Energies of Electrons Accelerated in Turbulent Reconnecting Current Sheets in Solar Flares

Yohkoh observations strongly suggest that electron acceleration in solar flares occurs in magnetic reconnection regions in the corona above the soft X-ray flare loops. Unfortunately, models for particle acceleration in reconnecting current sheets predict electron energy gains in terms of the reconnection electric field and the thickness of the sheet, both of which are extremely difficult to measure. It can be shown, however, that application of Ohm's law in a turbulent current sheet, combined with energy and Maxwell's equations, leads to a formula for the electron energy gain in terms of the flare power output, the magnetic field strength, the plasma density and temperature in the sheet, and its area. Typical flare parameters correspond to electron energies between a few tens of keV and a few MeV. The calculation supports the viewpoint that electrons that generate the continuum gamma-ray and hard X-ray emissions in impulsive solar flares are accelerated in a large-scale turbulent current sheet above the soft X-ray flare loops.     

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.     

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.     

Particle Acceleration by a Time-Varying Electric Field in Merging Magnetic Fields

Traditional models for particle acceleration by magnetic reconnection in solar flares assumed a constant electric field in a steady reconnecting magnetic field. Although this assumption may be justified during the gradual phase of flares, the situation is different during the impulsive phase. Observed rapid variations in flare emissions imply that reconnection is non-steady and a time-varying electric field is present in a reconnecting current sheet. This paper describes exploratory calculations of charged particle orbits in an oscillating electric field present either at a neutral plane or a neutral line of two-dimensional magnetic field. A simple analytical model makes it possible to explain the effects of particle trapping and resonant acceleration previously noted by Petkaki and MacKinnon in a numerical simulation. As an application, electron acceleration to X-ray generating energies in impulsive solar flares is discussed within the context of the model.     

Influence of the Variations of Current Sheet Parameters on the Acceleration of Electrons

By the test particle method, we have investigated the kinematic characteristics of the electrons in the reconnecting current sheet with a guiding magnetic field B_z after they are accelerated by the supper-Dreicer electric field E_z. Firstly, the influence of the guiding magnetic field B_z on the particle acceleration is discussed under the assumption that B_z is constant in magnitude but different in orientation with respect to the electric field. In this case, the variation of the B_z direction directly leads to the variation of electron trajectories and makes electrons leave the current sheet along different paths. If B_z is parallel to E_z, the pitch angles of the accelerated electrons are close to 180°. If B_z is anti-parallel to E_z, the pitch angles of the accelerated electrons are close to 0°. The orientation of the guiding magnetic field just makes the electric field accelerate selectively the electrons in different regions, but does not change the energy distribution of electrons, and the finally derived energy spectrum is the common power-law spectrum E^?γ. In typical coronal conditions, γ is about 2.9. The further study indicates that the magnitude of γ depends on the strengths of the guiding magnetic field and reconnecting electric field, as well as the scale of the current sheet. Then, the kinematic characteristics of the accelerated electrons in the current sheet with multiple X-points and O-points are also studied. The result indicates that the existences of the X-points and O-points have the particles constrained in the accelerating region to obtain the maximum acceleration, and the final energy spectrum has the characteristics of multi-power law spectra.     

Test particle acceleration in torsional spine magnetic reconnection

Three-dimensional (3D) magnetic reconnection is taking place commonly in astrophysical and space plasmas, especially in solar flares which are rich sources of highly energetic particles. One of the proposed mechanisms for steady-state 3D magnetic reconnection is “torsional spine reconnection”. By using the magnetic and electric fields for “torsional spine reconnection”, we numerically investigate the features of test particle acceleration with input parameters for the solar corona. We show that efficient acceleration of a relativistic proton is possible near the null point where it can gain up to 100 MeV of kinetic energy within a few milliseconds. However, varying the injection position results in different scenarios for proton acceleration. A proton is most efficiently accelerated when it is injected at the point where the magnetic field lines change their curvature in the fan plane. Moreover, a proton injected far away from the null point cannot be accelerated and, even in some cases, it is trapped in the magnetic field. In addition, adopting either spatially uniform or non-uniform localized plasma resistivity does not much influence the features of trajectory.     

Prompt particle acceleration around moving X-point magnetic field during impulsive phase of solar flares

We present a model for high-energy solar flares to explain prompt proton and electron acceleration, which occurs around moving X-point magnetic fields during the implosion phase of the current sheet. We derive the electromagnetic fields during the strong implosion of the current sheet, which is driven by the converging flow toward the center of the magnetic arcade. We investigated a test particle motion in the strong electromagnetic fields derived from the MHD equations. It is shown that both protons and electrons can be promptly (within 1 s) accelerated to 70 and 200 MeV, respectively. This acceleration mechanism can be applicable for the impulsive phase of the gradual gamma-ray and proton flares (gradual GR/P flare), which have been called two-ribbon flares.     

Acceleration and Storage of Energetic Electrons in Magnetic Loops in the Course of Electric Current Oscillations

A mechanism of electron acceleration and storage of energetic particles in solar and stellar coronal magnetic loops, based on oscillations of the electric current, is considered. The magnetic loop is presented as an electric circuit with the electric current generated by convective motions in the photosphere. Eigenoscillations of the electric current in a loop induce an electric field directed along the loop axis. It is shown that the sudden reductions that occur in the course of type IV continuum and pulsating type III observed in various frequency bands (25?–?180 MHz, 110?–?600 MHz, 0.7?–?3.0 GHz) in solar flares provide evidence for acceleration and storage of the energetic electrons in coronal magnetic loops. We estimate the energization rate and the energy of accelerated electrons and present examples of the storage of energetic electrons in loops in the course of flares on the Sun or on ultracool stars. We also discuss the efficiency of the suggested mechanism as compared with the electron acceleration during the five-minute photospheric oscillations and with the acceleration driven by the magnetic Rayleigh–Taylor instability.     

Particle acceleration in reconnecting current sheets

We study motions of charged particles in reconnecting current sheets (CS) which have both transverse (perpendicular to the current sheet plane) and longitudinal (parallel to the electric current inside the sheet) components of the magnetic field. Such CS, called non-neutral, are formed in regions of magnetic field line reconnection in the solar atmosphere. We develop an analytical technique which allows us to reproduce previous results concerning the influence of transverse fields on particle motion and acceleration. This technique also allows us to evaluate the effect of the longitudinal field. The latter increases considerably the efficiency of particle acceleration in CS. The energizing of electrons during the main phase of solar flares can be interpreted as their acceleration in non-neutral CS.     

Modeling of Proton Acceleration in a Magnetic Island Inside the Ripple of the Heliospheric Current Sheet

Crossings of the heliospheric current sheet (HCS) at the Earth’s orbit are often associated with observations of anisotropic beams of energetic protons accelerated to energies from hundreds of keV to several MeV and above. A connection between this phenomenon and the occurrence of small-scale magnetic islands (SMIs) near reconnecting current sheets has recently been found. This study shows how pre-accelerated protons can be energized additionally due to oscillations of multiple SMIs inside the ripple of the reconnecting HCS. A model of the electromagnetic field of an oscillating 3D SMI with a characteristic size of ~0.001 AU is developed. A SMI is supposed to be bombarded by protons accelerated by magnetic reconnection at the HCS to energies from ~1keV to tens of keV. Numerical simulations have demonstrated that the resulting longitudinal inductive electric fields can additionally reaccelerate protons injected into a SMI. It is shown that there is a local “acceleration” region within the island in which particles gain energy most effectively. As a result, their average escape energies range from hundreds of keV to 2 MeV and above. There is almost no particle acceleration outside the region. It is shown that energies gained by protons significantly depend on the initial phase and the place of their entry into a SMI but weakly depend on the initial energy. Therefore, low-energy particles can be accelerated more efficiently than high-energy particles, and all particles can reach the total energy limit upon their escape from a SMI. It is also found that the escape velocity possesses a strong directional anisotropy. The results are consistent with observations in the solar wind plasma.

     

Electron Acceleration in a Dynamically Evolved Current Sheet Under Solar Coronal Conditions

Electron acceleration in a drastically evolved current sheet under solar coronal conditions is investigated via the combined 2.5-dimensional (2.5D) resistive magnetohydrodynamics (MHD) and test-particle approaches. Having a high magnetic Reynolds number (10⁵), the long, thin current sheet is torn into a chain of magnetic islands, which grow in size and coalesce with each other. The acceleration of electrons is explored in three typical evolution phases: when several large magnetic islands are formed (phase 1), two of these islands are approaching each other (phase 2), and almost merging into a “monster” magnetic island (phase 3). The results show that for all three phases electrons with an initial Maxwell distribution evolve into a heavy-tailed distribution and more than 20 % of the electrons can be accelerated higher than 200 keV within 0.1 second and some of them can even be energized up to MeV ranges. The lower-energy electrons are located away from the magnetic separatrices and the higher-energy electrons are inside the magnetic islands. The most energetic electrons have a tendency to be around the outer regions of the magnetic islands or to appear in the small secondary magnetic islands. It is the trapping effect of the magnetic islands and the distributions of E _p that determine the acceleration and spatial distributions of the energetic electrons.     

The reason for magnetospheric substorms and solar flares

It has been proposed that magnetospheric substorms and solar flares are a result of the same mechanism. In our view this mechanism is connected with the escape, or attempted escape, of energized plasma from a region of closed magnetic field lines bounded by a magnetic bottle. In the case of the Earth, it must be plasma that is able to maintain a discrete auroral arc, and we propose that the cross-tail current connected to the arc is filamentary in nature to provide the field-aligned current sheet above the arc. A localized meander of such an intense current filament could be caused by a tearing instability in the neutral sheet. Such a meander will cause an inductive electric field opposing the current change everywhere. In trying to reduce the component of the induction electric field parallel to the magnetic field lines, the plasma must enhance the transverse or cross-tail component; this action leads to eruptive behavior, in agreement with tearing theories. This enhanced induction electric field will cause a discharge along the magnetic neutral line at the apex of the magnetic arches, constituting an impulsive acceleration of all charged particles originally near the neutral line. The products of this phase then undergo betatron acceleration for a second phase. This discharge eventually reduces the electric field along the neutral line, and thereafter the enclosed magnetic flux through the neutral line remains nearly constant. The result is a plasmoid that has definite identity; its buoyancy leads to its escape. The auroral breakup (and solar flare) is the complex plasma response to the changing electromagnetic field.     

Electron Acceleration in Reconnecting Current Sheets

We present the results of charged particle orbit calculations in prescribed electric and magnetic fields motivated by magnetic reconnection models. Due to the presence of a strong guide field, the particle orbits can be calculated in the guiding centre approximation. The electromagnetic fields are chosen to resemble a reconnecting magnetic current sheet with a localised reconnection region. An initially Maxwellian distribution function in the inflow region can develop a beam-like component in the outflow region. Possible implications of these findings for acceleration scenarios in solar flares will be discussed.     

On discontinuous plasma flows in the vicinity of reconnecting current sheets in solar flares

The question about the interpretation of numerical experiments on magnetic reconnection in solar flares is considered. A correspondence between the standard classification of magnetohydrodynamic discontinuities and the parameters characterizing the mass flux through a discontinuity and the magnetic field configuration has been established within a classical formulation of the problem on discontinuous magnetohydrodynamic flows. A pictorial graphical representation of the relationship between the angles of the magnetic field vector relative to the normal to the discontinuity plane on both its sides has also been found. The relations between the parameters of a two-dimensional discontinuous flow have the simplest form in a frame of reference where the magnetic field lines (B) are parallel to the matter velocity (u)—the deHoffmann-Teller frame. The question about the transformation of the magnetic field configuration when passing to a “laboratory” frame of reference where (v · B) ≠ 0, i.e., an electric field is present, is considered in this connection. The result is applied to the analytical solution of the problem on the magnetic field structure in the vicinity of a reconnecting current sheet obtained previously by Bezrodnykh et al. The regions of nonevolutionary shocks are shown to appear near the endpoints of a current sheet with reverse currents.     

Electron surfing acceleration by electrostatic waves in current sheet

The electron surfing acceleration in the current sheet with perpendicular propagating electrostatic waves is studied using analytical theories and test particle simulations. The trapped electron moving with the phase velocity v _p of wave may be accelerated effectively in the outflow direction by force until the electron is de-trapped from the wave potential. A criterion K>0 for the electron surfing acceleration is obtained. The electron will escape from the boundary of current sheet quickly, if this criterion does not hold. The maximum velocity of surfing acceleration is about the same as the electric drift velocity. Superposed longitudinal magnetic field along the wave propagation is favorable for the electron surfing acceleration in the current sheet.      

Time-dependent configuration changes of the magnetotail and plasma sheet thinning

The configuration of the magnetotail magnetic field has been calculated for a situation where a disruption of a portion of the tail current system develops. The decrease of the current in a localized region of the magnetotail leads to a collapse of the magnetic field in that vicinity. The calculated configuration of the field resembles what is predicted by reconnection models with the field lines moving toward the neutral sheet and then connecting and either moving toward or away from the earth. Associated with this changing magnetic field there is an induced electric field which will then influence the motion of the plasma in the magnetotail via E × B drifts.When the current from X_sm = ?20 to ?40 R_E in the tail is decreasing with a tune-constant of 0.5 h the electric field produced, which is primarily westward, has a maximum value of 0.83 mV m^?1 and produces plasma sheet thinning velocities of 0.3 km s^?1. Higher velocities result for more rapid rates of current decrease, and they agree well with experimental observations. The plasma flows in the sunward direction are, however, much smaller than what has been observed. This is due in part to the inability of the magnetic field model to adequately represent the magnetic field in the immediate vicinity of the neutral sheet. Use of an improved model would give better agreement with the observations.The calculations show that the induced electric field of a time-dependent magnetic field is able to explain certain observed features of the plasma sheet motions. Also, this agreement suggests that the assumption that there is no charge separation contribution to the electric field may be reasonable during situations of large scale and rapid current disruptions in the magnetotail.     

Electron acceleration by electric fields near the footpoints of current-carrying coronal magnetic loops

We analyze the electric fields that arise at the footpoints of a coronal magnetic loop from the interaction between a convective flow of partially ionized plasma and the magnetic field of the loop. Such a situation can take place when the loop footpoints are at the nodes of several supergranulation cells. In this case, the neutral component of the converging convective flows entrain electrons and ions in different ways, because these are magnetized differently. As a result, a charge-separating electric field emerges at the loop footpoints, which can efficiently accelerate particles inside the magnetic loop under appropriate conditions. We consider two acceleration regimes: impulsive (as applied to simple loop flares) and pulsating (as applied to solar and stellar radio pulsations). We have calculated the fluxes of accelerated electrons and their characteristic energies. We discuss the role of the return current when dense beams of accelerated particles are injected into the corona. The results obtained are considered in light of the currently available data on the corpuscular radiation from solar flares.     

The phase of particle acceleration in the flare development

Evidence is given that the particle acceleration in flares is confined to the initial phase of the flare development preceding the H flare maximum and lasting for less than 10 min. The impulsive acceleration process is confined to a relatively small limited volume of about 5 × 10²⁷ cm³ in the region of highest magnetic gradient in the flare, and its size represents about 0.05 or less of the total extent of the hot condensation which produces the soft X-ray and gradual microwave bursts. About one in fifty particles in this volume is accelerated to energy exceeding 100 keV, the total particle density being 10¹⁰ cm^–3. The accelerated electrons produce the impulsive hard X-ray burst, but synchrotron losses greatly reduce the number of relativistic electrons participating in the bremsstrahlung process. Protons above 20 MeV penetrate to the lowest chromosphere and upper photosphere and temporarily increase the temperature in the bombarded region. As the result a flash of continuous emission appears, which should be most expressive below 1527 Å. The associated white-light emission shows the bottom of the region where the impulsive acceleration process occurs.     

Relativistic acceleration of protons in reconnecting current sheets of solar flares

Acceleration of protons in a reconnecting current sheet (RCS), which forms as a consequence of filament eruption in the corona, is considered as a possible mechanism of generation of the relativistic particles during the late phase of solar flares. In order to explain the acceleration of protons and heavier ions up to several GeV in a time of < 0.1 s, the transverse electric field outside the RCS must be taken into account. Physically, this field is always present as a consequence of electric charge separation owing to the difference in the electron and proton masses. The new effect demonstrated in this paper is that the transverse electric field efficiently locks nonthermal ions in the RCS, thus allowing their acceleration by the direct electric field in the RCS. The mechanism considered may be useful in construction of a model for generation of relativistic ions in large gamma-ray/proton flares.     

Particle Acceleration in the Presence of Weak Turbulence at an X-Type Neutral Point

We simulate the likely noisy situation near a reconnection region by superposing many 2D linear reconnection eigenmodes. The superposition of modes on the steady state X-type magnetic field creates multiple X- and O-type neutral points close to the original neutral point and so increases the size of the non-adiabatic region. We study test particle trajectories of initially thermal protons in these fields. Protons become trapped in this region and are accelerated by the turbulent electric field to energies up to 1 MeV in time scales relevant to solar flares. Higher energies are achieved due to the interaction of particles with increasingly turbulent electric and magnetic fields.