Multifractal structure of the interplanetary magnetic field: Voyager 2 observations near 25 AU, 1987‐1988

This paper analyzes the large-scale fluctuations of the interplanetary magnetic field strength observed by Voyager 2 from 23.3 AU to 27.8 AU during the period from day 190, 1987 to day 345, 1988. The q-th moments of B{sub {tau}} show scaling behavior in the range of scales from 16 hours to 21 days for {minus}10 {le} q {le} 10, i.e., {approximately} {tau}{sup s(q)} in this range. s(q) is approximately a quadratic function of q for {minus}4 {le} q {le} 4, as one expects for a distribution that is approximately lognormal, but the higher moments diverge from those of a lognormal distribution. The function D{sub q}(q) = 1 + s(q)/(q {minus} 1) has the form that is characteristic of multifractals. For a multifractal magnetic field, the moments of the field should scale as {tau}{sup {alpha}} on a set with fractal dimension f({alpha}), where {alpha} has a continuum of values over some limited range. For the large-scale magnetic field fluctuations, the function f({alpha}) computed from D{sub q}(q) is approximately a fourth order polynomial for {minus}10 {le} q {le} 10, and positive values of f({alpha}) occur for 0.8 {le} {alpha} {le} 1.2. The multifractional character of the magnetic field strength fluctuations generalizes themore » concept that the magnetic field is organized into interaction regions (regions in which the magnetic field strength and pressure are higher than average for several hours) and rarefaction regions (regions in which the magnetic field strength and pressure are lower than average). Near solar maximum the interaction regions in the distant heliosphere might be viewed as cluster of strong disturbed fields with considerable fine structure on various scales.« less

[1]  Mixing, entrainment and fractal dimensions of surfaces in turbulent flows , 1989 .

[2]  G. P. Gupta,et al.  Effect of a parallel electric field on thermal damping of whistler waves , 1979 .

[3]  H. Stanley,et al.  Multifractal phenomena in physics and chemistry , 1988, Nature.

[4]  L. Burlaga,et al.  Fractal structure of the interplanetary magnetic field , 1986 .

[5]  Pietronero,et al.  Self-similarity of fluctuations in random multiplicative processes. , 1986, Physical review letters.

[6]  K. Sreenivasan,et al.  Singularities of the equations of fluid motion. , 1988, Physical review. A, General physics.

[7]  L. Burlaga,et al.  Intense interplanetary magnetic fields observed by geocentric spacecraft during 1963–1975 , 1979 .

[8]  C. Meneveau,et al.  The fractal geometry of interfaces and the multifractal distribution of dissipation in fully turbulent flows , 1989 .

[9]  W. H. Mish,et al.  Large-scale fluctuations in the interplanetary medium , 1987 .

[10]  Benoit B. Mandelbrot,et al.  Multifractal measures, especially for the geophysicist , 1989 .

[11]  A. Vulpiani,et al.  Anomalous scaling laws in multifractal objects , 1987 .

[12]  Antonio Coniglio.  Multifractal structure of clusters and growing aggregates , 1986 .

[13]  B. Mandelbrot.  Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier , 1974, Journal of Fluid Mechanics.

[14]  Jensen,et al.  Erratum: Fractal measures and their singularities: The characterization of strange sets , 1986, Physical review. A, General physics.

[15]  D. Schertzer,et al.  Nonlinear Variability in Geophysics: Multifractal Simulations and Analysis , 1989 .

[16]  T. Tél.  Fractals, Multifractals, and Thermodynamics , 1988 .

[17]  H. G. E. Hentschel,et al.  The infinite number of generalized dimensions of fractals and strange attractors , 1983 .

[18]  L. Burlaga,et al.  Large-scale fluctuations between 13 AU and 25 AU and their effects on cosmic rays , 1987 .

[19]  C. Meneveau,et al.  Simple multifractal cascade model for fully developed turbulence. , 1987, Physical review letters.

[20]  B. Mandelbrot.  Possible refinement of the lognormal hypothesis concerning the distribution of energy dissipation in intermittent turbulence , 1972 .

[21]  L. Burlaga.  Intermittent turbulence in the solar wind , 1991 .