely flares or coronal mass ejections(CMEs), which confirms the "heliolongitude rules" associated with solar energetic particle fluxes;(2) The solar particle release(SPR) times fall in the decay phase of the flare emission, and are in accordance with the times when the CMEs travel to an average height of 7.9 solar radii; and(3) The time differences between the SPR and the flare peak are also dependent on the locations of the solar active regions. The results tend to support the scenario of proton acceleration by the CME-driven shock,even though there exists a possibility of particle acceleration at the flare site, with subsequent perpendicular diffusion of accelerated particles in the interplanetary magnetic field. We derive the integral time-of-maximum spectra of solar protons in two forms: a single power-law distribution and a power law roll-over with an exponential tail. It is found that the unique ground level enhancement that occurred in the event on 2012 May 17 displays the hardest spectrum and the largest roll-over energy which may explain why this event could extend to relativistic energies.     

Nuclear processes and accelerated particles in solar flares

A detailed review of nuclear processes and particle acceleration in solar flares has been completed recently (Ramaty and Murphy, 1987). Included in this review were a comprehensive discussion of the theory of gamma-ray and neutron production, as well as the results of comparisons of calculations with gamma-ray, neutron and charged-particle observations of solar flares. The implications of these comparisons on particle energy spectra, total numbers, anisotropies and electron-to-proton ratios, as well as on acceleration mechanisms and the interaction site were also discussed. In addition, elemental and isotopic abundances of the ambient gas, derived from gamma-ray observations, were compared to abundances obtained from observations of escaping accelerated particles and other sources. The present paper is a synopsis of this review     

Acceleration of charged particles in the magnetosphere of a collapsing star and their nonthermal electromagnetic radiation

We investigate a transformation of a magnetic field and plasma in nonhomogeneous magnetospheres of collapsing stars with a dipole initial magnetic field and certain initial energy distributions of particles in the magnetosphere as the power low, relativistic Maxwell and Boltzmann. The betatron mechanism of the charged particles acceleration in a collapsing star’s magnetosphere is considered. When a magnetized star is compressed in the stage of the gravitational collapse, the magnetic field increases strongly. This variable magnetic field generates a vortical electric field. Our calculations show that this electric field will accelerate charged particles up to relativistic velocities. Thus, collapsing stars may be sources of high energy cosmic rays in our galaxy as in others. The acceleration of particles during the collapse happens mostly in polar regions of the magnetosphere that leads to polar relativistic streams (jets) formation. When moving in a magnetic field, these particles will generate nonthermal electromagnetic radiation in a broad electromagnetic wavelength band from radioto gamma rays. Thus, in the stage of the gravitational collapse, relativistic jets are formed in stellar magnetospheres. These jets are powerful sources of the nonthermal electromagnetic radiation.     

Towards the circuit theory of solar flares

It has been shown that the main problems of the circuit theory of solar flares - unlikely huge current growth time and the origin of the current interruption - have been resolved considering the case of magnetic loop emergence and the correct application of Ohm's law. The generalized Ohm's law for solar flares is obtained. The conditions for flare energy release are as follows: large current value, > 10¹¹ A, nonsteady-state character of the process, and the existence of a neutral component in a flare plasma. As an example, the coalescence of a flare loop and a filament is considered. It has been shown that the current dissipation has increased drastically as compared with that in a completely ionized plasma. The current dissipation provides effective Joule heating of the plasma and particle acceleration in a solar flare. The ion-atom collisions play the decisive role in the energy release process. As a result the flare loop resistance can grow by 8–10 orders of magnitude. For this we do not need the anomalous resistivity driven by small-scale plasma turbulence. The energy release emerging from the upper part of a flare loop stimulates powerful energy release from the chromospheric level.     

Nuclear processes and accelerated particles in solar flares

A detailed review of nuclear processes and particle acceleration in solar flares has been completed recently (Ramaty and Murphy, 1987). Included in this review were a comprehensive discussion of the theory of gamma-ray and neutron production, as well as the results of comparisons of calculations with gamma-ray, neutron and charged-particle observations of solar flares. The implications of these comparisons on particle energy spectra, total numbers, anisotropies and electron-to-proton ratios, as well as on acceleration mechanisms and the interaction site were also discussed. In addition, elemental and isotopic abundances of the ambient gas, derived from gamma-ray observations, were compared to abundances obtained from observations of escaping accelerated particles and other sources. The present paper is a synopsis of this review

     

Imaging X-ray Polarimeter for Solar Flares (IXPS)

We describe the design of a balloon-borne Imaging X-ray Polarimeter for Solar flares (IXPS). This novel instrument, a Time Projection Chamber (TPC) for photoelectric polarimetry, will be capable of measuring polarization at the few percent level in the 20?C50 keV energy range during an M- or X-class flare, and will provide imaging information at the ??10 arcsec level. The primary objective of such observations is to determine the directivity of nonthermal high-energy electrons producing solar hard X-rays, and hence to learn about the particle acceleration and energy release processes in solar flares. Secondary objectives include the separation of the thermal and nonthermal components of the flare X-ray emissions and the separation of photospheric albedo fluxes from direct emissions.     

On the possible mechanism of the first ground level enhancement in cosmic ray intensity of solar cycle 24

We have carried out this work to comprehend the possible mechanisms of the first ground level enhancement (GLE71 17 May 2012 01:50 UT) in cosmic ray intensity of the solar cycle 24. For this, the cosmic ray intensities registered by neutron monitors at several sites have been analyzed and studied with concurrent solar flares of different energy channels. To assess empirically whether the GLE might have been caused by the energy released from solar flare or CME-driven shock, we identify the possible time line in terms of the lowest spectral index determined from proton fluxes. If the GLE is caused by the energy released from particle acceleration in solar flare, the intensive phase of the flare representing the extreme emission should exist within/around the possible time line. In this respect, it is observed that the possible time line lies within the prominent phase of CME-driven shock. For better understanding, we have checked the possible relativistic energy with respect to solar flare as well as CME-driven shock. As witnessed, if the extreme emission phase of the flare is considered as the reason for the causation of GLE peak, the flare components procured insufficient amount of energy (≤～0.085 GeV) to produce a GLE. If the extreme emission phase of the flare is also considered as the dominator along GLE onset, the possible energy procurement (≤～0.414 GeV) is still not adequate to produce a GLE. In contrast, the CME-driven shock is capable of procuring enough possible relativistic energy (≥～1.21 GeV) that is sufficient amount of the energy for a GLE production. Any amount of the energy (<0.414 GeV) released from preceding flare components is supposed to have been contributed to the shock process. Thus, it is assumed that the GLE71 was possibly caused by the energy released from the shock acceleration, which might have been boosted by the energy emanated from preceding flare.     

Gamma-ray,neutron, and hard X-ray studies and requirements for a high-energy solar physics facility

The requirements for future high-resolution spatial, spectral, and temporal observations of hard X-rays, gamma rays and neutrons from solar flares are discussed in the context of current high-energy flare observations. There is much promise from these observations for achieving a deep understanding of processes of energy release, particle acceleration and particle transport in a complicated environment such as the turbulent and highly magnetized atmosphere of the active Sun.     

X-ray emission characteristics of flares associated with CMEs

We present the study of 20 solar flares observed by “Solar X-ray Spectrometer (SOXS)” mission during November 2003 to December 2006 and found associated with coronal mass ejections (CMEs) seen by LASCO/SOHO mission. In this investigation, X-ray emission characteristics of solar flares and their relationship with the dynamics of CMEs have been presented. We found that the fast moving CMEs, i.e., positive acceleration are better associated with short rise time (< 150 s) flares. However, the velocity of CMEs increases as a function of duration of the flares in both 4.1–10 and 10–20 keV bands. This indicates that the possibility of association of CMEs with larger speeds exists with long duration flare events. We observed that CMEs decelerate with increasing rise time, decay time and duration of the associated X-ray flares. A total 10 out of 20 CMEs under current investigation showed positive acceleration, and 5 of them whose speed did not exceed 589 km/s were associated with short rise time (< 150 s) and short duration (< 1300 s) flares. The other 5 CMEs were associated with long duration or large rise time flare events. The unusual feature of all these positive accelerating CMEs was their low linear speed ranging between 176 and 775 km/s. We do not find any significant correlation between X-ray peak intensity of the flares with linear speed as well as acceleration of the associated CMEs. Based on the onset time of flares and associated CMEs within the observing cadence of CMEs by LASCO, we found that in 16 cases CME preceded the flare by 23 to 1786 s, while in 4 cases flare occurred before the CME by 47 to 685 s. We argue that both events are closely associated with each other and are integral parts of one energy release system.