On the generation of high-energy particles in solar flares

This paper discusses the relationship between some characteristics of microwave type IV radio bursts and solar cosmic ray protons of MeV energy. It is shown that the peak flux intensity of those bursts is almost linearly correlated with the MeV proton peak flux observed by satellites near the Earth and that protons and electrons would be accelerated simultaneously by a similar mechanism during the explosive phase of solar flares.Brief discussion is given on the propagation of solar cosmic rays in the solar envelope after ejection from the flare regions.     

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.     

Influence of the magnetosheath on solar proton penetration into the magnetosphere

The observation of solar protons (1–9 MeV) aboard HEOS-2 in the high-latitude magnetotail and magnetosheath on 9 June 1972, and their comparison with simultaneous measurements on Explorers 41 and 43, both in interplanetary space, indicate the existence of a distinct region of the inner magnetosheath (about 3 Earth radii thick) near the high-latitude magnetopause in which the solar particle flow is almost reversed with respect to the flow observed in interplanetary space. The region can also be seen by comparing magnetic field measurements on the three spacecraft. The observations in the outer layer of the magnetotail show solar protons predominantly entering the magnetosphere somewhere near the Earth, perhaps the cusp region.     

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.     

On the ground level enhancement beginning

Based on our analysis of the data fromthe global network of neutronmonitors for several events, we have found the times of the first increases in count rate at individual stations that precede the main solar cosmic-ray enhancement. The onset time of proton acceleration at the Sun has been determined from the appearance of a broad gamma-ray line with its maximum near 70 MeV that is generated during the decay of neutral pions, which, in turn, are produced when protons with energies above 300 MeV interact with the solar atmosphere. The time of the first recording of energetic protons at the Earth is delayed relative to the time at which these protons appeared at the Sun by 60–300 s, i.e., by a value comparable to the difference between the direct photon and particle propagation times. At least two conclusions follow from the existence of such “precursors”. First, the protons begin to escape from the solar atmosphere into interplanetary space immediately after their acceleration. Second, some of the protons traverse a path shorter than the nominal length of interplanetary magnetic field lines.     

Optimization of the interplanetary energetic proton flux database and its application in modeling radiation conditions

The dissimilarity of the results of solar and galactic proton flux measurements made on different spacecraft is pointed out. It is caused, in addition to instrument errors, by differences in the temporal and spatial conditions of the measurements. We suggest using statistical analysis of proton fluences calculated for different long time intervals, from half a year to 10 years, for the optimization of the interplanetary proton database. An example of such analysis is presented and a probabilistic model of total proton fluences at the Earth’s orbit outside the magnetosphere, constructed using the analysis, is described. A formalized method for separating proton fluxes in solar proton events from protons of galactic cosmic rays is suggested. A conclusion is made that sources of cosmic ray protons with energies of less than 4 MeV should be examined in more detail.     

Galactic cosmic ray modulation from 1965–1970

Numerical solutions of the cosmic-ray equation of transport within the solar cavity and including the effects of diffusion, convection, and energy losses due to adiabatic deceleration, have been used to reproduce the modulation of galactic electrons, protons and helium nuclei observed during the period 1965–1970. Kinetic energies between 10 and 10⁴ MeV/nucleon are considered. Computed and observed spectra (where data is available) are given for the years 1965, 1968, 1969 and 1970 together with the diffusion coefficients. These diffusion coefficients are assumed to be of separable form in rigidity and radial dependence, and are consistent with the available magneticfield power spectra. The force-field solutions are given for these diffusion coefficients and galactic spectra and compared with the numerical solutions. For each of the above years we have (i) determined the radial density gradients near Earth; (ii) found the mean energy losses suffered by galactic particles as they diffuse to the vicinity of the Earth's orbit; (iii) shown quantitatively the exclusion of low-energy galactic protons and helium nuclei from near Earth by convective effects; and (iv), for nuclei of a given energy near Earth, obtained their distribution in energy before entering the solar cavity. It is shown that the energy losses and convection lead to near-Earth nuclei spectra at kinetic energies ≤100 MeV/nucleon in which the differential intensity is proportional to the kinetic energy with little dependence on the form of the galactic spectrum. This dependence is in agreement with the observed spectra of all species of atomic nuclei and we argue that this provides strong observational evidence for the presence of energy losses in the propagation process; and for the exclusion of low energy galactic nuclei from near Earth.     

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.     

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.

     

Energy Spectra of low-Flux Protons in the Inner Heliosphere under Quiet Solar Conditions

The energy spectra of protons at energies in the range of about 1–100 MeV are investigated during time periods of low solar activity using data sets from near Earth spacecraft. These populations pose a tough experimental and theoretical problem that remains unsolved up to now. We attempt to provide a consistent definition of low-flux quiet-time periods relevant to low solar activity as well as quasi-stationary periods useful at higher levels of solar activity. Using statistical methods, the possible instrumental contribution to the lowest observed proton fluxes for various detectors is estimated. We suggest and prove that there exists a low-flux population of charged particles in the energy range of about 1–10 MeV, which is present in the inner heliosphere even during the quietest conditions at lowest solar activity. The dynamics of the variations of proton spectra over the solar cycle is investigated. A series of low-flux periods is examined in detail and energy spectra of protons are approximated in the form of J(E)=AE ^–+CE. By determining the best fitting parameters to the energy spectra correlations are made among them as well as with monthly sunspot numbers characterizing solar activity. It has been demonstrated that the value of the energy minimum of proton spectrum E _min that `divides' the two populations – `solar/heliospheric' and `galactic' – is shifted towards higher values with increasing solar activity. Protons have been argued to be predominantly of solar origin up to several MeV near the solar cycle minimum and up to 20–30 MeV at maximum. The slope of the lower spectrum branch (parameter ) slightly decreases with increasing solar activity. The minimum fluxes observed during the last 3 minima of solar activity are compared; the lowest fluxes were those during the 1985–1987 period.     

Size Distributions of Solar Proton Events: Methodological and Physical Restrictions

Based on the new catalogue of solar proton events (SPEs) for the period of 1997?–?2009 (Solar Cycle 23) we revisit the long-studied problem of the event-size distributions in the context of those constructed for other solar-flare parameters. Recent results on the problem of size distributions of solar flares and proton events are briefly reviewed. Even a cursory acquaintance with this research field reveals a rather mixed and controversial picture. We concentrate on three main issues: i) SPE size distribution for \({>}\,10~\mbox{MeV}\) protons in Solar Cycle 23; ii) size distribution of \({>}\,1~\mbox{GV}\) proton events in 1942?–?2014; iii) variations of annual numbers for \({>}\,10~\mbox{MeV}\) proton events on long time scales (1955?–?2015). Different results are critically compared; most of the studies in this field are shown to suffer from vastly different input datasets as well as from insufficient knowledge of underlying physical processes in the SPEs under consideration. New studies in this field should be made on more distinct physical and methodological bases. It is important to note the evident similarity in size distributions of solar flares and superflares in Sun-like stars.     

Effects of convection electric field on the distribution of ring current type protons

The topology of the boundaries of penetration (or inversely the boundaries of the forbidden regions) of 90° pitch angle equatorial protons with energies less than 100 keV are explored for an equatorial convection E-field which is directed in general from dawn to dusk. Due to the dependence of drift path on energy (or magnetic moment) complex structural features are expected in the proton energy spectra detected on satellites since the penetration distance of a proton is not a monotonically increasing or decreasing function of energy. During a storm when the convection E is enhanced, model calculations predict elongations of the forbidden regions analogous to plasmatail extensions of the plasmasphere. Following a reduction in the convection field, spiral-structured forbidden regions can occur. Structural features inherent to large scale convection field changes may be seen in the noselike proton spectrograms observed near dusk by instrumentation on the satellite Explorer 45 (S³) (Smith and Hoffman, 1974). These nose events are modelled by using an electric field model developed originally by Volland (1973). The strength of the field is related to K_p through night-time equatorial plasmapause measurements.     

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.     

A Study of the Solar Proton Flux Model

The solar proton event (SPE) may become a serious threat to the cosmonautical activities of human beings, so the prediction of the flux of solar protons within a certain period has important guiding significance for the projection of the anti-radiation solidification of space vehicles. On the basis of a statistical analysis of the data of SPEs in the 20th to 23rd cycles of solar activity, a new model of solar proton fluxes with E > 10 MeV and E > 30 MeV is established. In comparison with the JPL model, which is frequently adopted in the present aerospace engineering, the influence factor of solar activity on the occurrence of proton events is introduced, and it can be used to estimate the proton fluxes under various levels of solar activity. The results can better match the characteristics of the distribution of proton events.     

A summary of major solar proton events

Solar proton events have been routinely detected by satellites since the 20th solar cycle; however, before that time only very major proton events were detected at the Earth. Even though the detection thresholds differed between the 19th and more recent cycles, more than 200 solar proton events with a flux of over 10 particles (cm² s ster)^–1 above 10 MeV have been recorded at the Earth in the last three solar cycles. At least 15% of these events had protons with energies greater than 450 MeV detected at the Earth. Other than an increase in solar proton event occurrence with increasing solar cycle, no recognizable pattern could be identified between the occurrence of solar proton events and the solar cycle. The knowledge we have gained from the data acquired over the past 40 years illustrates the difficulty in extrapolating back in time to infer the number and intensity of major solar proton events at the Earth.The U.S. Government retains a nonexclusive, royalty-free license to publish or reproduce the published form of this contribution, or allow others to do so, for U.S. Government purposes.     

A joint analysis of high-energy neutrons and neutron-decay protons from a flare

A joint analysis of neutron monitor and GOES data is performed to study the production of high-energy neutrons at the Sun. The main objects of the research are the spectrum of >50 MeV neutrons and a possible spectrum of primary (interacting) protons which produced those neutrons during the major 1990 May 24 solar flare. Different possible scenarios of the neutron production are presented. The high magnitude of the 1990 May 24 neutron event provided an opportunity to detect neutron decay protons of higher energies than ever before. We compare predictions of the proposed models of neutron production with the observations of protons on board GOES 6 and 7. It is shown that the precursor in high-energy GOES channels observed during 20:55–21:09 UT can be naturally explained as originating from decay of neutrons in the interplanetary medium. The ratio of counting rates observed in different GOES channels can ensure the selection of the model parameters.The set of experimental data can be explained in the framework of a scenario which assumes the existence of two components of interacting protons in the flare. A hard spectrum component (the first component) generates neutrons during a short time while the interaction of the second (soft spectrum) component lasts longer. Alternative scenarios are found to be of lesser likelihood. The intensity-time profile of neutron - decay protons as predicted in the framework of the two-component exponential model of neutron production (Kocharov et al., 1994a) is in an agreement with the proton profiles observed on board GOES. We compare the deduced characteristics of interacting high-energy protons with the characteristics of protons escaping into the interplanetary medium. It is shown that, in the 100–1000 MeV range, the spectrum of the second component of interacting protons was close to the spectrum of the prompt component of interplanetary protons. However, it is most likely that, at 300 MeV, the interacting proton spectrum was slightly softer than the spectrum of interplanetary protons. An analysis of gamma-ray emission is required to deduce the spectrum of interacting protons below 100 MeV and above 1 GeV.     

Use of Simultaneous EUV and Soft X-ray Measurements for Diagnostics of the Solar Flare Radiation Danger

The fluxes of extreme ultraviolet (EUV) and soft X-ray emission are key parameters for modelling the ionosphere and upper atmosphere. A new aspect is considered in using these fluxes for diagnostics and short-term prediction of proton radiation danger from the flare. The EUV (λ < 105 nm) and soft X-ray (0.1–0.8 nm) fluxes were compared for two types of solar flares. The first type is followed by a strong enhancement in solar energetic (E >10 MeV) proton flux, the second is not followed by any enhancement in proton flux. It was discovered that the flare UV flux was considerably higher for flares with protons than for those without protons. Soft X-ray fluxes were approximately equal in both cases. An excess of EUV emission in proton flares grows with increasing proton flux. An analytic expression was found for the growth in proton flux as a function of the excess of EUV radiation at a given X-ray flux. These results can be used in predicting flare radiation danger.     

The effect of a geomagnetic storm on energetic trapped protons at low altitudes

The irreversible changes of the intensity of trapped protons with energy above 1 MeV in the Earth's magnetosphere near the outer boundary of trapping are observed after moderate geomagnetic storms on the low-altitude polar-orbiting satellite Intercosmos-17. These changes are interpreted in terms of nonadiabatical effects of proton motion in the disturbed geomagnetic field (assuming D_st variation) which affects the conditions for stable trapping of protons during the storm. The decrease of proton intensity is due to an adiabatic decrease of energy, an increase of mirror-point altitude and nonadiabatic scattering and losses. The interaction of two types of particle motion—gyrorotation and the ‘bounce’ motion, which leads to the instability of motion, is assumed. The importance of nonadiabatical losses of trapped protons with low equatorial pitch angles for changes near the proton boundary is pointed out.     

On proton and electron acceleration by shock waves during large solar flares

The data on optical, X-ray and gamma emission from proton flares, as well as direct observations of flare-associated phenomena, show energetic proton acceleration in the corona rather than in the flare region. In the present paper, the acceleration of protons and accompanying relativistic electrons is accounted for by a shock wave arising during the development of a large flare. We deal with a regular acceleration mechanism due to multiple reflection of resonance protons and fast electrons from a collisionless shock wave front which serves as a moving mirror. The height of the most effective acceleration in the solar corona is determined. The accelerated particle energy and density are estimated. It is shown in particular that a transverse collisionless shock wave may produce the required flux of protons with energy of 10 MeV and of relativistic electrons of 1–10 MeV.The proposed scheme may also serve as an injection mechanism when the protons are accelerated up to relativistic energies by other methods.     

Electromagnetic and corpuscular emission from the solar flare of 1991 June 15: Continuous acceleraton of relativistic particles

Data on X-,γ-ray, optical and radio emission from the 1991 June 15 solar flare are considered. We have calculated the spectrum of protons that producesγ-rays during the gradual phase of the flare. The primary proton spectrum can be described as a Bessel-function-type up to 0.8 GeV and a power law with the spectral index ≈3 from 0.8 up to 10 GeV or above. We have also analyzed data on energetic particles near the Earth. Their spectrum differed from that of primary protons producingγ-ray line emission. In the gradual phase of the flare additional pulses of energy release occurred and the time profiles of cm-radio emission andγ-rays in the 0.8–10 MeV energy band and above 50 MeV coincided. A continuous and simultaneous stochastic acceleration of the protons and relativistic electrons at the gradual phase of the flare is considered as a natural explanation of the data.