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

ABSTRACT The mean free path is widely used to measure the level of solar energetic particles' diffusive transport. We model a solar energetic particle event observed by Wind STEP at 0.31–0.62 MeV nucleon À1 , by solving the focused transport equation using the Markov stochastic process theory. With different functions of the pitch angle diffusion coefficient D , we obtain different parallel mean free paths for the same event. We show that the different values of the mean free path are due to the high anisotropy of the solar energetic particles. This makes it problematic to use just the mean free path to describe the strength of the solar energetic particle scattering, because the mean free path is only defined for a nearly isotropic distribution. Instead, a more complete function of pitch angle diffusion coefficient is needed.

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    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
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    ABSTRACT: We have studied ~0.3 to >100 MeV nucleon–1 H, He, O, and Fe in 17 large western hemisphere solar energetic particle events (SEP) to examine whether the often observed decrease of Fe/O during the rise phase is due to mixing of separate SEP particle populations, or is an interplanetary transport effect. Our earlier study showed that the decrease in Fe/O nearly disappeared if Fe and O were compared at energies where the two species interplanetary diffusion coefficient were equal, and therefore their kinetic energy nucleon–1 was different by typically a factor ~2 ("energy scaling"). Using an interplanetary transport model that includes effects of focusing, convection, adiabatic deceleration, and pitch angle scattering we have fit the particle spectral forms and intensity profiles over a broad range of conditions where the 1 AU intensities were reasonably well connected to the source and not obviously dominated by local shock effects. The transport parameters we derive are similar to earlier studies. Our model follows individual particles with a Monte Carlo calculation, making it possible to determine many properties and effects of the transport. We find that the energy scaling feature is preserved, and that the model is reasonably successful at fitting the magnitude and duration of the Fe/O ratio decrease. This along with successfully fitting the observed decrease of the O/He ratio leads us to conclude that this feature is best understood as a transport effect. Although the effects of transport, in particular adiabatic deceleration, are very significant below a few MeV nucleon–1, the spectral break observed in these events at 1 AU is only somewhat modified by transport, and so the commonly observed spectral breaks must be present at injection. For scattering mean free paths of the order of 0.1 AU adiabatic deceleration is so large below ~200 keV nucleon–1 that ions starting with such energies at injection are cooled sufficiently as to be unobservable at 1 AU. Because of the complicating factors of different spectral break energies for different elements, it appears that SEP abundances determined below the break are least susceptible to systematic distortions.
    The Astrophysical Journal 11/2012; 761(2):104. · 6.73 Impact Factor
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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

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