arXiv subjects

William H. Matthaeus

Publications and source records attributed to William H. Matthaeus.

At least 55 records · Page 3Linked to original sources

arXiv2022

Strategies for determining the cascade rate in MHD turbulence: isotropy, anisotropy, and spacecraft sampling

``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 Karman-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.

physics.space-ph↗

arXiv2022

Magnetic field intermittency in the solar wind: PSP and SolO observations ranging from the Alfven region out to 1 AU

$PSP$ and $SolO$ data are utilized to investigate magnetic field intermittency in the solar wind (SW). Small-scale intermittency $(20-100d_{i})$ is observed to radially strengthen when methods relying on higher-order moments are considered ($SF_q$, $SDK$), but no clear trend is observed at larger scales. However, lower-order moment-based methods (e.g., PVI) are deemed more appropriate for examining the evolution of the bulk of Coherent Structures (CSs), $PVI \ge 3$. Using PVI, we observe a scale-dependent evolution in the fraction of the dataset occupied by CSs, $f_{PVI \ge 3}$. Specifically, regardless of the SW speed, a subtle increase is found in $f_{PVI\ge3}$ for $\ell =20 d_i$, in contrast to a more pronounced radial increase in CSs observed at larger scales. Intermittency is investigated in relation to plasma parameters. Though, slower SW speed intervals exhibit higher $f_{PVI \geq 6}$ and higher kurtosis maxima, no statistical differences are observed for $f_{PVI \geq 3}$. Highly Alfvénic intervals, display lower levels of intermittency. The anisotropy with respect to the angle between the magnetic field and SW flow, $Θ_{VB}$ is investigated. Intermittency is weaker at $Θ_{VB} \approx 0^{\circ}$ and is strengthened at larger angles. Considering the evolution at a constant alignment angle, a weakening of intermittency is observed with increasing advection time of the SW. Our results indicate that the strengthening of intermittency in the inner heliosphere is driven by the increase in comparatively highly intermittent perpendicular intervals sampled by the probes with increasing distance, an effect related directly to the evolution of the Parker spiral.

astro-ph.SR↗

arXiv2022

Observations of Cross Scale Energy Transfer in the Inner Heliosphere by Parker Solar Probe

The solar wind, a continuous flow of plasma from the sun, not only shapes the near Earth space environment but also serves as a natural laboratory to study plasma turbulence in conditions that are not achievable in the lab. Starting with the Mariners, for more than five decades, multiple space missions have enabled in-depth studies of solar wind turbulence. Parker Solar Probe (PSP) was launched to explore the origins and evolution of the solar wind. With its state-of-the-art instrumentation and unprecedented close approaches to the sun, PSP is starting a new era of inner heliospheric exploration. In this review we discuss observations of turbulent energy flow across scales in the inner heliosphere as observed by PSP. After providing a quick theoretical overview and a quick recap of turbulence before PSP, we discuss in detail the observations of energy at various scales on its journey from the largest scales to the internal degrees of freedom of the plasma. We conclude with some open ended questions, many of which we hope that PSP will help answer.

physics.space-ph↗

arXiv2022

Isotropization and Evolution of Energy-Containing Eddies in Solar Wind Turbulence: Parker Solar Probe, Helios 1, ACE, WIND, and Voyager 1

We examine the radial evolution of correlation lengths perpendicular ($λ_C^{\perp}$) and parallel ($λ_C^{\parallel}$) to the magnetic-field direction, computed from solar wind magnetic-field data measured by Parker Solar Probe (PSP) during its first eight orbits, Helios 1, Advanced Composition Explorer (ACE), WIND, and Voyager 1 spacecraft. Correlation lengths are grouped by an interval's alignment angle; the angle between the magnetic-field and solar wind velocity vectors ($Θ_{\rm BV}$). Parallel and perpendicular angular channels correspond to angles $0^{\circ}~<~Θ_{\rm BV}~<~40^{\circ}$ and $50^{\circ}~<~Θ_{\rm BV}~<~90^{\circ}$, respectively. We observe an anisotropy in the inner heliosphere within 0.40~au, with $λ_C^{\parallel} / λ_C^{\perp} \approx 0.75$ at 0.10~au. This anisotropy reduces with increasing heliocentric distance and the correlation lengths roughly isotropize within 1~au. Results from ACE and WIND support a reversal of the anisotropy, such that $λ_C^{\parallel} /λ_C^{\perp} \approx 1.29$ at 1~au. The ratio does not appear to change significantly beyond 1~au, although the small number of parallel intervals in the Voyager dataset precludes unambiguous conclusions from being drawn. This study provides insights regarding the radial evolution of the large, most energetic interacting turbulent fluctuations in the heliosphere. We also emphasize the importance of tracking the changes in sampling direction in PSP measurements as the spacecraft approaches the Sun, when using these data to study the radial evolution of turbulence. This can prove to be vital in understanding the more complex dynamics of the solar wind in the inner heliosphere and can assist in improving related simulations.

astro-ph.SR↗

arXiv2022

Relativistic Particle Transport and Acceleration in Structured Plasma Turbulence

We discuss the phenomenon of energization of relativistic charged particles in three-dimensional (3D) incompressible MHD turbulence and the diffusive properties of the motion of the same particles. We show that the random electric field induced by turbulent plasma motion leads test particles moving in a simulated box to be accelerated in a stochastic way, a second-order Fermi process. A small fraction of these particles happen to be trapped in large-scale structures, most likely formed due to the interaction of islands in the turbulence. Such particles get accelerated exponentially, provided their pitch angle satisfies some conditions. We discuss at length the characterization of the accelerating structure and the physical processes responsible for rapid acceleration. We also comment on the applicability of the results to realistic astrophysical turbulence.

astro-ph.HE↗

arXiv2022

Magnetic Switchback Occurrence Rates in the Inner Heliosphere: Parker Solar Probe and 1 au

The subject of switchbacks, defined either as large angular deflections or polarity reversals of the magnetic field, has generated substantial interest in the space physics community since the launch of Parker Solar Probe (PSP) in 2018. Previous studies have characterized switchbacks in several different ways, and have been restricted to data available from the first few orbits. Here, we analyze the frequency of occurrence of switchbacks per unit distance for the first full eight orbits of PSP. In this work, are considered switchback only the events that reverse the sign of magnetic field relative to a regional average. A significant finding is that the rate of occurrence falls off sharply approaching the sun near 0.2 au (40 $R_\odot$), and rises gently from 0.2 au outward. The analysis is varied for different magnetic field cadences and for different local averages of the ambient field, confirming the robustness of the results. We discuss implications for the mechanisms of switchback generation. A publicly available database has been created with the identified reversals.

astro-ph.SR↗

arXiv2022

Pressure-Strain Interaction as the Energy Dissipation Estimate in Collisionless Plasma

The dissipative mechanism in weakly collisional plasma is a topic that pervades decades of studies without a consensus solution. We compare several energy dissipation estimates based on energy transfer processes in plasma turbulence and provide justification for the pressure-strain interaction as a direct estimate of the energy dissipation rate. The global and scale-by-scale energy balances are examined in 2.5D and 3D kinetic simulations. We show that the global internal energy increase and the temperature enhancement of each species are directly tracked by the pressure-strain interaction. The incompressive part of the pressure-strain interaction dominates over its compressive part in all simulations considered. The scale-by-scale energy balance is quantified by scale filtered Vlasov-Maxwell equations, a kinetic plasma approach, and the lag dependent von Kármán-Howarth equation, an approach based on fluid models. We find that the energy balance is exactly satisfied across all scales, but the lack of a well-defined inertial range influences the distribution of the energy budget among different terms in the inertial range. Therefore, the widespread use of the Yaglom relation to estimating dissipation rate is questionable in some cases, especially when the scale separation in the system is not clearly defined. In contrast, the pressure-strain interaction balances exactly the dissipation rate at kinetic scales regardless of the scale separation.

physics.space-ph↗

arXiv2022

Intermittency in the Expanding Solar Wind: Observations from Parker Solar Probe (0.16au), Helios 1 (0.3-1au), and Voyager 1 (1-10au)

We examine statistics of magnetic field vector components to explore how intermittency evolves from near sun plasma to radial distances as large as 10 au. Statistics entering the analysis include auto-correlation, magnetic structure functions of order n (SFn), and scale dependent kurtosis (SDK), each grouped in ranges of heliocentric distance. The Goddard Space Flight Center Space Physics Data Facility (SPDF) provides magnetic field measurements for resolutions of 6.8ms for Parker Solar Probe, 6s for Helios, and 1.92s for Voyager 1. We compute SF2 to determine the scales encompassing the inertial range and examine SDK to investigate degree of non-Gaussianity. Auto-correlations are used to resolve correlation scales. Correlation lengths and ion inertial lengths provide an estimate of effective Reynolds number (Re). Variation in Re allows us to examine for the first time the relationship between SDK and Re in an interplanetary plasma. A conclusion from this observed relationship is that regions with lower Re at a fixed physical scale have on average lower kurtosis, implying less intermittent behavior. Kolmogorov refined similarity hypothesis is applied to magnetic SFn and kurtosis to calculate intermittency parameters and fractal scaling in the inertial range. A refined Voyager 1 magnetic field dataset is generated.

physics.space-ph↗

arXiv2022

Statistical analysis of intermittency and its association with proton heating in the near Sun environment

We use data from the first six encounters of Parker Solar Probe and employ the Partial Variance of Increments ($PVI$) method to study the statistical properties of coherent structures in the inner heliosphere with the aim of exploring physical connections between magnetic field intermittency and observable consequences such as plasma heating and turbulence dissipation. Our results support proton heating localized in the vicinity of, and strongly correlated with, magnetic structures characterized by $PVI \geq 1$. We show that on average, such events constitute $\approx 19\%$ of the dataset, though variations may occur depending on the plasma parameters. We show that the waiting time distribution ($WT$) of identified events is consistent across all six encounters following a power-law scaling at lower $WTs$. This result indicates that coherent structures are not evenly distributed in the solar wind but rather tend to be tightly correlated and form clusters. We observe that the strongest magnetic discontinuities, $PVI \geq 6$, usually associated with reconnection exhausts, are sites where magnetic energy is locally dissipated in proton heating and are associated with the most abrupt changes in proton temperature. However, due to the scarcity of such events, their relative contribution to energy dissipation is minor. Taking clustering effects into consideration, we show that smaller scale, more frequent structures with PVI between, $1\lesssim PVI \lesssim 6$, play the major role in magnetic energy dissipation. The number density of such events is strongly associated with the global solar wind temperature, with denser intervals being associated with higher $T_{p}$.

astro-ph.SR↗

arXiv2022

An Extended and Fragmented Alfvén Zone in the Young Solar Wind

Motivated by theoretical, numerical, and observational evidence, we explore the possibility that the critical transition between sub-Alfvénic flow and super-Alfvénic flow in the solar atmosphere takes place in fragmented and disconnected subvolumes within a general Alfvén critical zone. The initial observations of sub-Alfvénic periods by Parker Solar Probe near $16~R_\odot$ do not yet provide sufficient evidence to distinguish this possibility from that of a folded surface that separates simply-connected regions. Subsequent orbits may well enable such a distinction, but here we use a global magnetohydrodynamic model of the solar wind, coupled to a turbulence transport model, to generate possible realizations of such an Alfvén critical zone. Understanding this transition will inform theories of coronal heating, solar wind origin, solar angular momentum loss, and related physical processes in stellar winds beyond the Sun.

astro-ph.SR↗

arXiv2021

Domains of Magnetic Pressure Balance in Parker Solar Probe Observations of the Solar Wind

The Parker Solar Probe (PSP) spacecraft is performing the first in situ exploration of the solar wind within 0.2 au of the Sun. Initial observations confirmed the Alfvénic nature of aligned fluctuations of the magnetic field B and velocity V in solar wind plasma close to the Sun, in domains of nearly constant magnetic field magnitude $|{\bf B}|$, i.e., approximate magnetic pressure balance. Such domains are interrupted by particularly strong fluctuations, including but not limited to radial field (polarity) reversals, known as switchbacks. It has been proposed that nonlinear Kelvin-Helmholtz instabilities form near magnetic boundaries in the nascent solar wind leading to extensive shear-driven dynamics, strong turbulent fluctuations including switchbacks, and mixing layers that involve domains of approximate magnetic pressure balance. In this work we identify and analyze various aspects of such domains using data from the first five PSP solar encounters. The filling fraction of domains, a measure of Alfvénicity, varies from median values of 90% within 0.2 au to 38% outside 0.9 au, with strong fluctuations. We find an inverse association between the mean domain duration and plasma $β$. We examine whether the mean domain duration is also related to the crossing time of spatial structures frozen into the solar wind flow for extreme cases of the aspect ratio. Our results are inconsistent with long, thin domains aligned along the radial or Parker spiral direction, and compatible with isotropic domains, which is consistent with prior observations of isotropic density fluctuations or ``flocculae'' in the solar wind.

astro-ph.SR↗

arXiv2021

Large-scale Structure and Turbulence Transport in the Inner Solar Wind -- Comparison of Parker Solar Probe's First Five Orbits with a Global 3D Reynolds-averaged MHD Model

Simulation results from a global magnetohydrodynamic model of the solar corona and solar wind are compared with Parker Solar Probe (PSP) observations during its first five orbits. The fully three-dimensional model is based on Reynolds-averaged mean-flow equations coupled with turbulence transport equations. The model includes the effects of electron heat conduction, Coulomb collisions, turbulent Reynolds stresses, and heating of protons and electrons via a turbulent cascade. Turbulence transport equations for average turbulence energy, cross helicity, and correlation length are solved concurrently with the mean-flow equations. Boundary conditions at the coronal base are specified using solar synoptic magnetograms. Plasma, magnetic field, and turbulence parameters are calculated along the PSP trajectory. Data from the first five orbits are aggregated to obtain trends as a function of heliocentric distance. Comparison of simulation results with PSP data shows good agreement, especially for mean-flow parameters. Synthetic distributions of magnetic fluctuations are generated, constrained by the local rms turbulence amplitude given by the model. Properties of this computed turbulence are compared with PSP observations.

physics.space-ph↗

arXiv2021

Subproton-scale Intermittency in Near-Sun Solar Wind Turbulence Observed by the Parker Solar Probe

High time-resolution solar wind magnetic field data is employed to study statistics describing intermittency near the first perihelion (~35.6 Rs) of the Parker Solar Probe mission. A merged dataset employing two instruments on the FIELDS suite enables broadband estimation of higher order moments of magnetic field increments, with five orders established with reliable accuracy. The duration, cadence, and low noise level of the data permit evaluation of scale dependence of the observed intermittency from the inertial range to deep subproton scales. The results support multifractal scaling in the inertial range, and monofractal but non-Gaussian scaling in the subproton range, thus clarifying suggestions based on data near Earth that had remained ambiguous due to possible interference of the terrestrial foreshock. The physics of the transition to monofractality remains unclear but we suggest that it is due to a scale-invariant population of current sheets between ion and electron inertial scales; the previous suggestion of incoherent kinetic-scale wave activity is disfavored as it presumably leads to re-Gaussianization which is not observed.

physics.space-ph↗

arXiv2020

Novel aspects of cosmic ray diffusion in synthetic magnetic turbulence

The diffusive motion of charged particles in synthetic magnetic turbulence with different properties is investigated by using numerical simulations with unprecedented dynamical range, which allow us to ensure that both the inertial range and the long wavelength part of the turbulent spectrum are properly described. This is of particular importance in evaluating previous suggestions that parallel and perpendicular diffusion coefficients differ in their energy dependence, an assertion at odds with the many claims of universality of the $D_{\perp}$ and $D_{\parallel}$ as functions of particle energy. Cases with and without an ordered magnetic field are discussed. Results of the numerical simulations are compared with available theoretical models, for slab, slab/2D and isotropic turbulence. We find widespread evidence that universality is broken, and that the ratio $D_{\perp}/D_{\parallel}$ is not independent of energy. The implications of this finding for the physics of cosmic ray transport are discussed in depth.

astro-ph.HE↗

arXiv2020

Random Walk and Trapping of Interplanetary Magnetic Field Lines: Global Simulation, Magnetic Connectivity, and Implications for Solar Energetic Particles

The random walk of magnetic field lines is an important ingredient in understanding how the connectivity of the magnetic field affects the spatial transport and diffusion of charged particles. As solar energetic particles (SEPs) propagate away from near-solar sources, they interact with the fluctuating magnetic field, which modifies their distributions. We develop a formalism in which the differential equation describing the field line random walk contains both effects due to localized magnetic displacements and a non-stochastic contribution from the large-scale expansion. We use this formalism together with a global magnetohydrodynamic simulation of the inner-heliospheric solar wind, which includes a turbulence transport model, to estimate the diffusive spreading of magnetic field lines that originate in different regions of the solar atmosphere. We first use this model to quantify field line spreading at 1 au, starting from a localized solar source region, and find rms angular spreads of about 20° - 60°. In the second instance, we use the model to estimate the size of the source regions from which field lines observed at 1 au may have originated, thus quantifying the uncertainty in calculations of magnetic connectivity; the angular uncertainty is estimated to be about 20°. Finally, we estimate the filamentation distance, i.e., the heliocentric distance up to which field lines originating in magnetic islands can remain strongly trapped in filamentary structures. We emphasize the key role of slab-like fluctuations in the transition from filamentary to more diffusive transport at greater heliocentric distances.

physics.space-ph↗

arXiv2020

Direct Measurement of the Solar-Wind Taylor Microscale using MMS Turbulence Campaign Data

Using the novel Magnetospheric Multiscale (MMS) mission data accumulated during the 2019 MMS Solar Wind Turbulence Campaign, we calculate the Taylor microscale $(λ_{\mathrm{T}})$ of the turbulent magnetic field in the solar wind. The Taylor microscale represents the onset of dissipative processes in classical turbulence theory. An accurate estimation of Taylor scale from spacecraft data is, however, usually difficult due to low time cadence, the effect of time decorrelation, and other factors. Previous reports were based either entirely on the Taylor frozen-in approximation, which conflates time dependence, or that were obtained using multiple datasets, which introduces sample-to-sample variation of plasma parameters, or where inter-spacecraft distance were larger than the present study. The unique configuration of linear formation with logarithmic spacing of the 4 MMS spacecraft, during the campaign, enables a direct evaluation of the $λ_{\mathrm{T}}$ from a single dataset, independent of the Taylor frozen-in approximation. A value of $λ_{\mathrm{T}} \approx 7000 \, \mathrm{km}$ is obtained, which is about 3 times larger than the previous estimates.

physics.space-ph↗

arXiv2020

Critical Balance and the Physics of MHD Turbulence

A discussion of the advantages and limitations of the concept of critical balance, as employed in turbulence phenomenologies, is presented. The incompressible magnetohydrodynamic (MHD) case is a particular focus. The discussion emphasizes the status of the original Goldreich & Sridhar (1995) critical balance conjecture relative to related theoretical issues and models in an MHD description of plasma turbulence. Issues examined include variance and spectral anisotropy, influence of a mean magnetic field, local and nonlocal effects, and the potential for effects of external driving. Related models such as Reduced MHD provide a valuable context in the considerations. Some new results concerning spectral features and timescales are presented in the course of the discussion. Also mentioned briefly are some adaptations and variations of critical balance.

physics.plasm-ph↗

arXiv2020

A Detailed Examination of Anisotropy and Timescales in Three-dimensional Incompressible Magnetohydrodynamic Turbulence

When magnetohydrodynamic turbulence evolves in the presence of a large-scale mean magnetic field, an anisotropy develops relative to that preferred direction. The well-known tendency is to develop stronger gradients perpendicular to the magnetic field, relative to the direction along the field. This anisotropy of the spectrum is deeply connected with anisotropy of estimated timescales for dynamical processes, and requires reconsideration of basic issues such as scale locality and spectral transfer. Here analysis of high-resolution three-dimensional simulations of unforced magnetohydrodynamic turbulence permits quantitative assessment of the behavior of theoretically relevant timescales in Fourier wavevector space. We discuss the distribution of nonlinear times, Alfvén times, and estimated spectral transfer rates. Attention is called to the potential significance of special regions of the spectrum, such as the two-dimensional limit and the "critical balance" region. A formulation of estimated spectral transfer in terms of a suppression factor supports a conclusion that the quasi two-dimensional fluctuations (characterized by strong nonlinearities) are not a singular limit, but may be in general expected to make important contributions.

physics.plasm-ph↗