Solar Wind Heating as a Non-Markovian Process: Lévy Flight, Fractional Calculus, and κ -functions

Details Solar Wind Heating as a Non-Markovian Process: Lévy Flight, Fractional Calculus, and κ -functions Solar Wind Heating as a Non-Markovian Process: Lévy Flight, Fractional Calculus, and κ -functions

May 2001

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2001agusm..sh22e09s&link_type=abstract

American Geophysical Union, Spring Meeting 2001, abstract #SH22E-09

Statistics

Computation

2164 Solar Wind Plasma, 2169 Sources Of The Solar Wind, 7219 Nuclear Explosion Seismology

Scientific paper

Many space and laboratory plasmas are found to possess non-Maxwellian distribution functions. An empirical function promoted by Stan Olbert, which superposes a Maxwellian core with a power-law tail, has been found to emulate many of the plasma distributions discovered in space. These κ -functions, with their associated power-law tail induced anomalous heat flux, have been used by theorists1\ as the origin of solar coronal heating of solar wind. However, the principle and prerequisite for the robust production of such a non-equilibrium distribution has rarely been explained. We report on recent statistical work2, which shows that the κ -function is one of a general class of solutions to a time-fractional diffusion equation, known as a Lévy stable probability distribution. These solutions arise from time-variable probability distribution (or equivalently, a spatially variable probability in a flowing medium), which demonstrate that anomalously high flux, or equivalently, non-equilibrium thermodynamics govern the outflowing solar wind plasma. We will characterize the parameters that control the degree of deviation from a Maxwellian and attempt to draw physical meaning from the mathematical formalism. 1Scudder, J. Astrophys. J., 1992.\2Mainardi, F. and R. Gorenflo, J. Computational and Appl. Mathematics, Vol. 118, No 1-2, 283-299 (2000).

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