Study On Propagation Of Solar Energetic Particles In Three-dimensional Interplanetary Magnetic Fields

In this dissertation, we have studied the propagation of solar energetic par-ticles (SEPs) in three-dimensional interplanetary magnetic fields with combina-tion of theoretical models, numerical simulations and spacecraft observations.We have mainly discussed the effects of perpendicular diffusion on propagationof SEPs. The main research results are as follows:1. Effects of sources on propagation of SEPs in three-dimensional inter-planetary magnetic fields. By investigating source locations, coverage of latitudeand longitude, and spatial variations with calculation of SEP ffux and anisotropyprofiles at different observation locations in heliosphere, we study the effects ofsources on propagation of SEPs. The following are main conclusions in thiswork: (1) Perpendicular diffusion mechanism plays a very important role in SEPpropagation. It can be used to explain many observational phenomena, partic-ularly when a spacecraft is not directly connected to the solar source by theinterplanetary magnetic field (IMF) lines. (2) The location of SEP source hasthe greatest effects on observed SEP ffux and anisotropy profiles. The fartherthe IMF footpoint of the observer is away from the source, the smaller the par-ticle ffux will be observed, and the later the onset and the peak of SEP ffux willappear. Particles from a source on east side or west side relative to the IMFfootpoint of the spacecraft will appear differently, even though the longitudinalseparation and other source characteristics are the same. This effect results fromthe azimuthal asymmetry of the Parker interplanetary magnetic field. When theIMF footpoint of the observer is very far away from the source in longitude, e.g.,by as large as 60 degrees, the first arriving SEPs could be moving towards thesun. These are the particles that first stream out along field lines to large radialdistances, diffuse across field lines onto the line that connects the observer, getscattered in pitch angle and then come back to the observer from outside. (3)The coverage of source in latitude and longitude also has large effects on the SEPffux and anisotropy profiles. Particles coming from a wider source tends to have large ffuxes. When the IMF footpoint of the observer is at the centers of theSEP sources, the onset and the peak ffuxes are almost the same for sources ofdifferent coverages in longitude and latitude. However, when the IMF footpointof the observer is not located inside the source region, a wider source coveragewill result in an earlier onset and peak ffux. (4) The ffux and anisotropy profilesin the cases with different normalized spatial variation of SEP source injectionappear almost the same if all the other conditions remain the same. It indicatethat the form of spatial variation is not very important in affecting the SEP ffuxand anisotropy, unless its distribution is extremely strange.2. An analytical method to determine SEPs'mean free path. SEPs'meanfree path, determined by physical properties of SEPs as well as those of solar wind,is a very important physical parameter in space weather. To accurately obtainthe mean free path of SEPs for a solar event, a so-called simulation method byfitting time-profiles of both ffux and anisotropy between spacecraft observationsand numerical simulations of SEPs transport process has to be used. However,such kind of fitting and simulations need a large amount of calculation resources,so they are time-consuming even with modern super-computers. It is necessaryto find a better way to get mean free path of SEPs quickly, especially in spaceweather forecast. Recently, Shalchi et al. provided an approximate analyticalformula of SEPs'anisotropy time-profile as a function of particles'mean freepath for impulsive events. In this work, we use a so-called analytical method todetermine SEPs'mean free path by fitting the anisotropy time-profiles betweenthe Shalchi et al.'s analytical formula and spacecraft observations. In addition,we compare the mean free path obtained with the traditional simulation methodwith that obtained with the new analytical method to show that the analyticalmethod, with some modifications, can give us a good approximation of SEPs'mean free path quickly for impulsive events.3. The simulation study on counter-streaming particle beam. Recently, Tanet al. studied the 2001 September 24 SEP event observed by the Wind space-craft at 1 AU and found that there is a counter-streaming particle beam witha deep depression of ffux at 90-degree pitch angle during the beginning of theevent. They suggested that it is a result of a reffecting boundary at some distance outside of 1 AU. While this scenario could be true under some specific config-uration of interplanetary magnetic field, in this work, we offer another possibleexplanation to it. We simulated the SEP event by solving the five-dimensionalfocused transport equation numerically for 40 keV electrons with perpendiculardiffusion. We find that a counter-streaming particle beam with deep depressionat 90-degree pitch angle can form on Parker magnetic field lines that do notdirectly connect to the main particle source on the sun in the beginning of anSEP event. It can happen when a significant number of observed particles comefrom adjacent field lines through parallel transport to large radial distance first,hopping across field lines through perpendicular diffusion, and then getting scat-tered back to 1 AU, where they combine the particles directly coming from thesun to form a counter-streaming particle beam.