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Moments of energetic particle distributions in the solar atmosphere
Received 10 July 2000 / Accepted 22 August 2000
This paper describes a theory that provides a direct link between observable properties of energetic particle distributions and the unobservable properties of the initial distributions. A general approach is first outlined and then applied to the specific situation of collisional electron transport in the solar atmosphere. By building on previous results, this treatment does not require explicit solution of the Fokker-Planck equation. In particular, we derive results for two important consequences of an energetic electron distribution: 1) The emission of hard X-ray bremsstrahlung radiation and 2) energy deposition in the background plasma by Coulomb collisions. For 1) we describe the energy spectrum of the emission completely and provide a description of its spatial and pitch angle properties in terms of the first and second order moments of the injected electron distribution. This means that for any assumed initial electron distribution, expressions are obtained that predict the HXR source's spatial position and extent for any photon energy. The results have most immediate application to phenomena associated with the early impulsive stage of solar flares involving energetic electrons. Other potential uses include: calculation of H impact polarisation; application to polarisational and directional properties of hard X-rays; and diagnostics of unobservably high energy features in the electron spectrum.
Key words: radiation mechanisms: non-thermal Sun: flares Sun: X-rays, gamma rays Sun: corona
© European Southern Observatory (ESO) 2000
Online publication: October 30, 19100