The Correlation Length of Turbulence in Magnetic Clouds

TL;DR

The study tackles the challenge of measuring the turbulence outer scale in magnetic clouds by removing the large-scale flux-rope trend from magnetic-field time series observed by the Parker Solar Probe. It employs force-free flux rope fits (Lundquist for Cloud 1 and Gold-Hoyle for Cloud 2) to detrend the data and compute the turbulence correlation length from rope-subtracted fluctuations, revealing significantly shorter lengths than un-detrended analyses. The results show an inertial-range turbulence spectrum near $P(k)\propto k^{-5/3}$ after detrending, while the flux rope contributes a $k^{-3}$ component at large scales, highlighting the importance of proper detrending to isolate turbulent dynamics. The work discusses the implications for understanding mesoscale structure in ICMEs and for future measurements at different heliocentric distances, including potential applications to space-weather monitoring strategies.

Abstract

The large-scale limit or outer scale of turbulence in the solar wind is associated with the correlation length of the magnetic field. Determining correlation lengths from magnetic field time series in magnetic clouds is complicated by the presence of the global flux rope: without removal of the flux rope trend, correlation length measurements will be sensitive to the flux rope as well as the turbulence, and give overestimates of the outer scale when turbulence amplitudes at the outer scale are small relative to the flux rope amplitude. We have used force-free flux rope fits to detrend magnetic field time series measured by Parker Solar Probe in two magnetic clouds and calculated the turbulence correlation length in the clouds using the detrended data. The detrended correlation length in terms of the proton inertial length, $d_p$, was $2.7\times10^{4} d_p$ in one cloud (observed at 0.77 au) and $1.6\times10^{4}d_p$ in the other (observed at 0.39 au), significantly smaller than the values obtained without detrending. Increments in the flux rope fits scaled equivalently to a $k^{-3}$ wavenumber power spectrum; this contribution from the flux rope considerably steepened the total spectrum at the largest scales but had a negligible effect in the inertial range, where scaling in both clouds equivalent to $\sim$$k^{-5/3}$ was observed. Finally, we discuss the possible relation of turbulence correlation lengths to mesoscale structure in magnetic clouds.

Figures (5)

• Figure 1: Magnetic cloud observations made by PSP in June 2021 at 0.77 au (left-hand panels) and March 2019 at 0.39 au (right-hand panels). The cloud intervals are bounded by vertical lines. From top to bottom, the panels show the magnetic field magnitude and components in RTN coordinates, the latitude angle, $\theta$, of the magnetic field vector relative to the $R$-$T$ plane, and longitude angle, $\phi$, between the $R$ direction and the projection of the magnetic field vector onto the $R$-$T$ plane. Smooth lines show flux rope fits to the data.
• Figure 2: Autocorrelation curves as functions of time lag for the mean-subtracted magnetic field (grey curves), fit-subtracted magnetic field (black curves) and mean-subtracted flux-rope fit (gold curves) in each magnetic cloud. The grey curves are sensitive to the rotation of the flux rope field and to small-scale turbulent fluctuations, while the black curves are sensitive to the turbulence only. The $1/e$ correlation times in the mean-subtracted fields, $\tau_c$, and fit-subtracted fields, $\tau'_c$, are marked by vertical dashed lines.
• Figure 3: PDFs of magnetic field fluctuation amplitudes normalised to the local mean field magnitude as functions of fluctuation timescale. Top and bottom panels show distributions obtained with the total and rope-subtracted field, respectively.
• Figure 4: Mean values of the PDFs in Figure \ref{['fig:distributions']} as functions of fluctuation timescale for the total field (grey lines) and rope-subtracted field (black lines). Also shown are the mean values of the equivalent PDFs calculated from the fitted flux rope fields (gold lines). Vertical dashed grey lines mark the rope-subtracted correlation timescales, $\tau'_c$, obtained from the autocorrelation curves shown in Figure \ref{['fig:correlations']}.
• Figure 5: Scaling of mean normalised increments in the Gold-Hoyle rope fit made to cloud 2 with the addition of $1/f$ noise at different amplitudes.