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Abstract We present a broad review of$$1/f$$ $1/f$noise observations in the heliosphere, and discuss and complement the theoretical background of generic$$1/f$$ $1/f$models as relevant to NASA’s Polarimeter to UNify the Corona and Heliosphere (PUNCH) mission. First observed in the voltage fluctuations of vacuum tubes, the scale-invariant$$1/f$$ $1/f$spectrum has since been identified across a wide array of natural and artificial systems, including heart rate fluctuations and loudness patterns in musical compositions. In the solar wind the interplanetary magnetic field trace spectrum exhibits$$1/f$$ $1/f$scaling within the frequency range from around$$\unit[2 \times 10^{-6}]{Hz}$$to around$$\unit[10^{-3}]{{Hz}}$$at 1 au. One compelling mechanism for the generation of$$1/f$$ $1/f$noise is the superposition principle, where a composite$$1/f$$ $1/f$spectrum arises from the superposition of a collection of individual power-law spectra characterized by a scale-invariant distribution of correlation times. In the context of the solar wind, such a superposition could originate from scale-invariant reconnection processes in the corona. Further observations have detected$$1/f$$ $1/f$signatures in the photosphere and corona at frequency ranges compatible with those observed at 1 au, suggesting an even lower altitude origin of$$1/f$$ $1/f$spectrum in the solar dynamo itself. This hypothesis is bolstered by dynamo experiments and simulations that indicate inverse cascade activities, which can be linked to successive flux tube reconnections beneath the corona, and are known to generate$$1/f$$ $1/f$noise possibly through nonlocal interactions at the largest scales. Conversely, models positing in situ generation of$$1/f$$ $1/f$signals face causality issues in explaining the low-frequency portion of the$$1/f$$ $1/f$spectrum. Understanding$$1/f$$ $1/f$noise in the solar wind may inform central problems in heliospheric physics, such as the solar dynamo, coronal heating, the origin of the solar wind, and the nature of interplanetary turbulence. 

Abstract A well-known property of solar wind plasma turbulence is the observed anisotropy of the autocorrelations, or equivalently the spectra, of velocity and magnetic field fluctuations. Here we explore the related but apparently not well-studied issue of the anisotropy of plasma density fluctuations in the energy-containing and inertial ranges of solar wind turbulence. Using 10 yr (1998–2008) of in situ data from the Advanced Composition Explorer mission, we find that for all but the fastest wind category, the density correlation scale is slightly larger in directions quasi-parallel to the large-scale mean magnetic field as compared to quasi-perpendicular directions. The correlation scale in fast wind is consistent with isotropic. The anisotropy as a function of the level of correlation is also explored. We find at small correlation levels, i.e., at energy-containing scales and larger, the density fluctuations are close to isotropy for fast wind, and slightly favor more rapid decorrelation in perpendicular directions for slow and medium winds. At relatively smaller (inertial range) scales where the correlation values are larger, the sense of anisotropy is reversed in all speed ranges, implying a more “slablike” structure, especially prominent in the fast wind samples. We contrast this finding with published results on velocity and magnetic field correlations. 

Abstract Exact laws for evaluating cascade rates, tracing back to the Kolmogorov “4/5” law, have been extended to many systems of interest including magnetohydrodynamics (MHD), and compressible flows of the magnetofluid and ordinary fluid types. It is understood that implementations may be limited by the quantity of available data and by the lack of turbulence symmetry. Assessment of the accuracy and feasibility of such third-order (or Yaglom) relations is most effectively accomplished by examining the von Kármán–Howarth equation in increment form, a framework from which the third-order laws are derived as asymptotic approximations. Using this approach, we examine the context of third-order laws for incompressible MHD in some detail. The simplest versions rely on the assumption of isotropy and the presence of a well-defined inertial range, while related procedures generalize the same idea to arbitrary rotational symmetries. Conditions for obtaining correct and accurate values of the dissipation rate from these laws based on several sampling and fitting strategies are investigated using results from simulations. The questions we address are of particular relevance to sampling of solar wind turbulence by one or more spacecraft. 

Unlike the vast majority of astrophysical plasmas, the solar wind is accessible to spacecraft, which for decades have carried in-situ instruments for directly measuring its particles and fields. Though such measurements provide precise and detailed information, a single spacecraft on its own cannot disentangle spatial and temporal fluctuations. Even a modest constellation of in-situ spacecraft, though capable of characterizing fluctuations at one or more scales, cannot fully determine the plasma’s 3-D structure. We describe here a concept for a new mission, the Magnetic Topology Reconstruction Explorer (MagneToRE), that would comprise a large constellation of in-situ spacecraft and would, for the first time, enable 3-D maps to be reconstructed of the solar wind’s dynamic magnetic structure. Each of these nanosatellites would be based on the CubeSat form-factor and carry a compact fluxgate magnetometer. A larger spacecraft would deploy these smaller ones and also serve as their telemetry link to the ground and as a host for ancillary scientific instruments. Such an ambitious mission would be feasible under typical funding constraints thanks to advances in the miniaturization of spacecraft and instruments and breakthroughs in data science and machine learning. 

This white paper is on the HMCS Firefly mission concept study. Firefly focuses on the global structure and dynamics of the Sun's interior, the generation of solar magnetic fields, the deciphering of the solar cycle, the conditions leading to the explosive activity, and the structure and dynamics of the corona as it drives the heliosphere.