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.     

具平缓电子能谱的伽玛射线暴的解析光变曲线

在标准的伽玛暴余辉模型中,电子通过费米一级加速后形成单幂律能谱分布dn/dγe∝γe-p(p≈2.3),但在某些伽玛暴事件中观测到了平缓的电子能谱分布(即p＜2).在单幂律谱和分段幂律谱两种情况下,分别给出了具有平缓电子能谱的伽玛暴余辉的解析光变曲线,并以GRB 060908为例进行了讨论.同时提出了伽玛暴低能谱危机的...     

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.     

Analytical Afterglow Light Curves of Gamma-ray Bursts: the Case of a Flat Electron Spectrum

In the standard afterglow model, the swept electrons have a single power-law energy distribution dn/dγe ∝ γ−p e (p ∼ 2.3), owing to the first order Fermi acceleration process. However, in some events people find a lot of evidence for a flat electron spectrum (i.e., p < 2). In this work, the analytical afterglow light curves in the case of a flat electron energy distribution are presented respectively for a single power-law spectrum and a broken power-law spectrum, then the results are applied to the specific burst GRB 060908. Besides, we have also speculated a possible solution of the so-called low energy spectrum crisis of Gamma-ray Bursts     

The betatron effect in collapsing magnetic traps

We consider the question of how the betatron effect affects the particle acceleration in a magnetic trap with a rapidly decreasing length. We show that the additional increase in energy caused by the betatron acceleration as the trap contracts is exactly offset by the decrease in the time of particle confinement in the trap, because the loss cone becomes larger during the contraction. As a result, the particle energy at the time of escape from the trap remains the same as that in a collapsing trap without contraction. We estimate the Alfvén-pumping efficiency in a collapsing trap in connection with the problem of particle acceleration in solar flares. The additional energy acquired by particles from magnetic-field oscillations is shown to be negligible. We discuss the possible observational manifestations of the betatron effect in solar flares.     

On the problem of power-law spectrum of particles accelerated in solar flares

The formation of power-law energy spectrum of particles accelerated in solar flares is investigated. The distinct difference between the mechanism and the model of acceleration is pointed out. It is shown that Fermi's model is described by linear differential equation of the first order and therefore a power-law spectrum is formed only for some special conditions which apparently are not fulfilled for flares. A satisfactory alternative to Fermi's model hasn't yet been found. In conclusion the connection between the mechanism of acceleration and a charge spectrum of accelerated particles is examined.     

Simulating Poynting Flux Acceleration in the Laboratory with Colliding Laser Pulses

We review recent PIC simulation results which show that double-sided irradiation of a thin over-dense plasma slab with ultra-intense laser pulses from both sides can lead to sustained comoving Poynting flux acceleration of electrons to energies much higher than the conventional ponderomotive limit. The result is a robust power-law electron momentum spectrum similar to astrophysical sources. We discuss future ultra-intense laser experiments that may be used to simulate astrophysical particle acceleration.     

Particle acceleration during the explosive phase of a solar flare

Starting with the quasi-linear equation of the distribution function of particles in a regular electric field, a combined diffusion coefficient in the momentum space conbining the effects of the regular field and a turbulent field is obtained and a combined mechanism of acceleration by the regular and turbulent fields in the neutral sheet of solar proton flares is proposed. It is shown by calculation that conditions in solar proton flares are such that the charged particles can be effectively accelerated to tens of MeV, even ~1 GeV. It is shown that the combined acceleration by a regular electric field and ion-acoustic turbulence pumps the protons and other heavy ions into ranges of energy where they can be accelerated by Langmuir turbulence. By considering the combined acceleration by Langmuir turbulence and the regular electric field, the observed spectrum of energetic protons and the power-law spectrum of energetic electrons can be reproduced.     

Relation between X-ray flux and radio flux from cosmic objects

The relationship between the X-ray flux and the radio flux from cosmic objects is investigated. We consider the emission from energetic electrons on the condition in which a plasma and a magnetic field exist. As energetic electrons under the circumstances emit both X-rays by the bremsstrahlung mechanism and radio waves by the gyrosynchrotron mechanism simultaneously, it is shown that the radio flux density is closely related to the X-ray flux density. Solving an integral equation describing the X-ray flux density at Earth, we obtain the energy spectrum of electrons in the emitting region. Inserting the result into equation of the radio flux density at Earth, we obtain the direct formula between the X-ray flux density and the radio flux density. The relation is independent of the distance between Earth and cosmic sources. Assuming a power-law X-ray spectrum, we evaluate the numerical relation between two flux densities.     

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 ...     

Spectral properties of shocked accretion flows— a self-consistent study

Magnetized accretion flows around black holes which include standing or oscillating shock waves can produce very realistic spectrum till a few MeV. These shocks accelerate hot electrons which produce power-law spectrum. The post-shock region intercepts soft-photons from an external source, namely, a Keplerian disk and also from distributed sources such as the synchrotron photons emitted from thermal and non-thermal electrons originated in the pre-shock and post-shock flow. These photons are inverse Comptonized by the thermal and the non-thermal electrons present in the CENBOL region. Computations show that the emitted radiation is extended till a few MeV. We include the bulk motion Comptonization as well and discuss its importance vis-a-vis the power-law spectrum produced by non-thermal electrons.      

The efficiency of electron acceleration in solar type-IV radio pulsations with a zebra pattern

Based on a comprehensive analysis of the October 25, 1994 event, we consider the balance of energetic particles in a type-IV solar radio emission source with a zebra-type fine structure (in a coronal magnetic loop). The zebra pattern is formed through the injection of fast electrons into a trap and the formation of a ring-type nonequilibrium electron distribution function. We estimated the characteristic zebra-pattern lifetime, which is determined by the escape of fast particles from the trap into the loss cone. In addition, we determined the number of fast particles that must be injected into the trap to provide the observed radio brightness temperature in zebra-pattern stripes by analyzing the plasma emission mechanism responsible for the zebra-pattern generation. As a result, we estimated the efficiency of the electron acceleration mechanism in coronal magnetic loops at the post-flare evolutionary phase of an active region.     

On Integrated Hard X-Ray Broken-Up Spectra of Solar Flares

The summation of two single power-law spectra with a rather big difference of the spectral indices and with comparable intensities looks like a broken-up spectrum. The spatially integrated hard X-rays contain contributions from different sources, like footpoint and looptop sources. Within the standard scenario of solar flares, the power-law index difference between the footpoints and looptop should be two. Taking the M7.6 flare on 24 October 2003 as an example, we showed that the hard X-ray spectrum itself for footpoints and looptop is a single power-law, but the spatially integrated spectrum presents a broken-up form. It is also shown that the time-integrated spectrum could present a broken-up form, although the spectrum in further refined intervals presents a single power-law. It is concluded that the integrated broken-up spectrum observed here is produced either by the summation of individual sources or by the temporal variation of a single source, not by the acceleration itself.     

磁重联电流片的参数变化对电子加速的影响

通过采用试验粒子的方法,研究了在有引导磁场Bz存在的磁重联电流片中,电子被super-Dreicer电场Ez加速后的运动特征.首先,考虑了引导磁场恒定且与电场有不同方向时对粒子加速的影响.在这种情况下,Bz方向的改变直接改变了电子的运动轨迹,使其沿着不同的路径离开电流片.在Bz和Ez同向时,高能电子的pitch-angle接近于180°.然而,当2者反向时,高能电子的pitch-angle接近0°.引导磁场的取向只是使电场有选择地对不同区域的电子进行加速,不会最终影响电子的能量分布,最终得到的能谱是普遍的幂率谱E-γ.在典型的日冕条件下, γ大约等于2.9.进一步的研究表明γ的大小依赖于引导磁场及磁重联电场的强弱,以及电流片的尺度.随后,也研究了包含多个X-点和O-点电流片中被加速粒子的运动特征.结果表明X-点和O-点的存在使得粒子被束缚在加速区并获得最大的加速,而且最终的能谱具有多幂率谱的特征.     

The electron-proton abundance ratio in cosmic rays

An attempt has been made to understand the electron-proton abundance ratio in cosmic rays observed near the Earth. After correction for interplanetary and interstellar effects, the ratio has been obtained near the source boundary. A leaky source model which can describe consistently all components of the cosmic radiation was then used to obtain the abundance inside the source. Possible effects of injection and acceleration processes on the ratio are examined. From these considerations the most plausible mechanism seems to be injection of electrons and protons by hot gas, and their acceleration by a mixture of Fermi and betatron processes; this is followed by leakage of particles into interstellar space in a rigidity dependent fashion.     

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.     

Radiative losses and cut-offs of energetic particles at relativistic shocks

We investigate the acceleration and simultaneous radiative losses of electrons in the vicinity of relativistic shocks. Particles undergo pitch angle diffusion, gaining energy as they cross the shock by the Fermi mechanism and also emitting synchrotron radiation in the ambient magnetic field. A semi-analytic approach is developed which allows us to consider the behaviour of the shape of the spectral cut-off and the variation of that cut-off with the particle pitch angle. The implications for the synchrotron emission of relativistic jets, such as those in gamma-ray burst sources and blazars, are discussed.     

The time-dependent distribution of relativistic electrons in radio sources

The time-dependent distribution of relativistic electrons is very important to the discussion of light and the spectrum. This letter provides a general, time-dependent solution for the continuity equation of electron number density (CEEND). Several special solutions with the first Fermi acceleration and different injection patterns are obtained.     

The role of betatron acceleration in complex solar bursts

The betatron mechanism was proposed by Brown and Hoyng (1975) as a means of producing the continuous, quasi-periodic electron acceleration which may occur in long-lasting hard X-ray events. In the present work, two pertinent facets of the betatron model are investigated: The possibility that the multiplicity characteristic of complex impulsive bursts is due to the betatron process; and the possibility that some or all of the second-stage emission during two-stage bursts can be attributed to betatron acceleration. To test for the pattern of X-ray spectral behavior predicted by the betatron model, a number of multiply-impulsive events (cf., Karpen et al., 1979) and two-stage bursts (cf., Frost and Dennis, 1971) were selected from the OSO-5 hard X-ray spectrometer data for in-depth analysis. The purely impulsive emissions show no signs of the effects of betatron action, thus eliminating this process as a potential source of impulsive-phase multiplicity. However, the spectral characteristics determined during the first few minutes of the second stage are found to be consistent with the predictions of the betatron model for the majority of the two-stage events studied. The betatron-acceleration mechanism thus is proposed as a common second-stage phenomenon, closely associated with the diverse phenomena at other wavelengths which characterize this phase of emission. The physical significance of the source parameters derived according to the model-fitting procedure are discussed in detail, and the role of the betatron process is evaluated in the broader context of present-day concepts of the second stage.