| From the launch of the Fermi satellite in 2008 to 2018,45 flares with>100 MeV gamma-ray emission have been observed.This radiation is caused by nuclear reactions excited by>300 MeV protons colliding with the solar atmosphere.However,flares or coronal mass ejections(CMEs)driven shocks can also accelerate protons to>300 MeV,and the origin of high-energy protons is still controversial.If the>100 MeV gamma-ray emission lasts for more than two hours,it can be classified as a persistent gamma-ray event.For this type of event,it is generally believed to be related to protons accelerated by CME-driven shocks.Part of the protons accelerated by the CME shock propagates away from the sun along the magnetic field lines and produces solar energetic particle(SEP)events,while another part of the protons can propagate towards the sun along the magnetic field lines,collide with the solar surface,and produce gamma rays.Because CME-driven shocks can last for a long time,and the magnetic field lines of coronal shocks can connect to positions far from the flare,this explanatory framework is suitable for explaining gamma-ray flares that last a long time,where the gamma-ray source is far from the flare,and gamma-ray flares associated with SEP events.However,whether>300 MeV protons accelerated by CME-driven shocks can return to the solar surface is an unresolved question,as is the proportion of protons that can return to the solar surface.Is the location where the returning protons collide with the solar surface consistent with the position of gamma-ray observations?These questions remain unanswered.Furthermore,studying the mechanism of producing persistent>100 MeV gamma-ray emissions is of great significance for understanding the acceleration and propagation of solar high-energy particles.In Chapter 2,the Parker transport equation and the focused transport equation are introduced.The numerical solutions to the Parker transport equation and the focused transport equation are obtained using the forward stochastic differential equation method.The focused transport equation is used to simulate the particle acceleration by shocks with an oblique angle of 450 between the shock normal and the upstream magnetic field.The trajectories,pitch angle and momentum variations of single protons during the acceleration process,as well as the spatial distribution,energy spectrum and pitch angle distribution of high-energy protons are obtained.It is found that the magnetic focusing effect causes particles to tend to move towards the upstream region when they pass through the shock.The higher the pitch angle diffusion coefficient,the more efficient the shock is in accelerating particles,and the pitch angle distribution shows a cone loss distribution.In Chapter 3,numerical simulations are conducted to study the transport of protons in the persistent gamma-ray flare event that occurred on September 1,2014,This event had three important characteristics.Firstly,the flare was located on the far side of the Sun,with no visible flare on the front side,yet>100 MeV gamma-ray emission was observed with a longitude offset of 52°.Secondly,the gamma-ray emission lasted for two hours,while the flare on the far side of the Sun only lasted for 40 minutes,indicating that this is a persistent gamma-ray flare event.Thirdly,the event was accompanied by a solar energetic particle(SEP)event that was observed by the STEREO and GOES satellites.Based on the three characteristics stated above,it is believed that the event was caused by the acceleration of>300 MeV protons by a CME-driven shock on the far side of the Sun.These protons then propagated towards the front side of the Sun along magnetic field lines,colliding with the solar surface and producing the observed gamma-ray emission.The remaining protons propagated towards interplanetary space,producing the SEP event observed by the STEREO and GOES satellites.In this study,we conducted numerical simulations of the process by coupling the magnetohydrodynamic(MHD)model with the particle transport model.For the MHD simulation,we first simulated the background solar wind by inputting the photospheric magnetic field into the model under the Space Weather Modeling Framework(SWMF)framework.Then,we inserted a magnetic flux rope in the active region to simulate the eruption process of the coronal mass ejection(CME),and obtained the changes in the plasma parameters at different times.For the particle simulation,we used the MHD simulation data near the peak time of the gamma-ray emission(11:20 UT)to determine the position of the shock and the shock compression ratio.We then uniformly selected 954 points on the shock front and injected protons with a power-law spectrum and an exponential cutoff at each point.We used the forward stochastic differential equation method to numerically solve the focused transport equation and simulated the transport process of the protons.Our simulations yielded the spatial distribution of protons and their characteristics upon reaching the solar surface.We found that the distribution of protons returning to the solar surface is related to the magnetic connectivity with the shock,and the spatial distribution of>300 MeV protons reaching the solar surface is consistent with the position of the observed gamma-ray emission.The spectral index of the integral energy spectrum of returning protons is close to the spectral index of protons estimated using gamma-ray photon data and the pion decay model at around 300 MeV.We also simulated the proportion of>300 MeV protons deposited on the solar surface at different locations of the shock,and found that the proportion of deposition in the forward direction of the shock is lower than that in the flank,while the proportion of accelerated protons deposited on the solar surface is close to the proportion estimated using observational data.Finally,we analyzed the effects of magnetic mirroring,pitch angle scattering,and solar wind convective speed on the deposition... |
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