Magnetohydrodynamic Turbulence Research Articles

Transport of energetic particles in turbulent space plasmas: pitch-angle scattering, telegraph, and diffusion equations

Introduction: In this article, we revisit the pitch-angle scattering equation describing the propagation of energetic particles through magnetized plasma. In this case, solar energetic particles and cosmic rays interact with magnetohydrodynamic turbulence and experience stochastic changes in the pitch-angle. Since this happens over an extended period of time, a pitch-angle isotropization process occurs, leading to parallel spatial diffusion. This process is described well by the pitch-angle scattering equation. However, the latter equation is difficult to solve analytically even when considering special cases for the scattering coefficient.Methods: In the past, a so-called subspace approximation was proposed, which has important applications in the theory of perpendicular diffusion. Alternatively, an approach based on the telegraph equation (also known as telegrapher’s equation) has been developed. We show that two-dimensional subspace approximation and the description based on the telegraph equation are equivalent. However, it is also shown that the obtained distribution functions contain artifacts and inaccuracies that cannot be found in the numerical solution to the problem. Therefore, an N-dimensional subspace approximation is proposed corresponding to a semi-analytical/semi-numerical approach. This is a useful alternative compared to standard numerical solvers.Results and Discussion: Depending on the application, the N-dimensional subspace approximation can be orders of magnitude faster. Furthermore, the method can easily be modified so that it can be used for any pitch-angle scattering equation.

Characterization of Turbulent Fluctuations in the Sub-Alfvénic Solar Wind

Parker Solar Probe (PSP) observed sub-Alfvénic solar wind intervals during encounters 8–14, and low-frequency magnetohydrodynamic (MHD) turbulence in these regions may differ from that in super-Alfvénic wind. We apply a new mode decomposition analysis to the sub-Alfvénic flow observed by PSP on 2021 April 28, identifying and characterizing entropy, magnetic islands, forward and backward Alfvén waves, including weakly/nonpropagating Alfvén vortices, forward and backward fast and slow magnetosonic (MS) modes. Density fluctuations are primarily and almost equally entropy- and backward-propagating slow MS modes. The mode decomposition provides phase information (frequency and wavenumber k) for each mode. Entropy density fluctuations have a wavenumber anisotropy of k ∥ ≫ k ⊥, whereas slow-mode density fluctuations have k ⊥ > k ∥. Magnetic field fluctuations are primarily magnetic island modes (δ B i ) with an O(1) smaller contribution from unidirectionally propagating Alfvén waves (δ B A+) giving a variance anisotropy of 〈δBi2〉/〈δBA2〉=4.1 . Incompressible magnetic fluctuations dominate compressible contributions from fast and slow MS modes. The magnetic island spectrum is Kolmogorov-like k⊥−1.6 in perpendicular wavenumber, and the unidirectional Alfvén wave spectra are k∥−1.6 and k⊥−1.5 . Fast MS modes propagate at essentially the Alfvén speed with anticorrelated transverse velocity and magnetic field fluctuations and are almost exclusively magnetic due to β p ≪ 1. Transverse velocity fluctuations are the dominant velocity component in fast MS modes, and longitudinal fluctuations dominate in slow modes. Mode decomposition is an effective tool in identifying the basic building blocks of MHD turbulence and provides detailed phase information about each of the modes.

Towards synthetic magnetic turbulence with coherent structures

Abstract Synthetic turbulence is a relevant tool to study complex astrophysical and space plasma environments inaccessible by direct simulation. However, conventional models lack intermittent coherent structures, which are essential in realistic turbulence. We present a novel method featuring coherent structures, conditional structure function scaling and fieldline curvature statistics comparable to magnetohydrodynamic turbulence. Enhanced transport of charged particles is investigated as well. This method presents significant progress towards physically faithful synthetic turbulence.

Parametric description of intermittent probability distribution functions in solar wind and magnetohydrodynamic turbulence

Abstract In this work, we find empirical evidence that the scale-dependent statistical properties in solar wind and Magnetohydrodynamic (MHD) turbulence can be described in terms of a family of parametric probability distribution functions (PDFs) known as Normal Inverse Gaussian (NIG). Understanding these PDFs is one of the most important goals in turbulence theory, as they are inherently connected to the intermittent properties of solar wind turbulence. We investigate the properties of PDFs of Elsasser increments based on a large statistical sample from solar wind observations and high-resolution numerical simulations of MHD turbulence. In order to measure the PDFs and their corresponding properties, three experiments are presented: fast and slow solar wind for experimental data and a simulation of reduced MHD (RMHD) turbulence. Conditional statistics on a 23-year-long sample of WIND data near 1 au and high-resolution pseudo-spectral simulation of steadily driven RMHD turbulence on a 20483 mesh are used to construct scale-dependent PDFs. The empirical PDFs are fitted to NIG distributions, which depend on four free parameters. Our analysis shows that NIG distributions accurately capture the evolution of the PDFs, with scale-dependent parameters, from large scales characterized by a Gaussian distribution, turning to exponential tails within the inertial range and stretched exponentials at dissipative scales. We also show that empirically-measured NIG parameters exhibit well-defined scaling properties that are similar across the three empirical data sets, which may be indicative of universal behavior.

On the properties and implications of collapse-driven MHD turbulence

ABSTRACT We investigate the driving of MHD turbulence by gravitational contraction using simulations of an initially spherical, isothermal, magnetically supercritical molecular cloud core with transonic and trans-Alfvénic turbulence. We perform a Helmholtz decomposition of the velocity field, and investigate the evolution of its solenoidal and compressible parts, as well as of the velocity component along the gravitational acceleration vector, a proxy for the infall component of the velocity field. We find that (1) In spite of being supercritical, the core first contracts to a sheet perpendicular to the mean magnetic field, and the sheet itself collapses. (2) The solenoidal component of the turbulence remains at roughly its initial level throughout the simulation, while the compressible component increases continuously, implying that turbulence does not dissipate towards the centre of the core. (3) The distribution of simulation cells in the B–ρ plane occupies a wide triangular region at low densities, bounded below by the expected trend for fast MHD waves (B ∝ ρ, applicable for high-local Alfvénic Mach number MA) and above by the trend expected for slow waves (B ∼ constant, applicable for low local MA). At high densities, the distribution follows a single trend $B \propto \rho ^{\gamma _{\rm eff}}$, with 1/2 < γeff < 2/3, as expected for gravitational compression. (4) The mass-to-magnetic flux ratio λ increases with radius r due to the different scalings of the mass and magnetic flux with r. At a fixed radius, λ increases with time due to the accretion of material along field lines. (5) The solenoidal energy fraction is much smaller than the total turbulent component, indicating that the collapse drives the turbulence mainly compressibly, even in directions orthogonal to that of the collapse.

Dynamics of cold circumstellar gas in debris disks

Abstract Mounting observational evidence indicates that cold circumstellar gas is present in debris disk systems. This work focuses on various dynamical processes that debris-disk gas may undergo. We review five mechanisms that can transport angular momentum and their applications to debris disks. These include molecular viscosity, hydrodynamic turbulence, magnetohydrodynamic turbulence, magnetized disk winds, and laminar magnetic stress. We find that molecular viscosity can result in α as high as ≲ 0.1 for sufficiently low densities, while the Rossby wave instability is a possible source of hydrodynamic turbulence and structure formation. We argue that the vertical shear instability is unlikely due to the long cooling times. The onset of the magnetorotational instability (MRI) is dichotomous: for low density disks the MRI can be excited at the midplane, while for high mass disks it may only be operating at z > 2 − 3H, if at all. The MHD wind and laminar magnetic stress mechanisms rely on the configuration and strength of any background large-scale magnetic field, the existence of which is uncertain and possibly unlikely. We conclude that the dominant mechanism and its efficiency in transporting angular momentum varies from one system to the other, depending especially closely on the gas density. More detailed analyses shall be performed in the future focusing on representative, nearby debris disks.

The turbulent variability of accretion discs observed at high energies

Abstract We use numerical stochastic-viscous hydrodynamic simulations and new analytical results from thin disc theory to probe the turbulent variability of accretion flows, as observed at high energies. We show that the act of observing accretion discs in the Wien tail exponentially enhances small-scale temperature variability in the flow, which in a real disc will be driven by magnetohydrodynamic turbulence, to large amplitude luminosity fluctuations (as predicted analytically). In particular, we demonstrate that discs with more spatially coherent turbulence (as might be expected of thicker discs), and relativistic discs observed at larger inclinations, show significantly enhancement in their Wien-tail variability. We believe this is the first analysis of relativistic viewing-angle effects on turbulent variability in the literature. Using these results we argue that tidal disruption events represent particularly interesting systems with which to study accretion flow variability, and may in fact be the best astrophysical probes of small scale disc turbulence. This is a result of a typical tidal disruption event disc being naturally observed in the Wien-tail and likely having a somewhat thicker disc and cleaner X-ray spectrum than other sources. We argue for dedicated X-ray observational campaigns of tidal disruption events, with the aim of studying accretion flow variability.

Identification of the weak-to-strong transition in Alfvénic turbulence from space plasma

AbstractPlasma turbulence is a ubiquitous dynamical process that transfers energy across many spatial and temporal scales in astrophysical and space plasma systems. Although the theory of anisotropic magnetohydrodynamic (MHD) turbulence has successfully described natural phenomena, its core prediction of an Alfvénic transition from weak to strong MHD turbulence when energy cascades from large to small scales has not been observationally confirmed. Here we report evidence for the Alfvénic weak-to-strong transition in small-amplitude, turbulent MHD fluctuations in Earth’s magnetosheath using data from four Cluster spacecraft. Our observations demonstrate the universal existence of strong turbulence accompanied by weak turbulent fluctuations on large scales. Moreover, we find that the nonlinear interactions of MHD turbulence are crucial to the energy cascade, as they broaden the cascade directions and fluctuating frequencies. The observed connection between weak and strong MHD turbulence systems may be present in many astrophysical environments, such as star formation, energetic particle transport, turbulent dynamos, and solar corona or solar wind heating.

Dust-gas coupling in turbulence- and MHD wind-driven protoplanetary disks: Implications for rocky planet formation

The degree of coupling between dust particles and their surrounding gas in protoplanetary disks is quantified by the Stokes number. The Stokes number governs particle size and spatial distributions, in turn establishing the dominant mode of planetary accretion in different disk regions. In this paper, we model the characteristic Stokes number of dust particles across time in disks evolving under both turbulent viscosity and MHD disk winds. In both turbulence- and wind-dominated disks, we find that collisional fragmentation is the limiting mechanism of particle growth. The water-ice sublimation line constitutes a critical transition point between dust settling, drift, and size regimes. For a fiducial value disk evolution parameter α̃≃10−3, silicate particles interior to the ice-line in our model are characterized by low Stokes numbers (≲10−2) and sizes in the sub-mm- to 1cm-scale. Icy particle/boulders beyond the ice-line are characterized by high Stokes numbers (≳10−2) and sizes in the cm to dm size range. Hence, icy particles settle into a thin layer at the outer disk midplane and drift inward at velocities exceeding the gaseous accretionary flow due to substantial headwind. Silicate particles in the inner disk remain relatively well dispersed and are to a large extent advected inward with their surrounding gas.The dichotomy in Stokes number also translates to distinct planet formation pathways between the inner and outer disk. While rocky embryos in the inner disk are largely confined to inefficient pebble accretion in the 3D regime, sufficiently massive volatile-rich embryos in the outer disk can partake in rapid 2D pebble accretion when turbulence therein is sufficiently low. Through simulations of rocky planet growth, we demonstrate that the dominance of pebble accretion can only be realized in disks that are driven by MHD winds, slow-evolving (α̃∼10−4), and devoid of pressure maxima that may concentrate solids and give rise to planetesimal rings. Such disks are extremely quiescent, with Shakura-Sunyaev turbulence parameters on the order of αν∼10−5. We conclude that for most of parameter space reflected in astronomical observations of protoplanetary disks, pairwise planetesimal collisions constitute the dominant pathway of rocky planet accretion. Our results lend support to proposition that rocky planets formed in planetesimal rings and argue against a significant contribution (≳ 10%) of outer disk, carbonaceous, material to the proto-Earth in the form of pebbles.

Magnetic Field Strength Effects on Nucleosynthesis from Neutron Star Merger Outflows

Magnetohydrodynamic turbulence drives the central engine of post-merger remnants, potentially powering both a nucleosynthetically active disk wind and the relativistic jet behind a short gamma-ray burst. We explore the impact of the magnetic field on this engine by simulating three post-merger black hole accretion disks using general relativistic magnetohydrodynamics with Monte Carlo neutrino transport, in each case varying the initial magnetic field strength. We find increasing ejecta masses associated with increasing magnetic field strength. We find that a fairly robust main r-process pattern is produced in all three cases, scaled by the ejected mass. Changing the initial magnetic field strength has a considerable effect on the geometry of the outflow and hints at complex central engine dynamics influencing lanthanide outflows. We find that actinide production is especially sensitive to magnetic field strength, with the overall actinide mass fraction calculated at 1 Gyr post-merger increasing by more than a factor of 6 with a tenfold increase in magnetic field strength. This hints at a possible connection to the variability in actinide enhancements exhibited by metal-poor, r-process-enhanced stars.

Particle trapping and acceleration in turbulent post-flare coronal loops

ABSTRACT We present a study of energetic-electron trapping and acceleration in the Kelvin–Helmholtz-induced magnetohydrodynamic (MHD) turbulence of post-flare loops in the solar corona. Using the particle-tracing capabilities of MPI-AMRVAC 3.0, we evolve ensembles of test electrons (i.e. without feedback to the underlying MHD) inside the turbulent looptop, using the guiding-centre approximation. With the MHD looptop model of Ruan et al., we investigate the relation between turbulence and particle trapping inside the looptop structure, showing that better-developed turbulent cascades result in more efficient trapping primarily due to mirror effects. We then quantify the electron acceleration in the time-evolving MHD turbulence, and find that ideal-MHD processes inside the looptop can produce non-thermal particle spectra from an initial Maxwellian distribution. Electrons in this turbulence are preferentially accelerated by mirror effects in the direction perpendicular to the local magnetic field while remaining confined within small regions of space between magnetic islands. Assuming dominance of Bremsstrahlung radiation mechanisms, we employ the resulting information from accelerated electrons (combined with the MHD background) to construct HXR spectra of the post-flare loop that include non-thermal-particle contributions. Our results pave the way to constructing more realistic simulations of radiative coronal structure for comparison with current and future observations.

Mind the gap: non-local cascades and preferential heating in high-β Alfvénic turbulence

ABSTRACT Characterizing the thermodynamics of turbulent plasmas is key to decoding observable signatures from astrophysical systems. In magnetohydrodynamic (MHD) turbulence, non-linear interactions between counter-propagating Alfvén waves cascade energy to smaller spatial scales where dissipation heats the protons and electrons. When the thermal pressure far exceeds the magnetic pressure, linear theory predicts a spectral gap at perpendicular scales near the proton gyroradius where Alfvén waves become non-propagating. For simple models of an MHD turbulent cascade that assume only local non-linear interactions, the cascade halts at this gap, preventing energy from reaching smaller scales where electron dissipation dominates, leading to an overestimate of the proton heating rate. In this work, we demonstrate that non-local contributions to the cascade, specifically large-scale shearing and small-scale diffusion, can bridge the non-propagating gap, allowing the cascade to continue to smaller scales. We provide an updated functional form for the proton-to-electron heating ratio accounting for this non-local energy transfer by evaluating a non-local weakened cascade model over a range of temperature and pressure ratios. In plasmas where the thermal pressure dominates the magnetic pressure, we observe that the proton heating is moderated compared to the significant enhancement predicted by local models.

Angular momentum and chemical transport by azimuthal magnetorotational instability in radiative stellar interiors

Context. The transport of angular momentum and chemical elements within evolving stars remains poorly understood. Asteroseismic and spectroscopic observations of low-mass main sequence stars and red giants reveal that their radiative cores rotate orders of magnitude slower than classical predictions from stellar evolution models and that the abundances of their surface light elements are too small. Magnetohydrodynamic (MHD) turbulence is considered a primary mechanism to enhance the transport in radiative stellar interiors but its efficiency is still largely uncertain. Aims. We explore the transport of angular momentum and chemical elements due to azimuthal magnetorotational instability, one of the dominant instabilities expected in differentially rotating radiative stellar interiors. Methods. We employed 3D MHD direct numerical simulations in a spherical shell of unstratified and stably stratified flows under the Boussinesq approximation. The background differential rotation was maintained by a volumetric body force. We examined the transport of chemical elements using a passive scalar. Results. We provide evidence of magnetorotational instability for purely azimuthal magnetic fields in the parameter regime expected from local and global linear stability analyses. Without stratification and when the Reynolds number Re and the background azimuthal field strength are large enough, we observed dynamo action driven by the instability at values of the magnetic Prandtl number Pm in the range 0.6 − 1, which is the smallest ever reported in a global setup. When considering stable stratification at Pm = 1, the turbulence is transitional and becomes less homogeneous and isotropic upon increasing buoyancy effects. The transport of angular momentum occurs radially outward and is dominated by the Maxwell stresses when stratification is large enough. We find that the turbulent viscosity decreases when buoyancy effects strengthen and scales with the square root of the ratio of the reference rotation rate Ωa to the Brunt–Väisälä frequency N. The chemical turbulent diffusion coefficient scales with stratification similarly to the turbulent viscosity, but is lower in amplitude so that the transport of chemicals is slower than the one of angular momentum, in agreement with recent stellar evolution models of low-mass stars. Conclusions. We show that the transport induced by azimuthal magnetorotational instability scales somewhat slowly with stratification and may enforce rigid rotations of red giant cores on a timescale of a few thousand years. In agreement with recent stellar evolution models of low-mass stars, the instability transports chemical elements less efficiently than angular momentum.

Deep learning cosmic ray transport from density maps of simulated, turbulent gas

The coarse-grained propagation of galactic cosmic rays (CRs) is traditionally constrained by phenomenological models of Milky Way CR propagation fit to a variety of direct and indirect observables; however, constraining the fine-grained transport of CRs along individual magnetic field lines—for instance, diffusive vs streaming transport models—is an unsolved challenge. Leveraging a recent training set of magnetohydrodynamic turbulent box simulations, with CRs spanning a range of transport parameters, we use convolutional neural networks (CNNs) trained solely on gas density maps to classify CR transport regimes. We find that even relatively simple CNNs can quite effectively classify density slices to corresponding CR transport parameters, distinguishing between streaming and diffusive transport, as well as magnitude of diffusivity, with class accuracies between 92% and 99%. As we show, the transport-dependent imprints that CRs leave on the gas are not all tied to the resulting density power spectra: classification accuracies are still high even when image spectra are flattened (85%–98% accuracy), highlighting CR transport-dependent changes to turbulent phase information. We interpret our results with saliency maps and image modifications, and we discuss physical insights and future applications.

The Statistical Mechanics of Ideal Magnetohydrodynamic Turbulence and a Solution of the Dynamo Problem

We review and extend the theory of ideal, homogeneous, incompressible, magnetohydrodynamic (MHD) turbulence. The theory contains a solution to the ‘dynamo problem’, i.e., the problem of determining how a planetary or stellar body produces a global dipole magnetic field. We extend the theory to the case of ideal MHD turbulence with a mean magnetic field that is aligned with a rotation axis. The existing theory is also extended by developing the thermodynamics of ideal MHD turbulence based on entropy. A mathematical model is created by Fourier transforming the MHD equations and dynamical variables, resulting in a dynamical system consisting of the independent Fourier coefficients of the velocity and magnetic fields. This dynamical system has a large but finite-dimensional phase space in which the phase flow is divergenceless in the ideal case. There may be several constants of the motion, in addition to energy, which depend on the presence, or lack thereof, of a mean magnetic field or system rotation or both imposed on the magnetofluid; this leads to five different cases of MHD turbulence that must be considered. The constants of the motion (ideal invariants)—the most important being energy and magnetic helicity—are used to construct canonical probability densities and partition functions that enable ensemble predictions to be made. These predictions are compared with time averages from numerical simulations to test whether or not the system is ergodic. In the cases most pertinent to planets and stars, nonergodicity is observed at the largest length-scales and occurs when the components of the dipole field become quasi-stationary and dipole energy is directly proportional to magnetic helicity. This nonergodicity is evident in the thermodynamics, while dipole alignment with a rotation axis may be seen as the result of dynamical symmetry breaking, i.e., ‘broken ergodicity’. The relevance of ideal theoretical results to real (forced, dissipative) MHD turbulence is shown through numerical simulation. Again, an important result is a statistical solution of the ‘dynamo problem’.

The Intermittency of Turbulence in Magneto-Hydodynamical Simulations and in the Cosmos

Turbulent dissipation is a central issue in the star and galaxy formation process. Its fundamental property of space–time intermittency, well characterised in incompressible laboratory experiments, remains elusive in cosmic turbulence. Progress requires the combination of state-of-the-art modelling, numerical simulations and observations. The power of such a combination is illustrated here, where the statistical method intended to locate the extrema of velocity shears in a turbulent field, which are the signposts of intense dissipation extrema, is applied to numerical simulations of compressible magneto-hydrodynamical (MHD) turbulence dedicated to dissipation scales and to observations of a turbulent molecular cloud. We demonstrate that increments of several observables computed at the smallest lags can detect coherent structures of intense dissipation. We apply this statistical method to the observations of a turbulent molecular cloud close to the Sun in our galaxy and disclose a remarkable structure of extremely large velocity shear. At the location of the largest velocity shear, this structure is found to foster 10× more carbon monoxide molecules than standard diffuse molecular gas, an enrichment supported by models of non-equilibrium warm chemistry triggered by turbulent dissipation. In our simulations, we also compute structure functions of various synthetic observables and show that they verify Extended Self-Similarity. This allows us to compute their intermittency exponents, and we show how they constrain some properties of the underlying three-dimensional turbulence. The power of the combination of modelling and observations is also illustrated by the observations of the CH+ cation that provide unique quantitative information on the kinetic energy trail in the massive, multi-phase and turbulent circum-galactic medium of a galaxy group at redshift z=2.8.

Small-amplitude Compressible Magnetohydrodynamic Turbulence Modulated by Collisionless Damping in Earth’s Magnetosheath: Observation Matches Theory

Plasma turbulence is a ubiquitous dynamical process that transfers energy across many spatial and temporal scales and affects energetic particle transport. Recent advances in the understanding of compressible magnetohydrodynamic (MHD) turbulence demonstrate the important role of damping in shaping energy distributions on small scales, yet its observational evidence is still lacking. This study provides the first observational evidence of substantial collisionless damping (CD) modulation on the small-amplitude compressible MHD turbulence cascade in Earth’s magnetosheath using four Cluster spacecraft. Based on an improved compressible MHD decomposition algorithm, turbulence is decomposed into three eigenmodes: incompressible Alfvén modes and compressible slow and fast (magnetosonic) modes. Our observations demonstrate that CD enhances the anisotropy of compressible MHD modes because CD has a strong dependence on wave propagation angle. The wavenumber distributions of slow modes are mainly stretched perpendicular to the background magnetic field ( B 0) and weakly modulated by CD. In contrast, fast modes are subjected to a more significant CD modulation. Fast modes exhibit a weak, scale-independent anisotropy above the CD truncation scale. Below the CD truncation scale, the anisotropy of fast modes enhances as wavenumbers increase. As a result, fast-mode fractions in the total energy of compressible modes decrease with the increase of perpendicular wavenumber (to B 0) or wave propagation angle. Our findings reveal how the turbulence cascade is shaped by CD and its consequences for anisotropies in the space environment.

Space–time structure of weak magnetohydrodynamic turbulence

The two-time energy spectrum of weak magnetohydrodynamic turbulence is found by applying a wave-turbulence closure to the cumulant hierarchy constructed from the dynamical equations. Solutions are facilitated via asymptotic expansions in terms of the small parameter $\varepsilon$ , describing the ratio of time scales corresponding to Alfvénic propagation and nonlinear interactions between counter-propagating Alfvén waves. The strength of nonlinearity at a given spatial scale is further quantified by an integration over all possible delta-correlated modes compliant in a given set of three-wave interactions that are associated with energy flux through the said scale. The wave-turbulence closure for the two-time spectrum uncovers a secularity occurring on a time scale of order $\varepsilon ^{-2}$ , and the asymptotic expansion for the spectrum is reordered in a manner comparable to the one-time case. It is shown that for the regime of stationary turbulence, the two-time energy spectrum exponentially decays on a lagged time scale $(\varepsilon ^2 \gamma _k^s)^{-1}$ in proportion to the strength of the associated three-wave interactions, characterized by nonlinear decorrelation frequency $\gamma _k^s$ . The scaling of the form $k_{\perp } v_0 \chi _0$ exhibited by this frequency is reminiscent of random sweeping by the outer scale with characteristic fluctuation velocity $v_0$ that is modified due to competition with Alfvénic propagation (characterized by $\chi _0$ ) at the said scale. A brief calculation of frequency broadening of the power spectrum due to nonlinear interactions is also presented.

Are Coronal Loops Projection Effects?

We report results of an in-depth numerical investigation of three-dimensional projection effects that could influence the observed loop-like structures in an optically thin solar corona. Several archetypal emitting geometries are tested, including collections of luminous structures with circular cross sections of fixed and random size, and light-emitting structures with highly anisotropic cross sections, as well as two-dimensional stochastic current density structures generated by fully developed magnetohydrodynamic turbulence. A comprehensive set of statistical signatures is used to compare the line-of-sight (LOS) integrated emission signals predicted by the constructed numerical models with the loop profiles observed by the extreme ultraviolet telescope on board the flight 2.1 of the High-Resolution Coronal Imager (Hi-C). The results suggest that typical cross-sectional emission envelopes of the Hi-C loops are unlikely to have high eccentricity, and that the observed loops cannot be attributed to randomly oriented quasi-two-dimensional emitting structures, some of which would produce anomalously strong optical signatures due to an accidental LOS alignment, as expected in the ''coronal veil“ scenario proposed recently by Malanushenko et al. The possibility of apparent loop-like projections of very small (close to the resolution limit) or very large (comparable with the size of an active region) light-emitting sheets remains open, but the intermediate range of scales commonly associated with observed loop systems is most likely filled with true quasi-one-dimensional (roughly axisymmetric) structures embedded into the three-dimensional coronal volume.

The Diffusion and Scattering of Accelerating Particles in Compressible MHD Turbulence

We numerically study the diffusion and scattering of cosmic rays (CRs) together with their acceleration processes in the framework of the modern understanding of magnetohydrodynamic (MHD) turbulence. Based on the properties of compressible MHD turbulence obtained from observations and numerical experiments, we investigate the interaction of CRs with plasma modes. We find that (1) the gyroradius of particles exponentially increases with the acceleration timescale; (2) the momentum diffusion presents the power-law relationship with the gyroradius in the strong turbulence regime, and shows a plateau in the weak turbulence regime implying a stochastic acceleration process; (3) the spatial diffusion is dominated by the parallel diffusion in the sub-Alfvénic regime, while it is dominated by the perpendicular diffusion in the super-Alfvénic one; (4) as for the interaction of CRs with plasma modes, the particle acceleration is dominated by the fast mode in the high β case, while in the low β case, it is dominated by the fast and slow modes; and (5) in the presence of acceleration, magnetosonic modes still play a critical role in the diffusion and scattering processes of CRs, which is in good agreement with earlier theoretical predictions.