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on the solution of the continuity equation for precipitating electrons in solar flaresElectrons accelerated in solar flares are injected into the surrounding plasma, where they are subjected to the influence of collisional (Coulomb) energy losses. Their evolution is modeled by a partial differential equation describing continuity of electron number. In a recent paper, Dobranskis & Zharkova claim to have found an "updated exact analytical solution" to this continuity equation. Their solution contains an additional term that drives an exponential decrease in electron density with depth, leading them to assert that the well-known solution derived by Brown, Syrovatskii & Shmeleva, and many others is invalid. We show that the solution of Dobranskis & Zharkova results from a fundamental error in the application of the method of characteristics and is hence incorrect. Further, their comparison of the "new" analytical solution with numerical solutions of the Fokker-Planck equation fails to lend support to their result.We conclude that Dobranskis & Zharkova's solution of the universally accepted and well-established continuity equation is incorrect, and that their criticism of the correct solution is unfounded. We also demonstrate the formal equivalence of the approaches of Syrovatskii & Shmeleva and Brown, with particular reference to the evolution of the electron flux and number density (both differential in energy) in a collisional thick target. We strongly urge use of these long-established, correct solutions in future works.
Document ID
Document Type
Reprint (Version printed in journal)
Emslie, A. Gordon
(University of Western Kentucky Bowling Green, KY, United States)
Holman, Gordon D.
(NASA Goddard Space Flight Center Greenbelt, MD United States)
Litvinenko, Yuri E.
(Waikato Univ. Hamilton, New Zealand)
Date Acquired
September 17, 2015
Publication Date
August 7, 2014
Publication Information
Publication: The Astrophysical Journal
Volume: 792
Issue: 1
Subject Category
Space Sciences (General)
Report/Patent Number
Distribution Limits
Sun: flares
Sun: atmosphere
Sun: particle emission
methods: analytical
Sun: X-rays
gamma rays