Effect of intermittent structures on the spectral index of the magnetic field in the slow solar wind

Intermittent structures are ubiquitous in the solar wind turbulence, and they can significantly affect the power spectral index (which reflects the cascading process of the turbulence) of magnetic field fluctuations. However, to date, an analytical relationship between the intermittency level and the magnetic spectral index has not been shown. Here, we present the continuous variation in the magnetic spectral index in the inertial range as a function of the intermittency level. Using the measurements from the Wind spacecraft, we find 42 272 intervals with different levels of intermittency and with a duration of 5–6 min from 46 slow-wind streams between 2005 and 2013. Among them, each of the intermittent intervals is composed of one dominant intermittent structure and background turbulent fluctuations. For each interval, a magnetic spectral index inline-formulaα_B is determined for the Fourier spectrum of the magnetic field fluctuations in the inertial range between 0.01 and 0.3 Hz. A parameter inline-formulaI_max, which corresponds to the maximum of the trace of the partial variance increments of the intermittent structure, is introduced as an indicator of the intermittency level. Our statistical result shows that, as inline-formulaI_max increases from 0 to 20, the magnetic spectrum becomes gradually steeper and the magnetic spectral index inline-formulaα_B decreases from inline-formula−1.63 to inline-formula−2.01. Accordingly, for the first time, an empirical relation is established between inline-formulaα_B and inline-formulaI_max: inline-formula $M9inlinescrollmathml{\mathrm{italic\; \alpha }}_B=\mathrm{normal\; 0.4}\exp (-I_{\mathrm{normal\; max}}/\mathrm{normal\; 5})-\mathrm{normal\; 2.02}$ 140pt14ptsvg-formulamathimg0abea92eac561542d1490d8f03fca92b angeo-41-129-2023-ie00001.svg140pt14ptangeo-41-129-2023-ie00001.png . The result will help us to uncover more details about the contributions of the intermittent structures to the magnetic power spectra and, furthermore, about the physical nature of the energy cascade taking place in the solar wind. It will also help to improve turbulence theories that contain intermittent structures.