Tsallis distributions of magnetic field strength variations in the heliosphere:: 5 to 90 AU

[1] The Tsallis (q-exponential) distribution function, derived from the entropy principle of nonextensive statistical mechanics, describes fluctuations in the magnetic field strength on many scales throughout the heliosphere. This paper shows that a one-dimensional multifluid magnetohydrodynamic (MHD) model, with Advanced Composition Explorer (ACE) observations at 1 AU as input, predicts Tsallis distributions between 5 and 90 AU on scales from 1 to 128 days. At a scale of 1 day, the radial variation of the entropic index q decreases from q >= 5/ 3 at R <= 50 AU to q <= 5/ 3 at R >= 60 AU, corresponding to a change from a divergent to a convergent second moment of the Tsallis distribution, suggesting the possibility of a phase transition'' and/or a relaxation effect at approximate to 60 AU. The Tsallis distribution derived from the time series of one-dimensional MHD model is nearly identical to those observed by Voyager 1 at similar to 80 AU over the scales from 1 to 64 days during the year 2000. The Tsallis distribution appears over a wide range of scales and distances despite the complex nonlinear dynamical evolution of the heliospheric magnetic field during 1999/2000.