Energetic Particles Accelerated At Coronal Shocks And The Characteristics Of Double-power-law Energy Spectrum

The Sun is the star most closely associated with humanity and the source of disturbances to the Sun-Earth space environment.Coronal mass ejections(CMEs)and solar flares being two of the most violent eruptions in the solar system.During this period,a large number of charged particles are accelerated to high-energies(e.g.protons can be accelerated up to～GeV)in short time,resulting in the flux of high-energy particles increase suddenly in near-Earth space,known as Solar Energetic Particles(SEP)events.SEP events are catastrophic space weather events that occur during solar eruptions.These high-energy particles can cause severe effects in near-Earth space,destroying satellites and on-board equipment in space,threatening the lives of astronauts and affecting radio communications,etc.Therefore,the investigate of SEP acceleration and transport is not only a critical scientific issue in the field of space physics,but also very important for understanding the Sun-Earth space environment and the patterns of space weather.The acceleration mechanism of the SEP consists magnetic field reconnection during the flare and CME-driven shock.In some large SEP and GLE events,CME shocks can form in the low corona and effectively accelerate particles to high-energies.In this thesis,we use numerical simulations to study the acceleration of CME-shocks in the corona for different kinds of particles,including proton(H),helium(He),oxygen(O),magnesium(Mg),iron(Fe),etc.In chapter 2,we perform numerical modeling of particle acceleration at coronal shocks propagating through a streamer-like magnetic field by solving the Parker transport equation.In this model,the effects on the particle energy spectrum and spatial distribution are considered for different magnetic field structures and different turbulence spectral indices.This is followed by an analysis of whether the energy spectra of the particles are double power-laws,the relationship between the break energy and the particle charge-to-mass ratio,etc.In chapter 3,the formation of the double power-law energy spectrum of SEP is discussed.In chapter 4,the variation of elemental abundance ratios with energy for different kinds of particles is compared.In chapter 2,the effect of the coronal shocks propagating through different coronal magnetic field structures on particle acceleration is investigated based on the previously developed numerical model of particle acceleration at coronal shocks.The double-power-law characteristics of different ions and the relationship between the break energy EB and the charge-to-mass ratio Q/A are analysed.The integrated energy spectra of the different ion species(H,He,O,Mg,Fe)accelerated over the whole simulation domain are found to be approximately power-law spectra at low-energy in the case of the Kolmogorov turbulence spectrum when the shock propagating through the radial and streamer fields,respectively.The particles spectra agree well with the power-law slope predicted by the diffusive shock acceleration(DSA)theory.In the radial field,the particle spectra of different ions species at high-energy undergoes a roll over.While in the streamer field,the energy spectra exhibits another power-law spectrum at high-energy,with an overall double power-law spectra for different ion species.Furthermore,it can be observed from the energy spectrum that as the mass increases,i.e.the Q/A ratio decreases,the break energy also decreases.According to the theory of diffusion shock acceleration,the break energy of different ions is a power-law function of the charge-to-mass ratio Q/A,EB～(Q/A)α.In equal diffusion coefficients condition,the index α related to the turbulence spectrum index Γ,it can be inferred that α=2(2-Γ)/(3-Γ).The spatial distribution show that the low-energy(<10 MeV)protons are approximately uniformly distributed along the shock front when the shock propagating through the radial and streamer fields,respectively.However,the spatial distribution of high-energy protons is different.When the shock propagating through the radial magnetic field,the high-energy particles(>40 MeV)mainly distributed on the flanks of the shock.As the flank regions correspond to quasi-perpendicular shock,which allows the particles to be accelerated to high-energy.When the shock sweeping through the streamer structure,the high-energy particles(>90 MeV)mainly focused in the closed field region of streamer field.This is due to the closed magnetic field are beneficial to capture particles and accelerate particles through the shock surface several times,and the quasi-perpendicular shock,which also beneficial to particle acceleration.The effect of different turbulent magnetic field on particle acceleration is further investigated,and the energy spectra are given for three cases with turbulence spectral indices Γ of 1.9,1.1 and 0.5.The particle energy spectra integrated over the whole simulation domain were found to be double power-law spectra,which can be fitting with the Band equation.For all ions,the break energy EB and the Q/A satisfying the power-law relationship:EB～(Q/A)α,α range from 0.16～1.2.The results are agreed with the theoretical results obtained by Cohen based on the equal diffusion coefficient condition.In Chapter 3,we discussed the formation of the double power-law energy spectrum.If the whole simulation domain is simply divided into the open field region and the streamer closed field region,the energy spectra in both regions are in the form of "power-law × exponential rollover".In contrast,the energy spectrum integrated over the whole simulation domain is approximately a double power-law spectrum.Based on previous studies,we present a "superposition scenario" of SEP mixing from various source regions to explain the formation of the double power-law energy spectrum.Particle acceleration efficiency varies in different source regions,and the corresponding energy spectra are different.If mixing occurs under certain conditions,the mixed energy spectrum at highenergy can raised,and the energy spectrum will be a double power-law spectrum.We focused on the formation of the double power-law spectrum of SEP and tried to provide more support for our "superposition scenario".The energy spectra is analysed in three small regions,the streamer region,the non-streamer region and the transition region.Although the particles are effectively accelerated in the streamer region,the energy spectrum still resembles the form of "power-law ×exponential rollover".However,the energy spectrum in the transition region can be fitted by a double power-law spectrum.Because high-energy(>100 MeV/nuc)particles mainly come from streamer region where particle acceleration efficiency is more efficient,and these high-energy particles mix with locally accelerated low-energy particle population by diffusion to form a double power-law energy spectrum.In order to satisfy the isotropy condition of the diffusive shock acceleration theory,the anisotropy must be small enough,leading to the so-called "injected energy" problem.The numerical simulation shows that a double power-law energy spectrum can still be obtained in the transition region(region Ⅲ)when the injected energy dependence on the shock geometry,which indicating that the proposed "superposition scenario" is still reasonable.In addition,the particle density differs significantly between the streamer and non-streamer regions,which may affect the injection efficiency of particle along the shock front.We find that when the ratio of particle injection efficiency between the streamer and non-streamer regions is 10,double power-law spectral features still appear in the transition region(region Ⅲ).Because only a small fraction(5%)of high-energy particles diffuse into region Ⅲ,contributing to the high-energy particles of double power-law spectrum in region Ⅲ.In large SEP events,the element abundance ratios of different ions show different energy dependence.In some SEP events,the Fe/O ratio decreases with increasing energy;however,in other SEP events,the Fe/O ratio increases with energy.Based on the "superposition scenario" of double power-law spectrum,it is believed that the diffusion and mixing effects of high-energy particles can also provide an explanation for the different in the energy dependence of Fe/O.At high energy(>10 MeV/nuc),the ratio of Fe/O in the streamer region is much larger than that in non-streamer region.These high-energy particles escape from the streamer region into the transition region,resulting in Fe/O rising with the increasing energy at high-energy in the transition region.Similar conclusions as for Fe/O exist for other elemental abundance ratios in the transition region.He/H also rises with increasing energy at high-energy.This is also due to the mixing of the accelerated high-energy particles(with large He/H)in the streamer region with the particles(with low He/H)in the local region(region Ⅲ)through diffusion effect.According to our simulation results of coronal shock particle acceleration,there are important effects for SEP acceleration efficiency and the propagation of highenergy particles when considering a shock propagating through the large scale coronal magnetic field structures(e.g.streamer).The simulations predict that different forms of the SEP energy spectrum,and different variations of Fe/O with energy,are observed when magnetic field lines near the satellite are connected to different regions of the shock.Parker Solar Probe will be able to reach positions as close as～10 R⊙ to the Sun in the future.The perihelion observations of the SEP have the potential to validate our proposed scenario of the formation of the double power-law spectrum and the interpretation of the variation of Fe/O with energy.