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Title: The Role of Diffusion in the Transport of Energetic Electrons during Solar Flares

Abstract

The transport of the energy contained in suprathermal electrons in solar flares plays a key role in our understanding of many aspects of flare physics, from the spatial distributions of hard X-ray emission and energy deposition in the ambient atmosphere to global energetics. Historically the transport of these particles has been largely treated through a deterministic approach, in which first-order secular energy loss to electrons in the ambient target is treated as the dominant effect, with second-order diffusive terms (in both energy and angle) generally being either treated as a small correction or even neglected. Here, we critically analyze this approach, and we show that spatial diffusion through pitch-angle scattering necessarily plays a very significant role in the transport of electrons. We further show that a satisfactory treatment of the diffusion process requires consideration of non-local effects, so that the electron flux depends not just on the local gradient of the electron distribution function but on the value of this gradient within an extended region encompassing a significant fraction of a mean free path. Our analysis applies generally to pitch-angle scattering by a variety of mechanisms, from Coulomb collisions to turbulent scattering. We further show that the spatial transport ofmore » electrons along the magnetic field of a flaring loop can be modeled rather effectively as a Continuous Time Random Walk with velocity-dependent probability distribution functions of jump sizes and occurrences, both of which can be expressed in terms of the scattering mean free path.« less

Authors:
;  [1];  [2]
  1. School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, Scotland (United Kingdom)
  2. Department of Physics and Astronomy, Western Kentucky University, Bowling Green, KY 42101 (United States)
Publication Date:
OSTI Identifier:
22663899
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal; Journal Volume: 835; Journal Issue: 2; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ACCELERATION; COLLISIONS; CORRECTIONS; DIFFUSION; DISTRIBUTION FUNCTIONS; EMISSION; ENERGY ABSORPTION; ENERGY LOSSES; FLARING; GAMMA RADIATION; HARD X RADIATION; MAGNETIC FIELDS; MEAN FREE PATH; RANDOMNESS; SCATTERING; SOLAR FLARES; SPATIAL DISTRIBUTION; SUN; TAIL ELECTRONS; VELOCITY

Citation Formats

Bian, Nicolas H., Kontar, Eduard P., and Emslie, A. Gordon, E-mail: nicolas.bian@glasgow.gla.ac.uk, E-mail: emslieg@wku.edu. The Role of Diffusion in the Transport of Energetic Electrons during Solar Flares. United States: N. p., 2017. Web. doi:10.3847/1538-4357/835/2/262.
Bian, Nicolas H., Kontar, Eduard P., & Emslie, A. Gordon, E-mail: nicolas.bian@glasgow.gla.ac.uk, E-mail: emslieg@wku.edu. The Role of Diffusion in the Transport of Energetic Electrons during Solar Flares. United States. doi:10.3847/1538-4357/835/2/262.
Bian, Nicolas H., Kontar, Eduard P., and Emslie, A. Gordon, E-mail: nicolas.bian@glasgow.gla.ac.uk, E-mail: emslieg@wku.edu. Wed . "The Role of Diffusion in the Transport of Energetic Electrons during Solar Flares". United States. doi:10.3847/1538-4357/835/2/262.
@article{osti_22663899,
title = {The Role of Diffusion in the Transport of Energetic Electrons during Solar Flares},
author = {Bian, Nicolas H. and Kontar, Eduard P. and Emslie, A. Gordon, E-mail: nicolas.bian@glasgow.gla.ac.uk, E-mail: emslieg@wku.edu},
abstractNote = {The transport of the energy contained in suprathermal electrons in solar flares plays a key role in our understanding of many aspects of flare physics, from the spatial distributions of hard X-ray emission and energy deposition in the ambient atmosphere to global energetics. Historically the transport of these particles has been largely treated through a deterministic approach, in which first-order secular energy loss to electrons in the ambient target is treated as the dominant effect, with second-order diffusive terms (in both energy and angle) generally being either treated as a small correction or even neglected. Here, we critically analyze this approach, and we show that spatial diffusion through pitch-angle scattering necessarily plays a very significant role in the transport of electrons. We further show that a satisfactory treatment of the diffusion process requires consideration of non-local effects, so that the electron flux depends not just on the local gradient of the electron distribution function but on the value of this gradient within an extended region encompassing a significant fraction of a mean free path. Our analysis applies generally to pitch-angle scattering by a variety of mechanisms, from Coulomb collisions to turbulent scattering. We further show that the spatial transport of electrons along the magnetic field of a flaring loop can be modeled rather effectively as a Continuous Time Random Walk with velocity-dependent probability distribution functions of jump sizes and occurrences, both of which can be expressed in terms of the scattering mean free path.},
doi = {10.3847/1538-4357/835/2/262},
journal = {Astrophysical Journal},
number = 2,
volume = 835,
place = {United States},
year = {Wed Feb 01 00:00:00 EST 2017},
month = {Wed Feb 01 00:00:00 EST 2017}
}
  • Two-dimensional electrostatic particle simulations are performed in order to investigate energy transport associated with the propagation of energetic electrons through a flaring flux tube. Results indicate that as the energetic electrons flow outward, a return current of ambient plasma electrons is drawn inward (to maintain quasi-neutrality) which can be spatially separate from the primary current carried by the energetic electrons. Return current electrons are shown to accumulate on either side of the acceleration region of the energetic electrons, and depletions of ambient plasma electrons develop in the return current regions. Plasma ions accelerate across the field lines to produce currentmore » closure or charge neutralization, achieving energies comparable to those of the energetic electrons. 22 references.« less
  • The propagation of energetic electrons through a flaring flux tube is studied in an attempt to determine how the energy of the electrons is deposited in the flux tube. One-dimensional electrostatic particle simulations are used in the present investigation. As the energetic electrons propagate into the system, a return current of ambient plasma electrons and some of the energetic electrons is drawn into the energetic electron source. It is found that, as the ambient temperature relative to the ion temperature increases above about 3, the heated return-current electrons can excite ion-sound waves. 31 references.
  • The peak flux relationship between hard X-rays and microwaves from solar flares is studied using about 400 events simultaneously recorded with the hard X-ray burst spectrometer on the SMM satellite and the Nobeyama 17 GHz radiometer. The data indicate that the hard X-ray and microwave peak fluxes correlate best for X-ray energies of less than about 80 keV for impulsive flares and greater than about 360 keV for extended flares. By postulating that electrons responsible for microwave emission at 17 GHz are those emitting hard X-rays at these photon energies, it is concluded that: (1) in impulsive flares, microwaves atmore » about 20 GHz are emitted mainly by electrons of less than about 200 keV from a layer through which the electrons stream down into the thick-target hard X-ray source; and (2) in extended flares, microwaves are emitted mainly by MeV electrons trapped in a coronal loop or loops. 59 references.« less
  • We investigate the spectra and polarization of the gyrosynchrotron microwave (MW) emission generated by anisotropic electron beams in the solar corona. The electron distributions are selected from the steady propagation/precipitation model of beam electrons obtained from the time-dependent solutions of the Fokker-Planck equation taking into account particle anisotropic precipitation into a converging magnetic tube while losing energy in collisions and Ohmic losses induced by a self-induced electric field. We separate the effects of converging magnetic field from those of self-induced electric field for beams with different initial energy fluxes and spectral indices. The effect of returning electrons of the beammore » is negligible for the beams with relatively weak energy fluxes (F {approx}< 10{sup 10} erg cm{sup -2} s{sup -1}), while it becomes very important for the electron beams with F {approx}> 10{sup 12} erg cm{sup -2} s{sup -1}. Electric field-induced losses lead to the increase of MW emission intensity, especially at larger viewing angles ({theta} {approx}> 140{sup 0}, looking at the loop from a side). The polarization remains typical for the beam-like distributions. The combined effect of the self-induced electric field and converging magnetic field reveals a noticeable (up to a factor of 10) increase of the emission intensity (for the viewing angles {theta} {approx_equal} 140{sup 0}-150{sup 0}) in comparison with the models considering only collision factor, especially in the deeper precipitation layers (near the loop footpoints). Thus, considering the self-induced electric field is especially important for the resulting MW emission intensity, spectra shape, and polarization that can provide much closer correlation of simulations with observations in solar flares.« less