The solar-cycle dependence of the heliospheric diffusion tensor

Abstract

Long-term cosmic-ray modulation studies using ab initio numerical modulation models require an understanding of the solar-cycle dependence of the heliospheric diffusion tensor. Such an understanding requires information as to possible solar-cycle dependences of various basic turbulence quantities. In this study, 1-minute resolution data for the N-component of the heliospheric magnetic field spanning from 1974 to 2012 is analysed using second-order structure functions constructed assuming a simple three-stage power-law frequency spectrum. This spectrum is motivated observationally and theoretically, and has an inertial, an energycontaining and a cutoff-range at small frequencies to ensure a finite energy density. Of the turbulence quantities calculated from 27-day averaged second-order structure functions, only the magnetic variance and the spectral level show a significant solar-cycle dependence, much less so the spectral index in the energy range. The spectral indices in the inertial range, as well as the turnover and cutoff scales do not appear to depend on the level of solar activity. The ratio of the variance to the square of the magnetic field also appears to be solar-cycle independent. These results suggest that the dominant change in the spectrum over several solar-cycles is its level. Comparisons of the results found in this study with relevant published observations of turbulence quantities are very favourable. Furthermore, when the magnetic variances and heliospheric magnetic magnitudes calculated in this study are used as inputs for theoretically motivated expressions for the mean free paths and turbulence-reduced drift length scale, clear solar-cycle dependencies in these quantities are seen. Values for the diffusion and drift length scales during the recent unusual solar minimum are found to be significantly higher than during previous solar minima.