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      The telegraph equation for cosmic-ray transport with weak adiabatic focusing

      Litvinenko, Yuri E.; Schlickeiser, Reinhard
      DOI
       10.1051/0004-6361/201321327
      Link
       www.aanda.org
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      Citation
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      Litvinenko, Y. E. & Schlickeiser, R. (2013). The telegraph equation for cosmic-ray transport with weak adiabatic focusing. Astronomy & Astrophysics, 554, A59.
      Permanent Research Commons link: https://hdl.handle.net/10289/7912
      Abstract
      Time-dependent solutions of a spatial diffusion equation are often used to describe the transport of solar energetic particles, accelerated in large solar flares. Approximate analytical solutions of the diffusion approximation can complement and guide detailed numerical solutions of the Fokker-Planck equation for the particle distribution function. The accuracy of the diffusion approximation is limited, however, because the signal propagation speed is infinite in the diffusion limit. An improved description of cosmic-ray transport is provided by the telegraph equation, characterised by a finite signal propagation speed. We derive the telegraph equation for the particle density, taking into account adiabatic focusing in a large-scale interplanetary magnetic field in a weak focusing limit. As an illustration, we calculate a propagating pulse solution of the telegraph equation, determine the rise time when the maximum particle intensity is reached at a given distance from the Sun, and compare the results with those obtained in the diffusion approximation. In comparison with the diffusion equation, the telegraph equation predicts an asymmetrical shape of the pulse and a shorter rise time. These potentially significant differences suggest that the more accurate telegraph equation should be used in analysis of the solar energetic particle data, at least to quantify the accuracy of the focused diffusion model.
      Date
      2013
      Type
      Journal Article
      Publisher
      EDP SCIENCES S A
      Collections
      • Computing and Mathematical Sciences Papers [1455]
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