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A new frequency-stepped Doppler backscattering (DBS) system has been integrated with a real-time steerable electron cyclotron heating launcher to probe local background turbulence (f<10 MHz) and high-frequency (20-550 MHz) density fluctuations in the DIII-D tokamak. The launcher enables 2D steering (horizontal and vertical) over wide angular ranges to optimize probe location and wavenumber response, with vertical steering adjustable in real time during discharges. The DBS system utilizes a programmable frequency synthesizer with adjustable dwell time, capable of stepping across the E-band frequency range (60-90 GHz) in real time, launching either O or X-mode polarized millimeter waves. This setup facilitates diagnosis of the complex spatial structure of high-power (>200 kW) helicon waves (476 MHz) during current drive experiments. Real-time scans reveal broadband density fluctuations around the helicon frequency, attributed to backscattering of the DBS millimeter wave probe from plasma turbulence modulated by the helicon wave. These fluctuations appear as high-frequency sidebands in the turbulence spectrum, effectively 'tagging' the background turbulence with the helicon wave's electric field. This method allows for monitoring local helicon wave amplitude by comparing high-frequency signal amplitude to background turbulence. Coupled with real-time scanning of measurement location and wavenumber, this allows for rapid helicon wave power distribution determination during steady-state plasma operation, potentially validating predictive models like GENRAY or AORSA for helicon current drive in DIII-D plasmas., Comment: 14 Pages, 10 figs

The means by which the turbulent cascade of energy is dissipated in the solar wind, and in other astrophysical systems, is a major open question. It has recently been proposed that a barrier to the transfer of energy can develop at small scales, which can enable heating through ion-cyclotron resonance, under conditions applicable to regions of the solar wind. Such a scenario fundamentally diverges from the standard picture of turbulence, where the energy cascade proceeds unimpeded until it is dissipated. Here, using data from NASA's Parker Solar Probe, we find that the shape of the magnetic energy spectrum around the ion gyroradius varies with solar wind parameters in a manner consistent with the presence of such a barrier. This allows us to identify critical values of some of the parameters necessary for the barrier to form; we show that the barrier appears fully developed for ion plasma beta of below $\simeq0.5$ and becomes increasingly prominent with imbalance for normalised cross helicity values greater than $\simeq0.4$. As these conditions are frequently met in the solar wind, particularly close to the Sun, our results suggest that the barrier is likely playing a significant role in turbulent dissipation in the solar wind and so is an important mechanism in explaining its heating and acceleration.

The MHD equations, as a collisional fluid model that remains in local thermodynamic equilibrium (LTE), have long been used to describe turbulence in myriad space and astrophysical plasmas. Yet, the vast majority of these plasmas, from the solar wind to the intracluster medium (ICM) of galaxy clusters, are only weakly collisional at best, meaning that significant deviations from LTE are not only possible but common. Recent studies have demonstrated that the kinetic physics inherent to this weakly collisional regime can fundamentally transform the evolution of such plasmas across a wide range of scales. Here we explore the consequences of pressure anisotropy and Larmor-scale instabilities for collisionless, $\beta \gg 1$ turbulence, focusing on the role of a self-organizational effect known as `magneto-immutability'. We describe this self-organization analytically through a high-$\beta$, reduced ordering of the CGL-MHD equations, finding that it is a robust inertial-range effect that dynamically suppresses magnetic-field-strength fluctuations, anisotropic-pressure stresses, and dissipation due to heat fluxes. As a result, the turbulent cascade of Alfv\'enic fluctuations continues below the putative viscous scale to form a robust, nearly conservative, MHD-like inertial range. These findings are confirmed numerically via Landau-fluid CGL-MHD turbulence simulations that employ a collisional closure to mimic the effects of microinstabilities. We find that microinstabilities occupy a small ($\sim 5\%$) volume-filling fraction of the plasma, even when the pressure anisotropy is driven strongly towards its instability thresholds. We discuss these results in the context of recent predictions for ion-versus-electron heating in low-luminosity accretion flows and observations implying suppressed viscosity in ICM turbulence., Comment: 42 pages, 13 figures

Understanding the partitioning of turbulent energy between ions and electrons in weakly collisional plasmas is crucial for the accurate interpretation of observations and modelling of various astrophysical phenomena. Many such plasmas are "imbalanced", wherein the large-scale energy input is dominated by Alfv\'enic fluctuations propagating in a single direction. In this paper, we demonstrate that when strongly-magnetised plasma turbulence is imbalanced, nonlinear conservation laws imply the existence of a critical value of the electron plasma beta that separates two dramatically different types of turbulence in parameter space. For betas below the critical value, the free energy injected on the largest scales is able to undergo a familiar Kolmogorov-type cascade to small scales where it is dissipated, heating electrons. For betas above the critical value, the system forms a "helicity barrier" that prevents the cascade from proceeding past the ion Larmor radius, causing the majority of the injected free energy to be deposited into ion heating. Physically, the helicity barrier results from the inability of the system to adjust to the disparity between the perpendicular-wavenumber scalings of the free energy and generalised helicity below the ion Larmor radius; restoring finite electron inertia can annul, or even reverse, this disparity, giving rise to the aforementioned critical beta. We relate this physics to the "dynamic phase alignment" mechanism, and characterise various other important features of the helicity barrier, including the nature of the nonlinear wavenumber-space fluxes, dissipation rates, and energy spectra. The existence of such a critical beta has important implications for heating, as it suggests that the dominant recipient of the turbulent energy -- ions or electrons -- can depend sensitively on the characteristics of the plasma at large scales., Comment: 33 pages, 10 figures

Launched on 12 Aug. 2018, NASA's Parker Solar Probe had completed 13 of its scheduled 24 orbits around the Sun by Nov. 2022. The mission's primary science goal is to determine the structure and dynamics of the Sun's coronal magnetic field, understand how the solar corona and wind are heated and accelerated, and determine what processes accelerate energetic particles. Parker Solar Probe returned a treasure trove of science data that far exceeded quality, significance, and quantity expectations, leading to a significant number of discoveries reported in nearly 700 peer-reviewed publications. The first four years of the 7-year primary mission duration have been mostly during solar minimum conditions with few major solar events. Starting with orbit 8 (i.e., 28 Apr. 2021), Parker flew through the magnetically dominated corona, i.e., sub-Alfv\'enic solar wind, which is one of the mission's primary objectives. In this paper, we present an overview of the scientific advances made mainly during the first four years of the Parker Solar Probe mission, which go well beyond the three science objectives that are: (1) Trace the flow of energy that heats and accelerates the solar corona and solar wind; (2) Determine the structure and dynamics of the plasma and magnetic fields at the sources of the solar wind; and (3) Explore mechanisms that accelerate and transport energetic particles., Comment: 157 pages, 65 figures

Weakly collisional plasmas are subject to nonlinear relaxation processes, which can operate at rates much faster than the particle collision frequencies. This causes the plasma to respond like a magnetised fluid despite having long particle mean-free-paths. In this Letter the effective collisional mechanisms are modelled in the plasma kinetic equation to produce density, pressure and magnetic field responses to compare with spacecraft measurements of the solar wind compressive fluctuations at 1 AU. This enables a measurement of the effective mean-free-path of the solar wind protons, found to be 4.35 $\times 10^5$ km, which is $\sim 10^3$ times shorter than the collisional mean-free-path. These measurements are shown to support the effective fluid behavior of the solar wind at scales above the proton gyroradius and demonstrate that effective collision processes alter the thermodynamics and transport of weakly collisional plasmas.

The building of planetary systems is controlled by the gas and dust dynamics of protoplanetary disks. While the gas is simultaneously accreted onto the central star and dissipated away by winds, dust grains aggregate and collapse to form planetesimals and eventually planets. This dust and gas dynamics involves instabilities, turbulence and complex non-linear interactions which ultimately control the observational appearance and the secular evolution of these disks. This chapter is dedicated to the most recent developments in our understanding of the dynamics of gaseous and dusty disks, covering hydrodynamic and magnetohydrodynamic turbulence, gas-dust instabilities, dust clumping and disk winds. We show how these physical processes have been tested from observations and highlight standing questions that should be addressed in the future., Comment: 32 pages, 7 figures, to appear in Protostars and Planets VII, eds: Shu-ichiro Inutsuka, Yuri Aikawa, Takayuki Muto, Kengo Tomida, and Motohide Tamura

One of the striking observations from the Parker Solar Probe (PSP) spacecraft is the prevalence in the inner heliosphere of large amplitude, Alfv\'enic magnetic field reversals termed 'switchbacks'. These $\delta B_R/B \sim \mathcal{O}(1$) fluctuations occur on a range of timescales and in {\em patches} separated by intervals of quiet, radial magnetic field. We use measurements from PSP to demonstrate that patches of switchbacks are localized within the extensions of plasma structures originating at the base of the corona. These structures are characterized by an increase in alpha particle abundance, Mach number, plasma $\beta$ and pressure, and by depletions in the magnetic field magnitude and electron temperature. These intervals are in pressure-balance, implying stationary spatial structure, and the field depressions are consistent with overexpanded flux tubes. The structures are asymmetric in Carrington longitude with a steeper leading edge and a small ($\sim$1$^\circ$) edge of hotter plasma and enhanced magnetic field fluctuations. Some structures contain suprathermal ions to $\sim$85 keV that we argue are the energetic tail of the solar wind alpha population. The structures are separated in longitude by angular scales associated with supergranulation. This suggests that these switchbacks originate near the leading edge of the diverging magnetic field funnels associated with the network magnetic field - the primary wind sources. We propose an origin of the magnetic field switchbacks, hot plasma and suprathermals, alpha particles in interchange reconnection events just above the solar transition region and our measurements represent the extended regions of a turbulent outflow exhaust., Comment: 18 pages, 9 figures, submitted to Astrophys. J

Using hybrid-kinetic particle-in-cell simulation, we study the evolution of an expanding, collisionless, magnetized plasma in which strong Alfv\'enic turbulence is persistently driven. Temperature anisotropy generated adiabatically by the plasma expansion (and consequent decrease in the mean magnetic-field strength) gradually reduces the effective elasticity of the field lines, causing reductions in the linear frequency and residual energy of the Alfv\'{e}nic fluctuations. In response, these fluctuations modify their interactions and spatial anisotropy to maintain a scale-by-scale "critical balance" between their characteristic linear and nonlinear frequencies. Eventually the plasma becomes unstable to kinetic firehose instabilities, which excite rapidly growing magnetic fluctuations at ion-Larmor scales. The consequent pitch-angle scattering of particles maintains the temperature anisotropy near marginal stability, even as the turbulent plasma continues to expand. The resulting evolution of parallel and perpendicular temperatures does not satisfy double-adiabatic conservation laws, but is described accurately by a simple model that includes anomalous scattering. Our results have implications for understanding the complex interplay between macro- and micro-scale physics in various hot, dilute, astrophysical plasmas, and offer predictions concerning power spectra, residual energy, ion-Larmor-scale spectral breaks, and non-Maxwellian features in ion distribution functions that may be tested by measurements taken in high-beta regions of the solar wind., Comment: ApJL, in press. 9 pages, 5 figures

Using analytical theory and hybrid-kinetic numerical simulations, we demonstrate that, in a collisionless plasma, long-wavelength ion-acoustic waves (IAWs) with amplitudes $\delta n/n_0 \gtrsim 2/\beta$ (where $\beta\gg{1}$ is the ratio of thermal to magnetic pressure) generate sufficient pressure anisotropy to destabilize the plasma to firehose and mirror instabilities. These kinetic instabilities grow rapidly to reduce the pressure anisotropy by pitch-angle scattering and trapping particles, respectively, thereby impeding the maintenance of Landau resonances that enable such waves' otherwise potent collisionless damping. The result is wave dynamics that evince a weakly collisional plasma: the ion distribution function is near-Maxwellian, the field-parallel flow of heat resembles its Braginskii form (except in regions where large-amplitude magnetic mirrors strongly suppress particle transport), and the relations between various thermodynamic quantities are more `fluid-like' than kinetic. A nonlinear fluctuation-dissipation relation for self-sustaining IAWs is obtained by solving a plasma-kinetic Langevin problem, which demonstrates suppressed damping, enhanced fluctuation levels, and weakly collisional thermodynamics when IAWs with $\delta n/n_0 \gtrsim 2/\beta$ are stochastically driven. We investigate how our results depend upon the scale separation between the wavelength of the IAW and the Larmor radius of the ions, and discuss briefly their implications for our understanding of turbulence and transport in the solar wind and the intracluster medium of galaxy clusters., Comment: 25 pages, 10 figures, Journal of Plasma Physics, in press

While it is well-known that every nearly-periodic Hamiltonian system possesses an adiabatic invariant, extant methods for computing terms in the adiabatic invariant series are inefficient. The most popular method involves the heavy intermediate calculation of a non-unique near-identity coordinate transformation, even though the adiabatic invariant itself is a uniquely-defined scalar. A less well-known method, developed by S. Omohundro, avoids calculating intermediate sequences of coordinate transformations but is also inefficient as it involves its own sequence of complex intermediate calculations. In order to improve the efficiency of future calculations of adiabatic invariants, we derive generally-applicable, readily computable formulas for the first several terms in the adiabatic invariant series. To demonstrate the utility of these formulas, we apply them to charged particle dynamics in a strong magnetic field and magnetic field-line dynamics when the field lines are nearly closed., Comment: 32 pages, submitted to JPP special issue on Hamiltonian systems in plasma physics

The turbulent amplification of cosmic magnetic fields depends upon the material properties of the host plasma. In many hot, dilute astrophysical systems, such as the intracluster medium (ICM) of galaxy clusters, the rarity of particle--particle collisions allows departures from local thermodynamic equilibrium. These departures exert anisotropic viscous stresses on the plasma motions that inhibit their ability to stretch magnetic-field lines. We present a numerical study of the fluctuation dynamo in a weakly collisional plasma using magnetohydrodynamic (MHD) equations endowed with a field-parallel viscous (Braginskii) stress. When the stress is limited to values consistent with a pressure anisotropy regulated by firehose and mirror instabilities, the Braginskii-MHD dynamo largely resembles its MHD counterpart. If instead the parallel viscous stress is left unabated -- a situation relevant to recent kinetic simulations of the fluctuation dynamo and to the early stages of the dynamo in a magnetized ICM -- the dynamo changes its character, amplifying the magnetic field while exhibiting many characteristics of the saturated state of the large-Prandtl-number (${\rm Pm}\gtrsim{1}$) MHD dynamo. We construct an analytic model for the Braginskii-MHD dynamo in this regime, which successfully matches magnetic-energy spectra. A prediction of this model, confirmed by our simulations, is that a Braginskii-MHD plasma without pressure-anisotropy limiters will not support a dynamo if the ratio of perpendicular and parallel viscosities is too small. This ratio reflects the relative allowed rates of field-line stretching and mixing, the latter of which promotes resistive dissipation of the magnetic field. In all cases that do exhibit a dynamo, the generated magnetic field is organized into folds that persist into the saturated state and bias the chaotic flow to acquire a scale-dependent spectral anisotropy., Comment: 62 pages, 25 figures, 1 table, accepted for publication to Journal of Plasma Physics

This white paper submitted for 2020 Decadal Assessment of Plasma Science concerns the importance of multi-spacecraft missions to address fundamental questions concerning plasma turbulence. Plasma turbulence is ubiquitous in the universe, and it is responsible for the transport of mass, momentum, and energy in such diverse systems as the solar corona and wind, accretion discs, planet formation, and laboratory fusion devices. Turbulence is an inherently multi-scale and multi-process phenomenon, coupling the largest scales of a system to sub-electron scales via a cascade of energy, while simultaneously generating reconnecting current layers, shocks, and a myriad of instabilities and waves. The solar wind is humankind's best resource for studying the naturally occurring turbulent plasmas that permeate the universe. Since launching our first major scientific spacecraft mission, Explorer 1, in 1958, we have made significant progress characterizing solar wind turbulence. Yet, due to the severe limitations imposed by single point measurements, we are unable to characterize sufficiently the spatial and temporal properties of the solar wind, leaving many fundamental questions about plasma turbulence unanswered. Therefore, the time has now come wherein making significant additional progress to determine the dynamical nature of solar wind turbulence requires multi-spacecraft missions spanning a wide range of scales simultaneously. A dedicated multi-spacecraft mission concurrently covering a wide range of scales in the solar wind would not only allow us to directly determine the spatial and temporal structure of plasma turbulence, but it would also mitigate the limitations that current multi-spacecraft missions face, such as non-ideal orbits for observing solar wind turbulence. Some of the fundamentally important questions that can only be addressed by in situ multipoint measurements are discussed., Comment: 6 pages, submitted for the Plasma 2020 Decadal Survey

This white paper, submitted for the Plasma 2020 Decadal Survey, concerns the physics of weakly collisional, high-beta plasmas -- plasmas in which the thermal pressure dominates over the magnetic pressure and in which the inter-particle collision time is comparable to the characteristic timescales of bulk motions. This state of matter, although widespread in the Universe, remains poorly understood: we lack a predictive theory for how it responds to perturbations, how it transports momentum and energy, and how it generates and amplifies magnetic fields. Such topics are foundational to the scientific study of plasmas, and are of intrinsic interest to those who regard plasma physics as a fundamental physics discipline. But these topics are also of extrinsic interest: addressing them directly informs upon our understanding of a wide variety of space and astrophysical systems, including accretion flows around supermassive black holes, the intracluster medium (ICM) between galaxies in clusters, and regions of the near-Earth solar wind. Specific recommendations to advance this field of study are discussed., Comment: 6 pages, submitted for the Plasma 2020 Decadal Survey

Using two-dimensional hybrid-kinetic simulations, we explore the nonlinear "interruption" of standing and traveling shear-Alfv\'en waves in collisionless plasmas. Interruption involves a self-generated pressure anisotropy removing the restoring force of a linearly polarized Alfv\'enic perturbation, and occurs for wave amplitudes $\delta B_{\perp}/B_{0}\gtrsim \beta^{\,-1/2}$ (where $\beta$ is the ratio of thermal to magnetic pressure). We use highly elongated domains to obtain maximal scale separation between the wave and the ion gyroscale. For standing waves above the amplitude limit, we find that the large-scale magnetic field of the wave decays rapidly. The dynamics are strongly affected by the excitation of oblique firehose modes, which transition into long-lived parallel fluctuations at the ion gyroscale and cause significant particle scattering. Traveling waves are damped more slowly, but are also influenced by small-scale parallel fluctuations created by the decay of firehose modes. Our results demonstrate that collisionless plasmas cannot support linearly polarized Alfv\'en waves above $\delta B_{\perp}/B_{0}\sim \beta^{\,-1/2}$. They also provide a vivid illustration of two key aspects of low-collisionality plasma dynamics: (i) the importance of velocity-space instabilities in regulating plasma dynamics at high $\beta$, and (ii) how nonlinear collisionless processes can transfer mechanical energy directly from the largest scales into thermal energy and microscale fluctuations, without the need for a scale-by-scale turbulent cascade.

It is shown that low-collisionality plasmas cannot support linearly polarized shear-Alfv\'en fluctuations above a critical amplitude $\delta B_{\perp}/B_{0} \sim \beta^{\,-1/2}$, where $\beta$ is the ratio of thermal to magnetic pressure. Above this cutoff, a developing fluctuation will generate a pressure anisotropy that is sufficient to destabilize itself through the parallel firehose instability. This causes the wave frequency to approach zero, interrupting the fluctuation before any oscillation. The magnetic field lines rapidly relax into a sequence of angular zig-zag structures. Such a restrictive bound on shear-Alfv\'en-wave amplitudes has far-reaching implications for the physics of magnetized turbulence in the high-$\beta$ conditions prevalent in many astrophysical plasmas, as well as for the solar wind at $\sim 1 \mathrm{AU}$ where $\beta \gtrsim 1$., Comment: Accepted for publication in Astrophys. J. Lett

The difference between the guiding center phase-space Lagrangians derived in [J.W. Burby, J. Squire, and H. Qin, Phys. Plasmas {\bf 20}, 072105 (2013)] and [F.I. Parra, and I. Calvo, Plasma Phys. Control. Fusion {\bf 53}, 045001 (2011)] is due to a different definition of the guiding center coordinates. In this brief communication the difference between the guiding center coordinates is calculated explicitly., Comment: 6 pages

We report on the use of the recently-developed Mathematica package \emph{VEST} (Vector Einstein Summation Tools) to automatically derive the guiding center transformation. Our Mathematica code employs a recursive procedure to derive the transformation order-by-order. This procedure has several novel features. (1) It is designed to allow the user to easily explore the guiding center transformation's numerous non-unique forms or representations. (2) The procedure proceeds entirely in cartesian position and velocity coordinates, thereby producing manifestly gyrogauge invariant results; the commonly-used perpendicular unit vector fields $e_1,e_2$ are never even introduced. (3) It is easy to apply in the derivation of higher-order contributions to the guiding center transformation without fear of human error. Our code therefore stands as a useful tool for exploring subtle issues related to the physics of toroidal momentum conservation in tokamaks., Comment: 34 pages

We present a new variational principle for the gyrokinetic system, similar to the Maxwell-Vlasov action presented in Ref. 1. The variational principle is in the Eulerian frame and based on constrained variations of the phase space fluid velocity and particle distribution function. Using a Legendre transform, we explicitly derive the field theoretic Hamiltonian structure of the system. This is carried out with a modified Dirac theory of constraints, which is used to construct meaningful brackets from those obtained directly from Euler-Poincar\'{e} theory. Possible applications of these formulations include continuum geometric integration techniques, large-eddy simulation models and Casimir type stability methods. [1] H. Cendra et. al., Journal of Mathematical Physics 39, 3138 (1998), Comment: 36 pages, 1 figure