Acceleration of Electrons and Protons in Reconnecting Current Sheets Including Single or Multiple X-points

Kinematic characteristics of electrons and protons in the magnetic reconnecting current sheet in the presence of a guide field are investigated. Particle trajectories are calculated for different values of the guide field by a test-particle calculation. The relationship between the final energy and the initial position has also been studied. We found that the addition of a guide field not only allows particles to get more energy and not only results in the separation of electrons and protons, but also causes the reconnecting electric field to selectively accelerate electrons and protons for different initial positions. The energy spectrum eventually obtained is the common power-law spectrum, and as the guide field increases, the index for the spectrum of electrons decreases rapidly. However, for a weak background magnetic field, proton spectra are not very sensitive to the guide field; but for a strong background field, the dependence of the spectrum index is similar to the electron spectrum. Meanwhile, kinematic characteristics of the accelerated particles in the current sheet including multiple X-points and O-points were also investigated. The result indicates that the existence of the multiple X- and O-points helps particles trapped in the accelerating region to gain more energy, and yields the double or multiple power-law feature.     

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 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.     

Field line topology in the dayside cusp region inferred from low altitude particle observations

Dayside low altitude satellite observations of the pitch angle and energy distribution of electrons and protons in the energy range 1 eV to 100 eV during quite geomagnetic conditions reveal that at times there is a clear latitudinal separation between the precipitating low energy (keV) electrons and protons, with the protons precipitating poleward of the electrons. The high energy (100 keV) proton precipitation overlaps both the low energy (keV) electron and proton precipitation. These observations are consistent with a model where magnetosheath particles stream in along the cusp field lines and are at the same time convected poleward by an electric field.The electrons with energies of a few keV move fast and give the “ionospheric footprint” of the distant cusp. The protons are partly convected poleward of the cusp and into the polar cap. Here the mirroring protons populate the plasma mantle. Equatorward of the cusp the pitch angle distribution of both electrons and protons with energies above a few keV is pancake shaped indicating closed geomagnetic field lines. The 1 keV electrons, penetrate, however, into this region of closed field line structure maintaining an isotropic pitch angle distribution. The intensity is, however, reduced with respect to what it was in the cusp region. It is suggested that these electrons, the lowest energies measured on the satellite, are associated with the entry layer.     

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.     

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.     

On the interaction of auroral protons with the earth's atmosphere

The interaction of energetic auroral protons with the atmosphere is investigated. The results of a random number algorithm that describes the proton-hydrogen interconversion reactions as the beam loses energy are adopted to construct an energy deposition curve applicable over a wide range of initial proton energies. lonization rates and production rates of ejected electrons are computed and emission rates of hydrogen Balmer alpha and beta lines are evaluated using recently available low energy cross-sections.     

Jovian proton Aurora

The planet Jupiter possesses a magnetic field and is surrounded by a magnetosphere. The occurrence of auroral and polar cap phenomena similar to those found on earth is very likely. In this work auroral and polar cap emissions in a model Jovian atmosphere are determined for proton precipitation. The incident protons, which are characterized by representative spectra, are degraded in energy by applying the continuous slowing down approximation. All secondary and higher generation electrons are assumed to be absorbed locally and their contributions to the total emissions are included. Volume emission rates are calculated from the total direct excitation rates with corrections for cascading applied. Results show that most molecular hydrogen and helium emissions for polar cap precipitation are below the ambient dayglow values. Charge capture by precipitating protons is an important source of Lyman α and Balmer α emissions and offers a key to the detection of large fluxes of low energy protons.     

Ring Current Formed During the Bombardment of a Rotating Gas Torus by Neutral Beams

A new mechanism for the generation of the electric ring current is presented. During the radial bombardment of a rotating gas torus by a neutral beam, electrons and protons are dragged by rotating gas. Due to collisions electrons obtain the torus velocity faster than protons, therefore in some layer there is a difference in electron and proton beam toroidal velocities; the electric current is thus generated. This current is discussed as the seed magnetic field in early stages of evolving galaxies, which is then amplified by the dynamo process to present values of the magnetic field. This revised version was published online in July 2006 with corrections to the Cover Date.     

Effects associated with the sector boundary crossing on July 8, 1966

Thirty hours after the proton flare of July 7, 1966, the earth and nearby satellites crossed a sector boundary of the interplanetary magnetic field. This occurred before the flare-associated shockwave arrived at the earth, so that the space was filled with energetic particles ejected from the flare. Satellite measurements have shown that in such a case <20 MeV protons are stored within the range of the sector boundary and with decreasing energy the particles tend to accumulate towards and behind the Eastern boundary limit; low-energy particles, such as <50 keV electrons, are stored exclusively behind this Eastern limit.The boundary crossing caused a short-lived geomagnetic disturbance, a PCA enhancement in lower latitudes, a two-phase ionospheric disturbance, and a transient cosmic-ray decrease on neutron monitors looking westward immediately after the sector boundary passed the earth. The storage of low-energy particles on the Eastern side of the boundary may indicate a preference of the transverse diffusion for the Westward direction in interplanetary space.     

Particle Acceleration in Reconnecting Current Sheets in Impulsive Electron-Rich Solar Flares

Electron and proton acceleration in reconnecting current sheets in electron-rich solar flares is considered. A significant three-dimensional magnetic field is assumed in the current sheet where the particles are accelerated by the DC electric field. The tearing instability of a pre-flare current sheet leads to the formation of multiple singular lines of magnetic field where the electric and magnetic fields are coaligned. Magnetized electrons are shown to be accelerated to a few tens of MeV before they leave the vicinity of a singular line. The acceleration time is estimated to be less than 10^–3 s. By contrast, much heavier protons are unmagnetized and their energy gain is more modest. The model explains a high electron-to-proton ratio and the unusually intense gamma-ray continuum above 1 MeV observed in the electron-rich flares.     

A theory for the solar type-I radio continuum

The type-I radio continuum may arise from the combination of two electrostatic waves, both directed nearly normal to the magnetic field. One wave, near the upper-hybrid frequency, is generated by gyroresonance with superthermal electrons and comes into equilibrium with these electrons. The other wave, at the lower-hybrid frequency, is generated by the loss-cone instability of trapped superthermal protons in those wave directions for which the lower-hybrid frequency is an exact multiple of the proton gyrofrequency. The brightness temperature of the continuum indicates both the energy of the superthermal electrons and the existance of at least a small number of superthermal protons.     

Multiple compton scattering of electrons in a photon field

Consideration is given to the motion of electrons in a photon field of the monoenergetic or power-law spectrum under the conditions when the main mechanism of energy loss is the inverse Compton scattering by field photons. This process changes the primary spectrum of electrons and converts low-energy field photons to high-energy gamma-quanta for which the electron confinement region is assumed to be optically thin. The electron and gamma-ray spectra have been obtained in a wide energy interval including the Klein-Nishina and Thomson regions. A simple qualitative dependence of the solutions found on the field parameters and the primary spectrum of electrons has been established.The electron and gamma-ray spectra have been obtained by numerically solving the kinetic equation dependent on two variables: the energy of electrons and their path (or the time of motion) in a photon field. The results dramatically differ from the solution of the steady-state kinetic equation which depends only on the electron energy and is frequently used in the given problem.     

Regular and chaotic dynamics in 3D reconnecting current sheets

We consider the possibility of particles being injected at the interior of a reconnecting current sheet (RCS), and study their orbits by dynamical systems methods. As an example we consider orbits in a 3D Harris type RCS. We find that, despite the presence of a strong electric field, a 'mirror' trapping effect persists, to a certain extent, for orbits with appropriate initial conditions within the sheet. The mirror effect is stronger for electrons than for protons. In summary, three types of orbits are distinguished: (i) chaotic orbits leading to escape by stochastic acceleration, (ii) regular orbits leading to escape along the field lines of the reconnecting magnetic component, and (iii) mirror-type regular orbits that are trapped in the sheet, making mirror oscillations. Dynamically, the latter orbits lie on a set of invariant KAM tori that occupy a considerable amount of the phase space of the motion of the particles. We also observe the phenomenon of 'stickiness', namely chaotic orbits that remain trapped in the sheet for a considerable time. A trapping domain, related to the boundary of mirror motions in velocity space, is calculated analytically. Analytical formulae are derived for the kinetic energy gain in regular or chaotic escaping orbits. The analytical results are compared with numerical simulations.     

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.     

Jupiter's radiation belts

A model for the production and loss of energetic electrons in Jupiter's radiation belt is presented. It is postulated that the electrons originate in the solar wind and are diffused in toward the planet by perturbations which violate the particles' third adiabatic invariant. At large distances, magnetic perturbations, electric fields associated with magnotospheric convection, or interchange instabilities driven by thermal plasma gradients may drive the diffusion. Inside about 10 R_J the diffusion is probably driven by electric fields associated with the upper atmosphere dynamo which is driven by neutral winds in the ionosphere. The diurnal component of the dynamo wind fields produces a dawn-dusk asymmetry in the decimetric radiation from the electrons in the belts, and the lack of obvious measured asymmetries in the decimetric radiation measurements provides estimates of upper limits for these Jovian ionospheric neutral winds. The average diurnal winds are less than or comparable to those on earth, but only modest fluctuating winds are required to drive the energetic electron diffusion referred to above.The winds required to diffuse the energetic particles across the orbit of the satellite lo in a time equal to their drift period are also estimated. If Io is non-conducting, modest winds are required, but if Io is conducting, only small winds are needed. It is concluded that both protons and electrons are diffused in from the solar wind to small distances without serious losses occurring due to the particles being swept up by the satellites.Consideration of proton and electron diffusion in energy shows that once the electrons become relativistic, the ratio of proton to electron energy increases. Thus, if protons and electrons have the same energy in the solar wind, when the electrons reach nMeV, the protons will be nMeV if n ? 1 or n² MeV if n ? 1. If the proton-to-electron energy ratio is initially, e.g., 5, then these figures are 5n and 5n², respectively.     

Effect of solar corona conditions on flare particle propagation

Data on high energy electrons and protons in different energy windows are analyzed and compared for two solar flares which occurred at 37 W solar longitude on the 25th February 1969 and the 29th March 1970. While the data for the first of these flares can be interpreted in the framework of a diffusion model with suitable values of the parallel diffusion coefficient, in order to explain the time behaviour of the different particles after the second event, we are led to suppose that the coronal magnetic fields are such that particles of different rigidity are ejected at different longitudes and that there is no good magnetic connection of the Earth with the flare region.     

Field-aligned currents above an auroral arc

Simultaneous observations of precipitating electrons and protons in the energy range from 15 eV to 35 keV and magnetic field variations were made onboard a sounding rocket payload launched from the Andoya Rocket Range. The electric current density deduced from the electron precipitation observed during the passage over an auroral arc was comparable to that determined from the magnetic field variations. In addition, a downward current was observed by its magnetic field signature at the northern edge of the arc which was, however, not accompanied by significant particle fluxes in the energy range under consideration. It will be assumed that this current was carried by thermal electrons of ionospheric origin.     

An Improved Method to Derive the Lower Energy Cutoff of non-Thermal Electrons From Hard x-Rays of Solar Flares

By changing a dimensionless calculation to a dimensional one, introducing a more accurate bremsstrahlung cross section, and using a more reasonable fitting energy range, we have recalculated the hard X-ray bremsstrahlung produced by a beam of power-law electrons with a lower energy cutoff (E _c). The method to deduce E _c from the hard X-ray spectral observations has therefore been refined in comparison with our previous one. The universality of this method has been clarified and discussed. We have applied this improved method to the 54 BATSE/Compton Gamma Ray Observatory (CGRO) hard X-ray events. It was found that about 44% of sample hard X-ray spectra can be directly explained by a beam of power-law electrons with a lower energy cutoff. The value of E _c, varying from 45 keV to 97 keV, is on average 60 keV. Another 44% of sample hard X-ray spectra might be explained by a beam of power-law electrons with the energy cutoff lower than 45 keV, which is however beyond the availability of BATSE/CGRO. Still another 11% sample hard X-ray spectra cannot be explained by a beam of power-law electrons with a lower energy cutoff. These results, based on the lower energy resolution data, however, should be compared in the future with that based on a higher energy resolution data, like the data from HESSI.     

Relativistic electrons from solar flares

Observations of interplanetary relativistic electrons from several solar-flare events monitored through 1964 to mid-1967 are presented. These are the first direct spectral measurements and time histories, made outside the magnetosphere, of solar-flare electrons having relativistic velocities. The 3- to 12-MeV electrons detected have kinetic energies about two orders of magnitude higher than those solar electrons previously studied in space, and measurements of both the time histories and energy spectra for a number of events in the present solar cycle were carried out. These measurements of interplanetary electrons are also directly compared with solar X-ray data and with measurements of related interplanetary solar protons.The time histories of at least four electron events show fits to the typical diffusion picture. A demonstrated similarity between the electron and the medium-energy proton fits for the event of 7 July, in particular, indicates that at these electron energies, but over several orders of magnitude of rigidity, whatever diffusion does take place is very nearly on a velocity, rather than a rigidity or an energy, basis. Diffusion-fit time histories varied as a function of T ₀ also indicate that the electrons in certain flare events originate at times near the X-ray and microwave burst, establishing their likely identity as the same electrons which cause the impulsive radiations. Also, the energy spectra and total numbers of the interplanetary electrons, compared with those of the flare-site electrons calculated from X-ray and microwave measurements, indicate that probably a small fraction of flare electrons escape into interplanetary space.