A Novel Method for Estimating the Intrinsic Magnetic Field Spectrum of Kinetic-Range Turbulence

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.

Evolution of Magnetic Field Fluctuations and Their Spectral Properties within the Heliosphere: Statistical Approach

“…The median spectra show a steepening of the spectral slope near the ion spectral break (further called the kinetic range) toward the Sun. However, this evolution cannot be quantified from the median spectra because the slope can be affected by the magnetometer noise at larger distances (Pitňa et al 2021) and the part of the spectrum following the break is too short for a reliable fitting closer to the Sun. Therefore, we use the local slope determined from a full magnetic field vector which is calculated as follows.…”

Properties of Hall-MHD Turbulence at Sub-Ion Scales: Spectral Transfer Analysis

“…This scenario could be easily tested in spacecraft observations. Indeed, the fact that the solar wind often shows high levels of intermittency is likely the reason why the −7/3 slope is rarely observed [24,61]. Finally, multispacecraft observations (that allow direct measurement of the Hall energy transfer rate, e.g., [62]) of the pristine Hall-MHD regime would be the ideal test to confirm our findings.…”

“…In such range, the −7/3 slope is very stable in time, and lasts up to the end of the simulation, also in the decaying phase and for more than 4τ nl . Such slope is predicted by theoretical models of Hall-MHD turbulence, but it is rarely measured in spacecraft observations [22][23][24] and it has been only reported in early numerical studies of turbulence, e.g., [20,21].…”

“…Early theoretical and numerical studies [7,8,[18][19][20] had predicted and/or measured a steepening of the power spectrum to a spectral index of −7/3, caused by either the onset of Hall physics or by the change in the wave-like nature of the nonlinear interactions (e.g., kinetic Alfvén waves) that mediate the turbulent energy cascade. Although such slope has been measured in early 3D Hall-MHD numerical simulations, e.g., [21], it was rarely observed by spacecraft [22][23][24]. Instead, a steeper slope with an average value around −2.8 or −3 is routinely reported, e.g., [25,26], as well as in later numerical studies [4,13,14,16,[27][28][29][30].…”

Change of Spectral Properties of Magnetic Field Fluctuations across Different Types of Interplanetary Shocks

“…where f is the frequency, c 1 and c 2 are parameters of the fit, α in corresponds to the inertial range spectral index, a tr does to the transition range, and H is the Heaviside function. In order to avoid noise effect on the analysis of magnetic field fluctuations, we follow the methodology suggested by Pitňa et al (2021b), which introduces a noise level estimated by Woodham et al (2018), and we multiply the noise floor by a factor of 5 (SNR5) as shown in Figures 2(a)-(d) (dashed-dotted green lines). This fitting method is applied in a frequency range from 0.03 to 3 Hz or to the frequency where the PSD level is equal to SNR5 if it is lower than 3 Hz.…”