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Title: SHORT ACCELERATION TIMES FROM SUPERDIFFUSIVE SHOCK ACCELERATION IN THE HELIOSPHERE

Abstract

The analysis of time profiles of particles accelerated at interplanetary shocks allows particle transport properties to be inferred. The frequently observed power-law decay upstream, indeed, implies a superdiffusive particle transport when the level of magnetic field variance does not change as the time interval from the shock front increases. In this context, a superdiffusive shock acceleration (SSA) theory has been developed, allowing us to make predictions of the acceleration times. In this work we estimate for a number of interplanetary shocks, including the solar wind termination shock, the acceleration times for energetic protons in the framework of SSA and we compare the results with the acceleration times predicted by standard diffusive shock acceleration. The acceleration times due to SSA are found to be much shorter than in the classical model, and also shorter than the interplanetary shock lifetimes. This decrease of the acceleration times is due to the scale-free nature of the particle displacements in the framework of superdiffusion. Indeed, very long displacements are possible, increasing the probability for particles far from the front of the shock to return, and short displacements have a high probability of occurrence, increasing the chances for particles close to the front to cross themore » shock many times.« less

Authors:
;  [1]
  1. Dipartimento di Fisica, Università della Calabria, Ponte P. Bucci, I-87036 Rende (Italy)
Publication Date:
OSTI Identifier:
22521778
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal; Journal Volume: 815; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ACCELERATION; CHARGED-PARTICLE TRANSPORT; COMPARATIVE EVALUATIONS; DIFFUSION; HELIOSPHERE; LIFETIME; MAGNETIC FIELDS; PROBABILITY; SHOCK WAVES; SOLAR PROTONS; SOLAR WIND

Citation Formats

Perri, S., and Zimbardo, G., E-mail: silvia.perri@fis.unical.it. SHORT ACCELERATION TIMES FROM SUPERDIFFUSIVE SHOCK ACCELERATION IN THE HELIOSPHERE. United States: N. p., 2015. Web. doi:10.1088/0004-637X/815/1/75.
Perri, S., & Zimbardo, G., E-mail: silvia.perri@fis.unical.it. SHORT ACCELERATION TIMES FROM SUPERDIFFUSIVE SHOCK ACCELERATION IN THE HELIOSPHERE. United States. doi:10.1088/0004-637X/815/1/75.
Perri, S., and Zimbardo, G., E-mail: silvia.perri@fis.unical.it. 2015. "SHORT ACCELERATION TIMES FROM SUPERDIFFUSIVE SHOCK ACCELERATION IN THE HELIOSPHERE". United States. doi:10.1088/0004-637X/815/1/75.
@article{osti_22521778,
title = {SHORT ACCELERATION TIMES FROM SUPERDIFFUSIVE SHOCK ACCELERATION IN THE HELIOSPHERE},
author = {Perri, S. and Zimbardo, G., E-mail: silvia.perri@fis.unical.it},
abstractNote = {The analysis of time profiles of particles accelerated at interplanetary shocks allows particle transport properties to be inferred. The frequently observed power-law decay upstream, indeed, implies a superdiffusive particle transport when the level of magnetic field variance does not change as the time interval from the shock front increases. In this context, a superdiffusive shock acceleration (SSA) theory has been developed, allowing us to make predictions of the acceleration times. In this work we estimate for a number of interplanetary shocks, including the solar wind termination shock, the acceleration times for energetic protons in the framework of SSA and we compare the results with the acceleration times predicted by standard diffusive shock acceleration. The acceleration times due to SSA are found to be much shorter than in the classical model, and also shorter than the interplanetary shock lifetimes. This decrease of the acceleration times is due to the scale-free nature of the particle displacements in the framework of superdiffusion. Indeed, very long displacements are possible, increasing the probability for particles far from the front of the shock to return, and short displacements have a high probability of occurrence, increasing the chances for particles close to the front to cross the shock many times.},
doi = {10.1088/0004-637X/815/1/75},
journal = {Astrophysical Journal},
number = 1,
volume = 815,
place = {United States},
year = 2015,
month =
}
  • In this paper, we present a general scenario for nondiffusive transport and we investigate the influence of anomalous, superdiffusive transport on Fermi acceleration processes at shocks. We explain why energetic particle superdiffusion can be described within the Lévy walk framework, which is based on a power-law distribution of free path lengths and on a coupling between free path length and free path duration. A self-contained derivation of the particle mean square displacement, which grows as (Δx {sup 2}) = 2D {sub α} t {sup α} with α > 1, and the particle propagator, is presented for Lévy walks, making usemore » of a generalized version of the Montroll-Weiss equation. We also derive for the first time an explicit expression for the anomalous diffusion coefficient D {sub α} and we discuss how to obtain these quantities from energetic particle observations in space. The results are applied to the case of particle acceleration at an infinite planar shock front. Using the scaling properties of the Lévy walk propagator, the energy spectral indices are found to have values smaller than the ones predicted by the diffusive shock acceleration theory. Furthermore, when applying the results to ions with energies of a few MeV accelerated at the solar wind termination shock, the estimation of the anomalous diffusion coefficient associated with the superdiffusive motion gives acceleration times much smaller than the ones related to normal diffusion.« less
  • The protons in large solar energetic particle events are accelerated in the inner heliosphere by fast shocks produced by coronal mass ejections. Unless there are other sources, the protons these shocks act upon would be those of the solar wind (SW). The efficiency of the acceleration depends on the kinetic energy of the protons. For a 2000 km s{sup −1} shock, the most effective proton energies would be 30–100 keV; i.e., within the suprathermal tail component of the SW. We investigate one possible additional source of such protons: those resulting from the decay of solar-flare-produced neutrons that escape from themore » Sun into the low corona. The neutrons are produced by interactions of flare-accelerated ions with the solar atmosphere. We discuss the production of low-energy neutrons in flares and their decay on a interplanetary magnetic field line near the Sun. We find that even when the flaring conditions are optimal, the 30–100 keV neutron-decay proton density produced by even a very large solar flare would be only about 10% of that of the 30–100 keV SW suprathermal tail. We discuss the implication of a seed-particle source of more frequent, small flares.« less
  • The theory of diffusive shock acceleration is extended to the case of superdiffusive transport, i.e., when the mean square deviation grows proportionally to t{sup {alpha}}, with {alpha} > 1. Superdiffusion can be described by a statistical process called Levy random walk, in which the propagator is not a Gaussian but it exhibits power-law tails. By using the propagator appropriate for Levy random walk, it is found that the indices of energy spectra of particles are harder than those obtained where a normal diffusion is envisaged, with the spectral index decreasing with the increase of {alpha}. A new scaling for themore » acceleration time is also found, allowing substantially shorter times than in the case of normal diffusion. Within this framework we can explain a number of observations of flat spectra in various astrophysical and heliospheric contexts, for instance, for the Crab Nebula and the termination shock of the solar wind.« less
  • Voyagers 1 and 2 have observed interplanetary shock acceleration of {approx lt}2 MeV ions at radial distances of > 25 AU and heliographic latitudes of up to {approximately}30{degrees}. The previously reported negative latitude gradient in the intensities of accelerated ions at these energies persists over the entire range of latitudes and radial distances measured. The energy spectra of the shock acceleration events at Voyagers 1 and 2 are similar. A dramatic decrease in the flux of {approx lt}2 MeV ions in the outer heliosphere was observed by both Voyager spacecraft in 1985. The decrease was observed at {approximately}30{degrees} as wellmore » as in the solar equatorial plane. At the time of the decrease, Voyager 1 was at {approximately}22 and {approximately}6 AU further from the sun than Voyager 2. However, the decrease began within an {approximately}12 day interval at both spacecraft. Comparisons with data from the IMP 8 spacecraft near Earth show that the decrease propagated outward from the Sun at {approximately}570 km/s. The timing of the large decrease between the two Voyager spacecraft implies a latitude gradient in the velocity of interplanetary shocks of {approximately}4.2 km/s per degree of latitude above the solar equator.« less
  • Radially propagating shocks of solar flare origin are analyzed using plasma and charged particle measurments on Pioneer 10 to show that protons and helium nuclei are continuously accelerated to energies of up to roughly 70 MeV per nucleon. The discovery that electrons are simultaneously accelerated to relativistic energies places new constraints on models for acceleration by these quasi-perpendicular shocks in the outer heliosphere.