Fractal structures and power law spectra in the distant Earth's magnetotail

Abstract

This paper is aimed at the theoretical understanding of the results obtained from the survey of plasmas and magnetic fields in the Earth's distant magnetotail with the Geotail spacecraft. Our attention is concentrated on the “kink” power law spectrum of magnetic field fluctuations proposed by Hoshino et al. [1994] from an analysis of the Geotail data. In the framework of the present study, we discuss a self‐consistent theoretical model describing the magnetic field structures in the distant tail with the use of the basic concepts of fractal geometry. It is shown that the statistically significant number of the excited tearing modes in the Earth's distant magnetotail could be responsible for the development of self‐similar, fractal magnetic structures in the range of spatial scales between ∼ 4 × 102 km and ∼ 8 × 103 km. This actually leads to the existence of two kinks in the power spectrum, one around the turnover frequency ƒ* ≈ 0.03 Hz, in good agreement with the results by Hoshino et al. [1994], the other close to the turnover frequency ƒ** ≈ 0.5 Hz, beyond the Nyquist frequency in the relevant Geotail magnetic field data. The possible behavior of the power spectra of the magnetic fluctuations in a wide range of frequencies is discussed.