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Title: Acceleration of runaway electrons in solar flares

Abstract

The dc electric field acceleration of electrons out of a thermal plasma and the evolution of the runaway tail are studied numerically, using a relativistic quasi-linear code based on the Ritz-Galerkin method and finite elements. A small field-aligned electric field is turned on at a certain time. The resulting distribution function from the runaway process is used to calculate the synchrotron emission during the evolution of the runaway tail. It is found that, during the runaway tail formation, which lasts a few tens of seconds for typical solar flare conditions, the synchrotron emission level is low, almost ot the same order as the emission from the thermal plasma, at the high-frequency end of the spectrum. However, the emission is enhanced explosively in a few microseconds by several orders of magnitude at the time the runaway tail stops growing along the magnetic field and tends toward isotropy due to the pitch-angle scattering of the fast particles. Results indicate that, in order to account for the observed synchrotron emission spectrum of a typical solar flare, the electric field acceleration phase must be accompanied or preceded by a heating phase which yields an enhanced electron temperature of about 2-15 keV in the flaremore » region if the electric field is 0.1-0.2 times the Dreicer field and cyclotron-to-plasma frequency ratios are of order 1-2. 23 refs.« less

Authors:
;  [1]
  1. (Iowa Univ., Iowa City (USA))
Publication Date:
OSTI Identifier:
7041385
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal; (USA); Journal Volume: 352
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; RUNAWAY ELECTRONS; ACCELERATION; SOLAR FLARES; DIRECT CURRENT; DOPPLER EFFECT; ELECTRIC FIELDS; EMISSION SPECTRA; HOT PLASMA; MAGNETIC FIELDS; NUMERICAL SOLUTION; SOLAR ELECTRONS; SOLAR RADIO BURSTS; SYNCHROTRON RADIATION; BREMSSTRAHLUNG; CURRENTS; ELECTRIC CURRENTS; ELECTROMAGNETIC RADIATION; ELECTRONS; ELEMENTARY PARTICLES; FERMIONS; LEPTONS; PLASMA; RADIATIONS; RADIOWAVE RADIATION; SOLAR ACTIVITY; SOLAR PARTICLES; SOLAR RADIATION; SPECTRA; STELLAR RADIATION; 640104* - Astrophysics & Cosmology- Solar Phenomena

Citation Formats

Moghaddam-taaheri, E., and Goertz, C.K. Acceleration of runaway electrons in solar flares. United States: N. p., 1990. Web. doi:10.1086/168543.
Moghaddam-taaheri, E., & Goertz, C.K. Acceleration of runaway electrons in solar flares. United States. doi:10.1086/168543.
Moghaddam-taaheri, E., and Goertz, C.K. 1990. "Acceleration of runaway electrons in solar flares". United States. doi:10.1086/168543.
@article{osti_7041385,
title = {Acceleration of runaway electrons in solar flares},
author = {Moghaddam-taaheri, E. and Goertz, C.K.},
abstractNote = {The dc electric field acceleration of electrons out of a thermal plasma and the evolution of the runaway tail are studied numerically, using a relativistic quasi-linear code based on the Ritz-Galerkin method and finite elements. A small field-aligned electric field is turned on at a certain time. The resulting distribution function from the runaway process is used to calculate the synchrotron emission during the evolution of the runaway tail. It is found that, during the runaway tail formation, which lasts a few tens of seconds for typical solar flare conditions, the synchrotron emission level is low, almost ot the same order as the emission from the thermal plasma, at the high-frequency end of the spectrum. However, the emission is enhanced explosively in a few microseconds by several orders of magnitude at the time the runaway tail stops growing along the magnetic field and tends toward isotropy due to the pitch-angle scattering of the fast particles. Results indicate that, in order to account for the observed synchrotron emission spectrum of a typical solar flare, the electric field acceleration phase must be accompanied or preceded by a heating phase which yields an enhanced electron temperature of about 2-15 keV in the flare region if the electric field is 0.1-0.2 times the Dreicer field and cyclotron-to-plasma frequency ratios are of order 1-2. 23 refs.},
doi = {10.1086/168543},
journal = {Astrophysical Journal; (USA)},
number = ,
volume = 352,
place = {United States},
year = 1990,
month = 3
}
  • The electric-field acceleration of electrons out of a thermal plasma and the simultaneous Joule heating of the plasma are studied. Acceleration and heating time scales are derived and compared, and upper limits are obtained on the acceleration volume and the rate at which electrons can be accelerated. These upper limits, determined by the maximum magnetic-field strength observed in flaring regions, place stringent restrictions on the acceleration process. The implications of these results for the microwave and hard X-ray emission from solar flares are examined. The major conclusions are: (1) The simple electric-field acceleration of electrons is found, in agreement withmore » Spicer, to be incapable of producing a large enough electron flux to explain the bulk of the observed hard X-ray emission from solar flares as nonthermal bremsstrahlung. For the bulk of the X-ray emission to be nonthermal, at least 10/sup 4/ oppositely directed current channels are required, or an acceleration mechanism that does not result in a net current in the acceleration region is required. (2) lf the bulk of the X-ray emission is thermal, a single current sheet can yield the required heating and acceleration time scales and the required electron energies for the microwave emission. This is accomplished with an electric field that is much smaller than the Dreicer field (E/sub D//Eroughly-equal10--50). (3) The rise time of the nonthermal emission is determined by the time needed to generate the required number of runaway electrons rather than by the time needed to accelerate the electrons to the required energies, which is generally a much shorter time scale. (4) The acceleration of enough electrons to produce a microwave flare requires the resupply of electrons to both the current sheet and the runaway region of velocity space.« less
  • The observations of hard X-rays and nonrelativistic electrons in solar flares are interpreted. The inferred requirements for acceleration are compared with our knowledge of acceleration processes in a plasma, and the following sequence is proposed. Electrons are initially accelerated and heated locally to a few keV by direct induced electric fields along the magnetic field in current filaments or sheets by the tearing mode instability or magnetic field reconnection. The widths of the field reversal regions are of order 1 meter for typical solar conditions, and the central part of this region has an anomalous resistivity. The electrons leave thesemore » myriads of small initial acceleration regions and mix with the relatively cold plasma in a much larger volume, developing distributions which are unstable to the generation of electron plasma waves. These waves are transferred to large phase velocities by the weak turbulence process of nonlinear scattering on the polarization clouds of ions as their energy density grows. Finally, the wave energy density and spectrum satisfy the condition for strong electron plasma wave turbulence or the modulational instability of Paper I which transfers the waves to low phase velocities where they accelerate electrons with near power-law distributions. This sequence of plasma processes occurs repeatedly on a time scale much shorter than the tearing mode or reconnection time scale. It is surmised that this sequence only works effectively to 60--100 keV, which provides an explanation for the steepening in the electron distribution often inferred in this range. This plasma sequence provides a mechanism for redistributing the electron energy to a form consistent with the observations with an estimated efficiency of 40%.« less
  • We find that for two of the hard X-ray bursts of an energetic flare on 1980 June 27, the time profile of the hard X-rays above 235 keV is delayed by 3 s with respect to the time profiles of the lower energy X-rays and that the high energy spectrum becomes flatter with time during each of these bursts. From these findings we argue that during this flare a second-step mechanism accelerated further some of the high-energy tail population of the first-step electrons. By noticing that all of the flares with second-step delays produced interplanetary energetic protons, and that gamma-raymore » lines were detected from all of these flares except one that was not observed by any gamma-ray detector, we conclude that the second-step mechanism accelerates not only (mildly) relativistic electrons but also protons and heavy nuclei. Small delays of the nuclear gamma-ray time profiles with respect to the hard X-ray time profiles observed by SMM from the 1980 June 7 and 21 flares are consistent with this conclusion. After estimating the acceleration rate, we conclude that first-order Fermi acceleration operating in a closed flare loop is a very likely mechanism for the second-step acceleration.« less
  • The electric field acceleration of electrons out of a thermal plasma and the simultaneous Joule heating of the plasma are studied. Acceleration and heating timescales are derived and compared, and upper limits are obtained on the acceleration volume and the rate at which electrons can be accelerated. These upper limits, determined by the maximum magnetic field strength observed in flaring regions, place stringent restrictions upon the acceleration process. The role of the plasma resistivity in these processes is examined, and possible sources of anomalous resistivity are summarized. The implications of these results for the microwave and hard X-ray emission frommore » solar flares are examined.« less
  • It is shown by theory and fully relativistic, electromagnetic particle simulation that a collisionless fast magnetosonic shock wave can promptly accelerate protons and electrons to relativistic energies; proton energies greater than about 10 to the 9th eV and electron energies greater than about 10 to the 6th eV. The time needed for the proton acceleration is of the order of the ion cyclotron period and is quite short (much less than 1 s for solar plasmas). The electron acceleration time is shorter than the ion cyclotron period. The present shock acceleration mechanism can explain important features of observed particle accelerationmore » in the impulsive phase of solar flares; simultaneous and prompt acceleration of protons and electrons to relativistic energies. 31 references.« less