The multi-scale nature of the solar wind

The solar wind is a magnetized plasma and as such exhibits collective plasma behavior associated with its characteristic spatial and temporal scales. The characteristic length scales include the size of the heliosphere, the collisional mean free paths of all species, their inertial lengths, their gyration radii, and their Debye lengths. The characteristic timescales include the expansion time, the collision times, and the periods associated with gyration, waves, and oscillations. We review the past and present research into the multi-scale nature of the solar wind based on in-situ spacecraft measurements and plasma theory. We emphasize that couplings of processes across scales are important for the global dynamics and thermodynamics of the solar wind. We describe methods to measure in-situ properties of particles and fields. We then discuss the role of expansion effects, non-equilibrium distribution functions, collisions, waves, turbulence, and kinetic microinstabilities for the multi-scale plasma evolution.Comment: 155 pages, 24 figure

Nature of stochastic ion heating in the solar wind: testing the dependence on plasma beta and turbulence amplitude

The solar wind undergoes significant heating as it propagates away from the Sun; the exact mechanisms responsible for this heating are not yet fully understood. We present for the first time a statistical test for one of the proposed mechanisms, stochastic ion heating. We use the amplitude of magnetic field fluctuations near the proton gyroscale as a proxy for the ratio of gyroscale velocity fluctuations to perpendicular (with respect to the magnetic field) proton thermal speed, defined as $\epsilon_p$. Enhanced proton temperatures are observed when $\epsilon_p$ is larger than a critical value ($\sim 0.019 - 0.025$). This enhancement strongly depends on the proton plasma beta ($\beta_{||p}$); when $\beta_{||p} \ll 1$ only the perpendicular proton temperature $T_{\perp}$ increases, while for $\beta_{||p} \sim 1$ increased parallel and perpendicular proton temperatures are both observed. For $\epsilon_p$ smaller than the critical value and $\beta_{||p} \ll 1$ no enhancement of $T_p$ is observed while for $\beta_{||p} \sim 1$ minor increases in $T_{\parallel}$ are measured. The observed change of proton temperatures across a critical threshold for velocity fluctuations is in agreement with the stochastic ion heating model of Chandran et al. (2010). We find that $\epsilon_p > \epsilon_{\rm crit}$ in 76\% of the studied periods implying that stochastic heating may operate most of the time in the solar wind at 1 AU.Comment: Accepted for publication in The Astrophysical Journal Letter

Data-Driven Uncertainty Quantification of the Wave-Telescope Technique: General Equations and Application to HelioSwarm

The upcoming NASA mission HelioSwarm will use nine spacecraft to make the first simultaneous multi-point measurements of space plasmas spanning multiple scales. Using the wave-telescope technique, HelioSwarm's measurements will allow for both the calculation of the power in wavevector-and-frequency space and the characterization of the associated dispersion relations of waves present in the plasma at MHD and ion-kinetic scales. This technique has been applied to the four-spacecraft missions of CLUSTER and MMS and its effectiveness has previously been characterized in a handful of case studies. We expand this uncertainty quantification analysis to arbitrary configurations of four through nine spacecraft for three-dimensional plane waves. We use Bayesian inference to learn equations that approximate the error in reconstructing the wavevector as a function of relative wavevector magnitude, spacecraft configuration shape, and number of spacecraft. We demonstrate the application of these equations to data drawn from a nine-spacecraft configuration to both improve the accuracy of the technique, as well as expand the magnitudes of wavevectors that can be characterized.Comment: 20 pages, 13 figures, 3 table

Magnetic Reconnection May Control the Ion-Scale Spectral Break of Solar Wind Turbulence

The power spectral density of magnetic fluctuations in the solar wind exhibits several power-law-like frequency ranges with a well defined break between approximately 0.1 and 1 Hz in the spacecraft frame. The exact dependence of this break scale on solar wind parameters has been extensively studied but is not yet fully understood. Recent studies have suggested that reconnection may induce a break in the spectrum at a "disruption scale" $\lambda_D$, which may be larger than the fundamental ion kinetic scales, producing an unusually steep spectrum just below the break. We present a statistical investigation of the dependence of the break scale on the proton gyroradius $\rho_i$, ion inertial length $d_i$, ion sound radius $\rho_s$, proton-cyclotron resonance scale $\rho_c$ and disruption scale $\lambda_D$ as a function of $\beta_{\perp i}$. We find that the steepest spectral indices of the dissipation range occur when $\beta_e$ is in the range of 0.1-1 and the break scale is only slightly larger than the ion sound scale (a situation occurring 41% of the time at 1 AU), in qualitative agreement with the reconnection model. In this range the break scale shows remarkably good correlation with $\lambda_D$. Our findings suggest that, at least at low $\beta_e$, reconnection may play an important role in the development of the dissipation range turbulent cascade and causes unusually steep (steeper than -3) spectral indices.Comment: Accepted in ApJ

Collisionless Isotropization of the Solar-Wind Protons by Compressive Fluctuations and Plasma Instabilities

Compressive fluctuations are a minor yet significant component of astrophysical plasma turbulence. In the solar wind, long-wavelength compressive slow-mode fluctuations lead to changes in $\beta_{\parallel \mathrm p}\equiv 8\pi n_{\mathrm p}k_{\mathrm B}T_{\parallel \mathrm p}/B^2$ and in $R_{\mathrm p}\equiv T_{\perp \mathrm p}/T_{\parallel \mathrm p}$, where $T_{\perp \mathrm p}$ and $T_{\parallel \mathrm p}$ are the perpendicular and parallel temperatures of the protons, $B$ is the magnetic field strength, and $n_{\mathrm p}$ is the proton density. If the amplitude of the compressive fluctuations is large enough, $R_{\mathrm p}$ crosses one or more instability thresholds for anisotropy-driven microinstabilities. The enhanced field fluctuations from these microinstabilities scatter the protons so as to reduce the anisotropy of the pressure tensor. We propose that this scattering drives the average value of $R_{\mathrm p}$ away from the marginal stability boundary until the fluctuating value of $R_{\mathrm p}$ stops crossing the boundary. We model this "fluctuating-anisotropy effect" using linear Vlasov--Maxwell theory to describe the large-scale compressive fluctuations. We argue that this effect can explain why, in the nearly collisionless solar wind, the average value of $R_{\mathrm p}$ is close to unity.Comment: 11 pages, published in Ap