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In this Letter we investigate the dependency with scale of the empirical probability distribution functions (PDF) of Elsasser increments using large sets ofWINDdata (collected between 1995 and 2017) near 1 au. The empirical PDF are compared to the ones obtained from high-resolution numerical simulations of steadily driven, homogeneous reduced MHD turbulence on a 2048³rectangular mesh. A large statistical sample of Alfvénic increments is obtained by using conditional analysis based on the solar wind average properties. The PDF tails obtained from observations and numerical simulations are found to have exponential behavior in the inertial range, with an exponential decrement that satisfies power laws of the formα_l∝l^−μ, wherelis the scale size, withμbetween 0.17 and 0.25 for observations and 0.43 for simulations. PDF tails were extrapolated assuming their exponential behavior extends to arbitrarily large increments in order to determine structure function scaling laws at very high orders. Our results point to potentially universal scaling laws governing the PDF of Elsasser increments and to an alternative approach to investigate high-order statistics in solar wind observations.

 

Abstract In this Letter, we report observations of magnetic switchback (SB) features near 1 au using data from the Wind spacecraft. These features appear to be strikingly similar to the ones observed by the Parker Solar Probe mission closer to the Sun: namely, one-sided spikes (or enhancements) in the solar-wind bulk speed V that correlate/anticorrelate with the spikes seen in the radial-field component B R . In the solar-wind streams that we analyzed, these specific SB features near 1 au are associated with large-amplitude Alfvénic oscillations that propagate outward from the Sun along a local background (prevalent) magnetic field B 0 that is nearly radial. We also show that, when B 0 is nearly perpendicular to the radial direction, the large-amplitude Alfvénic oscillations display variations in V that are two sided (i.e., V alternately increases and decreases depending on the vector Δ B = B − B 0 ). As a consequence, SBs may not always appear as one-sided spikes in V , especially at larger heliocentric distances where the local background field statistically departs from the radial direction. We suggest that SBs can be well described by large-amplitude Alfvénic fluctuations if the field rotation is computed with respect to a well-determined local background field that, in some cases, may deviate from the large-scale Parker field. 

The fourth orbit of Parker Solar Probe (PSP) reached heliocentric distances down to 27.9 R ⊙ , allowing solar wind turbulence and acceleration mechanisms to be studied in situ closer to the Sun than previously possible. The turbulence properties were found to be significantly different in the inbound and outbound portions of PSP’s fourth solar encounter, which was likely due to the proximity to the heliospheric current sheet (HCS) in the outbound period. Near the HCS, in the streamer belt wind, the turbulence was found to have lower amplitudes, higher magnetic compressibility, a steeper magnetic field spectrum (with a spectral index close to –5/3 rather than –3/2), a lower Alfvénicity, and a ‘1∕ f ’ break at much lower frequencies. These are also features of slow wind at 1 au, suggesting the near-Sun streamer belt wind to be the prototypical slow solar wind. The transition in properties occurs at a predicted angular distance of ≈4° from the HCS, suggesting ≈8° as the full-width of the streamer belt wind at these distances. While the majority of the Alfvénic turbulence energy fluxes measured by PSP are consistent with those required for reflection-driven turbulence models of solar wind acceleration, the fluxes in the streamer belt are significantly lower than the model predictions, suggesting that additional mechanisms are necessary to explain the acceleration of the streamer belt solar wind. 

We investigate the validity of Taylor’s hypothesis (TH) in the analysis of velocity and magnetic field fluctuations in Alfvénic solar wind streams measured by Parker Solar Probe (PSP) during the first four encounters. The analysis is based on a recent model of the spacetime correlation of magnetohydrodynamic (MHD) turbulence, which has been validated in high-resolution numerical simulations of strong reduced MHD turbulence. We use PSP velocity and magnetic field measurements from 24 h intervals selected from each of the first four encounters. The applicability of TH is investigated by measuring the parameter ϵ  =  δu 0 /√2 V ⊥ , which quantifies the ratio between the typical speed of large-scale fluctuations, δu 0 , and the local perpendicular PSP speed in the solar wind frame, V ⊥ . TH is expected to be applicable for ϵ ≲ 0.5 when PSP is moving nearly perpendicular to the local magnetic field in the plasma frame, irrespective of the Alfvén Mach number M A = V SW ∕ V A , where V SW and V A are the local solar wind and Alfvén speed, respectively. For the four selected solar wind intervals, we find that between 10 and 60% of the time, the parameter ϵ is below 0.2 and the sampling angle (between the spacecraft velocity in the plasma frame and the local magnetic field) is greater than 30°. For angles above 30°, the sampling direction is sufficiently oblique to allow one to reconstruct the reduced energy spectrum E ( k ⊥ ) of magnetic fluctuations from its measured frequency spectra. The spectral indices determined from power-law fits of the measured frequency spectrum accurately represent the spectral indices associated with the underlying spatial spectrum of turbulent fluctuations in the plasma frame. Aside from a frequency broadening due to large-scale sweeping that requires careful consideration, the spatial spectrum can be recovered to obtain the distribution of fluctuation’s energy across scales in the plasma frame. 

A growing body of evidence suggests that the solar wind is powered to a large extent by an Alfvén-wave (AW) energy flux. AWs energize the solar wind via two mechanisms: heating and work. We use high-resolution direct numerical simulations of reflection-driven AW turbulence (RDAWT) in a fast-solar-wind stream emanating from a coronal hole to investigate both mechanisms. In particular, we compute the fraction of the AW power at the coronal base ( $P_\textrm {AWb}$ ) that is transferred to solar-wind particles via heating between the coronal base and heliocentric distance $r$ , which we denote by $\chi _{H}(r)$ , and the fraction that is transferred via work, which we denote by $\chi _{W}(r)$ . We find that $\chi _{W}(r_{A})$ ranges from 0.15 to 0.3, where $r_{A}$ is the Alfvén critical point. This value is small compared with one because the Alfvén speed $v_{A}$ exceeds the outflow velocity $U$ at $r < r_{A}$ , so the AWs race through the plasma without doing much work. At $r>r_{A}$ , where $v_{A} < U$ , the AWs are in an approximate sense ‘stuck to the plasma’, which helps them do pressure work as the plasma expands. However, much of the AW power has dissipated by the time the AWs reach $r=r_{A}$ , so the total rate at which AWs do work on the plasma at $r>r_{A}$ is a modest fraction of $P_\textrm {AWb}$ . We find that heating is more effective than work at $r < r_{A}$ , with $\chi _{H}(r_{A})$ ranging from 0.5 to 0.7. The reason that $\chi _{H} \geq 0.5$ in our simulations is that an appreciable fraction of the local AW power dissipates within each Alfvén-speed scale height in RDAWT, and there are a few Alfvén-speed scale heights between the coronal base and $r_{A}$ . A given amount of heating produces more magnetic moment in regions of weaker magnetic field. Thus, paradoxically, the average proton magnetic moment increases robustly with increasing $r$ at $r>r_{A}$ , even though the total rate at which AW energy is transferred to particles at $r>r_{A}$ is a small fraction of $P_\textrm {AWb}$ .