Parallel Magnetic Fluctuations Research Articles

A flexible gyro-fluid system of equations

Gyro-fluid equations are velocity space moments of the gyrokinetic equations. Special gyro-Landau-fluid closures have been developed that include the damping due to kinetic resonances by fitting to the collisionless local plasma response functions. This damping allows for accurate linear eigenmodes to be computed with a relatively low number of velocity space moments compared to the number of velocity quadrature points in gyrokinetic codes. However, none of the published gyro-Landau-fluid closure schemes considers the Onsager symmetries of the resulting quasi-linear fluxes as a constraint. Onsager symmetry guarantees that the matrix of diffusivities is positive definite, an important property for the numerical stability of a transport solver. A two parameter real closure for improving the accuracy of low resolution gyro-fluid equations, which preserves the Onsager symmetry and allows higher velocity space moments, is presented in this paper. The new linear gyro-fluid system (GFS) is used to extend the TGLF quasi-linear transport model so that it can compute the energy and momentum fluxes due to parallel magnetic fluctuations, completing the transport matrix. The GFS equations do not use a bounce average approximation. The GFS equations are fully electromagnetic with general flux surface magnetic geometry, pitch angle scattering for electron collisions, and subsonic equilibrium toroidal rotation. Using GFS eigenmodes in the quasi-linear TGLF model will be shown to yield a more accurate match to fluxes computed by CGYRO turbulence simulations. Prospects for future applications of a quasi-linear theory to new plasma transport regimes and magnetic confinement devices in addition to tokamaks are opened by the flexibility of the GFS eigensolver.

Electromagnetic turbulence in increased β plasmas in the Large Plasma Device

The variation of pressure-gradient-driven turbulence with plasma $\beta$ (up to $\beta \approx 15\,\%$ ) is investigated in linear, magnetized plasma. The magnitude of magnetic fluctuations is observed to increase substantially with increasing $\beta$ . More importantly, parallel magnetic fluctuations are observed to dominate at higher $\beta$ values, with $\delta B_\parallel / \delta B_\perp \approx 2$ and $\delta B / B_0 \approx 1\,\%$ . Parallel magnetic fluctuations are strongly correlated with density fluctuations and the two are observed to be out of phase. The relative magnitude of and cross-phase between density and parallel magnetic field fluctuations are consistent with the dynamic pressure balance ( $P+{B_{0}^2}/{2\mu _0} = \textrm {constant}$ ). A local slab model theory for electromagnetic, modified drift Alfvén waves, including parallel magnetic fluctuations, shows partial agreement with experimental observations.

Examination of stiff ion temperature gradient mode physics in simulations of DIII-D H-mode transport

A systematic evaluation of gyrokinetic and gyrofluid model predictions of ion temperature gradient (ITG) stability and transport using parameters from DIII-D high confinement mode (H-mode) plasmas has been performed. The nonlinear CGYRO code is used to make the gyrokinetic predictions, and the quasilinear TGLF model for the corresponding gyrofluid predictions. The assessments are made at three radii (normalized toroidal flux ρ tor = 0.4, 0.55, and 0.7) in three different plasma scenarios with varying levels of neutral beam heating and torque. For each of the nine cases (3 radii × 3 scenarios) considered, ITG turbulence is found to be the dominant long-wavelength instability and transport mechanism. The inclusions of both transverse magnetic fluctuations and dynamic fast beam ions are stabilizing for all cases considered, with strongest effects seen at ρ or = 0.4 where the fast ion population and normalized plasma pressure β = 2μ 0 nT/B 2 are highest. The further inclusion of parallel magnetic fluctuations does not have a meaningful impact on the ITG turbulence in these scenarios, but does destabilize (in combination with fast ions) new high-frequency instabilities at ρ tor = 0.4 in the high power scenarios. In each case the linear and nonlinear ITG critical gradients are predicted to be lower than the measured ITG scale lengths and their associated uncertainties. Inclusion of equilibrium flow shear in the transport predictions generally leads to an upshift in effective critical gradient rather than a qualitative change in the predicted stiffness, with stronger responses typically seen in the gyrokinetic predictions than in the gyrofluid results. However, in most cases these upshifted gradients still remain below the measured values and their uncertainties. Although the predicted critical gradients are below the measured gradients, both models predicted flux-matching gradients consistent with measured values in six of the nine cases considered, with no clear systematic over- or underprediction. Thus, while the experimental ion temperature profiles do not appear to be closely pinned to the ITG critical gradient, both gyrokinetic and gyrofluid models are able to accurately match the measured gradients reasonably well in most cases.

Turbulence Spectra of Electron Density and Magnetic Field Fluctuations in the Local Interstellar Medium

Abstract We present the turbulence spectra of magnetic and electron density fluctuations in situ measured by Voyager 1 in the local interstellar medium from 2012 to 2019. The magnetic spectrum shows a Kolmogorov power law with a one-dimensional power-law index −5/3 at mk ≤ 10−8.8, where k is a wavenumber and m is the unit meter. A bulge of enhanced magnetic power is found at mk = 10−8.8–10−8.2. Meanwhile, the electron density spectrum also shows a Kolmogorov power law with a one-dimensional power-law index −5/3 in the inertial range. A bulge of enhanced power is found around the kinetic scales of mk ≈ 10−5–10−1. Based on the observational data, the relationships between the outer scale of the turbulent system and the powers of electron density and magnetic fluctuations are obtained. We then calculate the spectra locally for six individual time periods, within which the electron density and magnetic fluctuations are simultaneously observed. It is found that the power of perpendicular magnetic fluctuations is usually higher than that of parallel magnetic fluctuations, which indicates the dominance of Alfvén waves in turbulence spectrum. Part of the observed turbulence spectra reveal that the normalized parallel magnetic power exhibits a much higher intensity than the normalized electron density power in the local interstellar medium of low to moderate plasma beta (β = 0.1–0.8). This dominance in the parallel magnetic power cannot be explained by the linear magnetohydrodynamic modes alone and may be associated with the arc/spherically polarized Alfvén mode.

Magnetic Reconnection as a Driver for a Sub-ion-scale Cascade in Plasma Turbulence

Abstract A new path for the generation of a sub-ion-scale cascade in collisionless space and astrophysical plasma turbulence, triggered by magnetic reconnection, is uncovered by means of high-resolution two-dimensional hybrid-kinetic simulations employing two complementary approaches, Lagrangian and Eulerian, and different driving mechanisms. The simulation results provide clear numerical evidence that the development of power-law energy spectra below the so-called ion break occurs as soon as the first magnetic reconnection events take place, regardless of the actual state of the turbulent cascade at MHD scales. In both simulations, the reconnection-mediated small-scale energy spectrum of parallel magnetic fluctuations exhibits a very stable spectral slope of , whether or not a large-scale turbulent cascade has already fully developed. Once a quasi-stationary turbulent state is achieved, the spectrum of the total magnetic fluctuations settles toward a spectral index of in the MHD range and of at sub-ion scales.

HIGH-RESOLUTION HYBRID SIMULATIONS OF KINETIC PLASMA TURBULENCE AT PROTON SCALES

ABSTRACT We investigate properties of plasma turbulence from magnetohydrodynamic (MHD) to sub-ion scales by means of two-dimensional, high-resolution hybrid particle-in-cell simulations. We impose an initial ambient magnetic field perpendicular to the simulation box, and we add a spectrum of large-scale magnetic and kinetic fluctuations with energy equipartition and vanishing correlation. Once the turbulence is fully developed, we observe an MHD inertial range, where the spectra of the perpendicular magnetic field and the perpendicular proton bulk velocity fluctuations exhibit power-law scaling with spectral indices of − 5 / 3 ?> and − 3 / 2 , ?> respectively. This behavior is extended over a full decade in wavevectors and is very stable in time. A transition is observed around proton scales. At sub-ion scales, both spectra steepen, with the former still following a power law with a spectral index of ∼ − 3 . ?> A − 2.8 ?> slope is observed in the density and parallel magnetic fluctuations, highlighting the presence of compressive effects at kinetic scales. The spectrum of the perpendicular electric fluctuations follows that of the proton bulk velocity at MHD scales, and flattens at small scales. All these features, which we carefully tested against variations of many parameters, are in good agreement with solar wind observations. The turbulent cascade leads to on overall proton energization with similar heating rates in the parallel and perpendicular directions. While the parallel proton heating is found to be independent on the resistivity, the number of particles per cell, and the resolution employed, the perpendicular proton temperature strongly depends on these parameters.

Enhanced magnetic reconnection in the presence of pressure gradients

Magnetic reconnection in the presence of background pressure gradients is studied, with special attention to parallel (compressional) magnetic fluctuations. A process is reported that reconnects fields through coupling of drift-wave-type instabilities with current sheets. Its time scale is set not by the reconnecting field but by inhomogeneities of the background density or temperature. The observed features can be attributed to a pressure-gradient-driven linear instability which interacts with the reconnecting system but is fundamentally different from microtearing. In particular, this mode relies on parallel magnetic fluctuations and the associated drift. For turbulent reconnection, similar or even stronger enhancements are reported. In the solar corona, this yields a critical pressure gradient scale length of about 200 km below which this new process becomes dominant over the tearing instability.

WHISTLER TURBULENCE WAVEVECTOR ANISOTROPIES: PARTICLE-IN-CELL SIMULATIONS

Two-dimensional electromagnetic particle-in-cell simulations of whistler turbulence in a magnetized, homogeneous, collisionless plasma of electrons and protons are carried out. Enhanced magnetic fluctuation spectra are initially imposed at relatively long wavelengths, and, as in previous such simulations, the temporal evolution shows a forward cascade of magnetic fluctuation energy to shorter wavelengths, with more fluctuation energy at a given wavenumber perpendicular to B o than at the same wavenumber parallel to the background field. The new result here is that the wavevector anisotropy is very different for each of the three components of the fluctuating magnetic field. Here, ∥ denotes the direction parallel to the background magnetic field B o , ⊥ indicates the direction perpendicular to B o and in the simulation plane, and the symbol ⊥⊥ denotes the direction perpendicular to both B o and the simulation plane. The parallel magnetic fluctuations show more energy at than at , whereas the perpendicular in-plane magnetic fluctuations show more energy at than at . Finally, the out-of-plane magnetic fluctuations, , strongly prefer to propagate in the direction.

Identification of low‐frequency magnetosheath waves

Four low‐frequency modes may propagate in a high‐beta, nearly bi‐Maxwellian plasma, the magnetosonic, Alfvén, ion acoustic, and mirror modes. This study uses a procedure based on linear Vlasov theory for the identification of these modes by use of transport ratios, dimensionless ratios of the fluctuating field and plasma quantities. A single parameter, the mode deviation, is calculated which characterizes the difference between the theoretical transport ratios of a particular mode and the observed ratios. As well as determining the mode that best describes the observed fluctuations, it gives us a measure of whether or not the resulting identification is unique. Unfortunately, a unique identification is not always possible because of problems discussed herein. One problem is that the parallel phase ratio (related to the phase angle between density and parallel magnetic fluctuations) is often not well defined. Using the plasma and magnetic field data gathered by the Active Magnetospheric Particle Tracer Explorers/Ion Release Module spacecraft, we calculate the mode deviations and identify the modes observed in the magnetosheath. The quasi‐perpendicular (with wave vector at a large angle to the background magnetic field) mirror mode is clearly identified in the inner (close to the magnetopause) and middle magnetosheath. The quasi‐parallel mirror mode may be observed in the inner magnetosheath, but that identification is not certain. Alfven‐like modes are observed for one event in the outer magnetosheath (near the bow shock) and are probably observed in two others.

Ion thermalization in quasi‐perpendicular shocks involving reflected ions

Ion thermalization mechanisms downstream of the quasi‐perpendicular Earth's bow shock are examined by means of plasma and magnetic field data from the AMPTE/IRM spacecraft which include three‐dimensional ion distributions, plasma fluid parameters derived every ∼4.3 s, and spectra of transverse and parallel magnetic fluctuations up to 16 Hz. The objects studied in detail are low‐Mach number, low‐β shocks in which reflected‐gyrating ions are present and contribute to the downstream ion temperature but where processes beyond the ramp take place slowly, so that the basic phenomenology becomes apparent. In MHD terms, most of these shocks qualify as marginally critical. Downstream of the ramp, the initially separated core and ring ions slowly merge into a joint, less anisotropic distribution possessing a high‐energy tail. The ion temperature ratio, T⊥/T∥, is high not only in the shock foot and ramp but also within some distance downstream; its speed of decline rises and the residual level lessens with increasing β. The ions diffuse about equally fast in energy and in pitch angle. An asymmetry of the distributions with respect to the field direction is present when the shock is slightly oblique. It decays only slowly, which might indicate that the pitch angle diffusion rate near zero pitch angle is reduced. Low‐frequency electromagnetic waves are present below the proton gyrofrequency; they are characterized by strong left‐hand‐polarized emissions and a low level of parallel fluctuations except very close to the shock. The left‐hand emissions are often concentrated into a narrow frequency band but sometimes they exhibit a double‐humped structure. Waves and ion distributions approach a slowly varying equilibrium some distance downstream of the shock. After extending the analysis to one supercritical shock representing the majority of bow shock encounters, we conclude that our deductions are more generally valid, although the thermalization is faster, usually, and appears to involve nonlinear processes which tend to obscure most of the features noted.