Statistics
Scientific paper
Sep 1981
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981jgr....86.7498b&link_type=abstract
Journal of Geophysical Research, vol. 86, Sept. 1, 1981, p. 7498-7506.
Statistics
42
Interplanetary Magnetic Fields, Magnetohydrodynamic Stability, Solar Wind, Stochastic Processes, Variance (Statistics), Fluctuation Theory, Fokker-Planck Equation, Mathematical Models, Plasma Dynamics
Scientific paper
The concept of minimum variance is investigated for nonplanar interplanetary Alfvenic fluctuations in which the field direction varies randomly. The theory of the random wandering of a vector of constant length is developed as a representation of the magnetic field, and it is found that the minimum variance tends to coincide with the mean field directions over the correlation time of the fluctuations. The Fokker-Planck limit of the theory is then developed and used to analyze the statistic distribution of field directions with and without a reflecting barrier. Results suggest that the tendency of the Alfvenic fluctuations to have a direction of minimum variance statistically aligned with the mean magnetic field may be purely a consequence of the randomness of the fluctuation and not imply that the fluctuations are necessarily plane waves. Extensive statistical studies of the observed directional variations of the interplanetary magnetic field are necessary to test this hypothesis.
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