Article

# The model dependence of solar energetic particle mean free paths under weak scattering

The Astrophysical Journal (Impact Factor: 6.73). 03/2005; 627(1):562-566. DOI:10.1086/430136

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**ABSTRACT:**The focused transport equation (FTE) includes all the necessary physics for modeling the shock acceleration of energetic particles with a unified description of first-order Fermi acceleration, shock drift acceleration, and shock surfing acceleration. It can treat the acceleration and transport of particles with an anisotropic distribution. In this study, the energy spectrum of pickup ions accelerated at shocks of various obliquities is investigated based on the FTE. We solve the FTE by using a stochastic approach. The shock acceleration leads to a two-component energy spectrum. The low-energy component of the spectrum is made up of particles that interact with shock one to a few times. For these particles, the pitch angle distribution is highly anisotropic, and the energy spectrum is variable depending on the momentum and pitch angle of injected particles. At high energies, the spectrum approaches a power law consistent with the standard diffusive shock acceleration (DSA) theory. For a parallel shock, the high-energy component of the power-law spectrum, with the spectral index being the same as the prediction of DSA theory, starts just a few times the injection speed. For an oblique or quasi-perpendicular shock, the high-energy component of the spectrum exhibits a double power-law distribution: a harder power-law spectrum followed by another power-law spectrum with a slope the same as the spectral index of DSA. The shock acceleration will eventually go into the DSA regime at higher energies even if the anisotropy is not small. The intensity of the energy spectrum given by the FTE, in the high-energy range where particles get efficient acceleration in the DSA regime, is different from that given by the standard DSA theory for the same injection source. We define the injection efficiency η as the ratio between them. For a parallel shock, the injection efficiency is less than 1, but for an oblique shock or a quasi-perpendicular shock it could be greater.The Astrophysical Journal 08/2011; 738(2):168. · 6.73 Impact Factor - [show abstract] [hide abstract]

**ABSTRACT:**Recently, Tan and coworkers studied the 2001 September 24 solar energetic particle (SEP) event observed by the Wind spacecraft at 1 AU and found that there is a counter-streaming particle beam with a deep depression of flux at 90 • pitch angle during the beginning of the event. They suggested that it is a result of a reflecting boundary at some distance outside of 1 AU. While this scenario could be true under some specific configuration of an interplanetary magnetic field, in this paper we offer another possible explanation. We simulated the SEP event by solving the five-dimensional focused transport equation numerically for 40 keV electrons with perpendicular diffusion. We find that a counter-streaming particle beam with deep depression at 90 • pitch angle can form on Parker magnetic field lines that do not directly connect to the main particle source on the Sun in the beginning of an SEP event. It can happen when a significant number of observed particles come from adjacent field lines through parallel transport to large radial distance first, hopping across field lines through perpendicular diffusion, and then getting scattered back to 1 AU, where they combine with the particles directly coming from the Sun to form a counter-streaming beam.The Astrophysical Journal 09/2011; 738:28. · 6.73 Impact Factor - [show abstract] [hide abstract]

**ABSTRACT:**In this paper, a model of solar energetic particle (SEP) propagation in the three-dimensional Parker interplanetary magnetic field is calculated numerically. We study the effects of the different aspects of particle sources on the solar surface, which include the source location, coverage of latitude and longitude, and spatial distribution of source particle intensity, on propagation of SEPs with both parallel and perpendicular diffusion. We compute the particle flux and anisotropy profiles at different observation locations in the heliosphere. From our calculations, we find that the observation location relative to the latitudinal and longitudinal coverage of particle source has the strongest effects on particle flux and anisotropy profiles observed by a spacecraft. When a spacecraft is directly connected to the solar sources by the interplanetary magnetic field lines, the observed particle fluxes are larger than when the spacecraft is not directly connected. This paper focuses on the situations when a spacecraft is not connected to the particle sources on the solar surface. We find that when the magnetic footpoint of the spacecraft is farther away from the source, the observed particle flux is smaller and its onset and maximum intensity occur later. When the particle source covers a larger range of latitude and longitude, the observed particle flux is larger and appears earlier. There is east-west azimuthal asymmetry in SEP profiles even when the source distribution is east-west symmetric. However, the detail of particle spatial distribution inside the source does not affect the profile of the SEP flux very much. When the magnetic footpoint of the spacecraft is significantly far away from the particle source, the anisotropy of particles in the early stage of an SEP event points toward the Sun, which indicates that the first arriving particles come from outside of the observer through perpendicular diffusion at large radial distances.The Astrophysical Journal 05/2011; 734(2):74. · 6.73 Impact Factor

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