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-tau show scaling behavior in the range of scales from 16 hours to 21 days for -10 less-than-or-equal-to q less-than-or-equal-to 10, i.e., [B-tau-q] approximately tau-s(q) in this range. s(q) is approximately a quadratic function of q for -4 less-than-or-equal-to q less-than-or-equal-to 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(q)(q) = 1 + s(q)/(q - 1) has the form that is characteristic of multifractals. For a multifractal magnetic field, the moments of the field should scale as tau-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(q)(q) is approximately a fourth order polynomial for -10 less-than-or-equal-to q less-than-or-equal-to 10, and positive values of f(alpha) occur for 0.8 less-than-or-equal-to alpha less-than-or-equal-to 1.2. The multifractal character of the magnetic field strength fluctuations generalizes the 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 clusters of strong disturbed fields with considerable fine structure on various scales. The multifractal description of the magnetic field suggests several problems for future study.