Abstract
Understanding plasma turbulence below the ion characteristic scales is one of the key open problems of solar wind physics. The bulk of our knowledge about the nature of the kinetic-scale fluctuations comes from the high-cadence measurements of the magnetic field. The spacecraft frame frequencies of the sub-ion scale fluctuations are frequently around the Nyquist frequencies of the magnetic field sampling rate. Thus, the resulting ‘measured’ time series may significantly differ from the ‘true’ ones. It follows that second-order moments (e.g., power spectral density, PSD) of the signal may also be highly affected in both their amplitude and their slope. In this paper, we focus on the estimation of the PSD slope for finitely sampled data and we unambiguously define a so-called local slope in the framework of Continuous Wavelet Transform. Employing Monte Carlo simulations, we derive an empirical formula that assesses the statistical error of the local slope estimation. We illustrate the theoretical results by analyzing measurements of the magnetic field instrument (MFI) on board the Wind spacecraft. Our analysis shows that the trace power spectra of magnetic field measurements of MFI can be modeled as the sum of PSD of an uncorrelated noise and an intrinsic signal. We show that the local slope strongly depends on the signal-to-noise (S/N) ratio, stressing that noise can significantly affect the slope even for S/N around 10. Furthermore, we show that the local slopes below the frequency corresponding to proton inertial length, 5≳kλpi>1, depend on the level of the magnetic field fluctuations in the inertial range (Pin), exhibiting a gradual flattening from about −11/3 for high Pin toward about −8/3 for low Pin.
Highlights
The importance of studying the kinetic/dissipation range of solar wind turbulence has been widely agreed upon
We show that the analysis of large statistical sample of empirically estimated local slopes can provide a physically sound insight into the inertial and kinetic range physics
The aim of our study is twofold: (1) we introduce a new way of analyzing the slope of the power spectrum of a physical quantity through the unambiguously defined local slope; and (2) we quantify the effect of an additive noise on the local slope of the spectrum
Summary
The importance of studying the kinetic/dissipation range of solar wind turbulence has been widely agreed upon. Processes that occur within this range play a crucial role in dissipating the energy in the turbulent fluctuations. Unlike in the case of hydrodynamic turbulence, where the dissipation of turbulent eddies is independent on the large-scale driving and the dissipation range has a universal shape, a similar universality is yet to be proven in magnetized turbulent plasmas. Magnetohydrodynamic (MHD) turbulence and the nonlinear phenomena that operate within the so-called inertial range are not entirely understood. Open issues include the presence of residual energy [5,6], the interplay between the slab and 2D populations of turbulent fluctuations [7,8,9], the parametric instability decay of large-scale high-amplitude
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