Analytical solutions of fractional diffusion-advection equation for solar cosmic-ray transport

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dc.contributor.authorLitvinenko, Yuri E.
dc.contributor.authorEffenberger, Frederic
dc.date.accessioned2014-12-02T21:19:00Z
dc.date.available2014
dc.date.available2014-12-02T21:19:00Z
dc.date.issued2014
dc.description.abstractMotivated by recent applications of superdiffusive transport models to shock-accelerated particle distributions in the heliosphere, we analytically solve a one-dimensional fractional diffusion-advection equation for the particle density. We derive an exact Fourier transform solution, simplify it in a weak diffusion approximation, and compare the new solution with previously available analytical results and with a semi-numerical solution based on a Fourier series expansion. We apply the results to the problem of describing the transport of energetic particles, accelerated at a traveling heliospheric shock. Our analysis shows that significant errors may result from assuming an infinite initial distance between the shock and the observer. We argue that the shock travel time should be a parameter of a realistic superdiffusive transport model.
dc.format.extent1-4
dc.format.mimetypeapplication/pdf
dc.identifier125
dc.identifier.citationLitvinenko, Y. E., & Effenberger, F. (2014). Analytical solutions of fractional diffusion-advection equation for solar cosmic-ray transport. The Astrophysical Journal, 796(2). http://doi.org/10.1088/0004-637X/796/2/125en
dc.identifier.doi10.1088/0004-637X/796/2/125
dc.identifier.eissn1538-4357
dc.identifier.urihttps://hdl.handle.net/10289/8875
dc.publisherThe American Astronomical Society
dc.relation.isPartOfThe Astrophysical Journal
dc.rightsThis article is published in the Astrophysical Journal. © 2014 The American Astronomical Society.
dc.titleAnalytical solutions of fractional diffusion-advection equation for solar cosmic-ray transport
dc.typeJournal Article
pubs.begin-page125en_NZ
pubs.elements-id117875
pubs.end-page125en_NZ
pubs.issue2
pubs.organisational-group/Waikato
pubs.organisational-group/Waikato/FCMS
pubs.organisational-group/Waikato/FCMS/Mathematics
pubs.volume796
uow.identifier.article-no125en_NZ
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