Perpendicular Transport in the Inner Heliosphere: A Quick and Dirty Approach

In previous studies, transport of solar energetic particles in the inner heliosphere was regarded as one-dimensional along the Archimedean field spiral; i.e., any perpendicular transport is neglected. We extend Roelof’s equation of focused transport for solar energetic particles to accommodate perpendicular transport in the plane of the ecliptic. Numerically, this additional term is solved with an implicit Laasonen scheme. In this first approximation, it is solved for azimuthal instead of perpendicular transport – these are similar in the inner heliosphere where the Archimedean field is almost radial. The intent of the study is to estimate the possible influence of perpendicular transport, but not to fit energetic particle events; thus, the particle source stays fixed on the Sun. For typical ratios κ _⊥ /κ _‖ between 0.02 and 0.1 at 1 AU scaled with r ² as suggested in nonlinear guiding-center theory, we find that i) an azimuthal spread over some 10° occurs within a few hours, ii) the variation of maximum intensities with longitude is comparable to the ones inferred from multispacecraft observations, and iii) on a given field line, intensity and anisotropy-time profiles are modified such that fits with the two-dimensional transport model give different combinations of injection profiles and mean free paths. Implications for the interpretation of intensity and anisotropy-time profiles observed in interplanetary space and consequences for our understanding of particle propagation and acceleration in space are discussed.     

Magnetic clouds and interplanetary particle transport: a numerical model

Magnetic clouds modify the structure of the interplanetary magnetic field on spatial scales of tenth of AU. Their influence on the transport of energetic charged particles is studied with a numerical model that treats the magnetic cloud as an outward propagating modification of the focusing length. As a rule of thumb, the influence of the magnetic cloud on particle intensity and anisotropy profiles increases with decreasing particle mean free path and decreasing particle speed. Three cases are considered: (1) when the magnetic cloud is the driver of a shock that accelerates particles as it propagates outward, (2) when the magnetic cloud interacts with a prior solar energetic particle event, and (3) when a magnetic cloud already is present in interplanetary space at the time of a solar energetic particle event. In the latter case the cloud acts as a barrier, storing the bulk of the particles in its downstream medium.     

The participation of nuclei in type-III-related electron streams

We study 27 increases of the flux of 300–800 keV electrons on board HELIOS A or B, associated with intense type III radio bursts close to perihelion passages of the two spacecraft, during the solar minimum. Electrons can be detected inside cones with an angular width between 30° and 60°. Though only intense type III bursts are associated with recognizable electron events in space, such an association does not exist for all of them; this fact and great differences in fluxes of the individual events indicate that, apart from the intensity, also some other charactefistic of the type III burst acceleration or propagation process determines the resulting flux of electrons in space; the energy spectrum of the accelerated electrons is one of the likely candidates. A comparison of the electron flux in these events with the flux of 1.7–3.7 MeV nucl^–1 helium reveals very large variations of the helium/electron flux ratio, by a factor of at least 15 and possibly much higher. We demonstrate that these variations are not caused by propagation effects in interplanetary space. Therefore, they must be due either to propagation effects in the solar corona or, more likely, to intrinsic variations in the relative production of electrons and nuclei in the type III burst process. An extrapolation of the observed fluxes to 1 AU shows that in only 7 of the 27 electron events studied might a marginal > 1.7 MeV helium flux be recognized ar the Earth distance.     

Multi-spacecraft observations of particle events and interplanetary shocks during November/December 1982

We present a sample of solar energetic particle events observed between November 18 and December 31, 1982 by the HELIOS 1, the VENERA 13, and IMP 8 spacecraft. During the entire time period all three spacecraft were magnetically connected to the western hemisphere of the Sun with varying radial and angular distances from the flares. Eleven proton events, all of them associated with interplanetary shocks, were observed by the three spacecraft. These events are visible in the low-energy (about 4 MeV) as well as the high-energy (30 MeV) protons. In the largest events protons were observed up to energies of about 100 MeV. The shocks were rather fast and in some cases extended to more than 90% east of the flare site. Assuming a symmetrical configuration, this would correspond to a total angular extent of some interplanetary shocks of about 180%. In addition, due to the use of three spacecraft at different locations we find some indication for the shape of the shock front: the shocks are fastest close to the flare normal and are slower at the eastern flank. For particle acceleration we find that close to the flare normal the shock is most effective in accelerating energetic particles. This efficiency decreases for observers connected to the eastern flank of the shock. In this case, the efficiency of shock acceleration for high-energy protons decreases faster than for low-energy protons. Observation of the time-intensity profiles combined with variations of the anisotropy and of the steepness of the proton spectrum allows one in general to define two components of an event which we term solar and interplanetary. We attempt to describe the results in terms of a radially variable efficiency of shock acceleration. Under the assumption that the shock is responsible not only for the interplanetary, but also for the solar component, we find evidence for a very efficient particle acceleration while the shock is still close to the Sun, e.g., in the corona. In addition, we discuss this series of strong flares and interplanetary shocks as a possible source for the formation of a superevent.     

Interplanetary type III radiobursts and relativistic electrons

For the time periods 1979 April 22–May 17 and 1980 May 9–June 10, when the HELIOS spacecraft were located inside 0.5 AU, we compared the antenna temperature T _A of the 466 kHz type III bursts measured by the SBH instrument on ISEE 3 with the fluxes of 0.5 MeV electrons measured by HELIOS. For 51 flare-associated kilometric type III bursts (FAIII bursts) with log(T _A) > 10 we find: (1) 25 bursts (49%) are accompanied by a relativistic electron event in interplanetary space, (2) the probability for detection of an electron event decreases from more than 74% inside a cone of ± 20 ° to 56% inside a cone of ± 60° around the flare site, (3) there is only a small correlation between the brightness temperature of the radio burst and the size of the electron event, and (4) despite the broad scatter of these values there is a clear indication that for a given size of the relativistic electron event the intensity of the type III burst is about a factor of 5 higher if it is accompanied by a type II burst. These results give evidence (a) that at least part of the relativistic electrons frequently is accelerated together with non-relativistic electrons and (b) that the coronal shock associated with the metric type II burst has a weaker effect on relativistic than on non-relativistic electrons.Now at DFVLR, Oberpfaffenhofen, Germany.