Low-beta Plasma Research Articles

Constraints on the accretion properties of quasi-periodic erupters from GRMHD simulations

Some apparently quiescent supermassive black holes (BHs) at centers of galaxies show quasi-periodic eruptions (QPEs) in the X-ray band, the nature of which is still unknown. A possible origin for the eruptions is an accretion disk. However, the properties of such disks are restricted by the timescales of recurrence and the duration of the flares. In this work, we test the possibility that the temporal properties of known QPEs can be explained by accretion from a compact accretion disk with an outer radius out g and we focus on a particular object, GSN 069. We ran several 3D general relativistic magnetohydrodynamic (GRMHD) simulations with the H-AMR code of thin and thick disks and studied how the initial disk parameters such as thickness, magnetic field configuration, magnetization, and Kerr parameter affect the observational properties of QPEs. We show that accretion onto a slowly rotating BH through a small, moderately thin accretion disk with an initially low plasma beta can explain the observed time between outbursts and the lack of evidence for a variable jet emission. In order to form such a disk, the accreting matter should have a low net angular momentum. A potential source for such low angular momentum matter with a quasi-periodic feeding mechanism might be a tight binary of wind-launching stars. Apart from their primary application, our results can also be useful for general studies of systems with small accretion disks, in which evolution occurs very rapidly so that the disks cannot be considered stationary. For such systems, it is important to understand how the initial conditions affect the results.

Self-similar Solutions of Oscillatory Reconnection: Parameter Study of Magnetic Field Strength and Background Temperature

Oscillatory reconnection is a specific type of time-dependent reconnection which involves periodic changes in the magnetic topology of a null point. The mechanism has been reported for a variety of magnetic field strengths and configurations, background temperatures, and densities. All these studies report an oscillation in the current density at the null point, but also report a variety of periods, amplitudes, and overall behaviors. We conduct a parametric study for equilibrium magnetic field strength and initial background temperature, solving two-dimensional resistive magnetohydrodynamic equations around a magnetic X-point. We introduce a parameter space for the ratio of internal to magnetic energy and find self-similar solutions for simulations where this ratio is below 0.1 (which represents a magnetically dominated environment or, equivalently, a low-beta plasma). Self-similarity can be seen in oscillations in the current density at the null (including amplitude and period), ohmic heating, and the temperature generated via reconnection jets. The parameter space of energy ratios also allows us to contextualize previous studies of the oscillatory reconnection mechanism and bring those different studies together into a single unified understanding.

Electron Shock Drift Acceleration at a Low-Mach-number, Low-plasma-beta Quasi-perpendicular Shock

Shock drift acceleration (SDA) plays an important role in generating high-energy electrons at quasi-perpendicular shocks, but its efficiency in low-beta plasmas is questionable. In this article, we perform a two-dimensional particle-in-cell simulation of a low-Mach-number, low-plasma-beta quasi-perpendicular shock, and find that the electron cyclotron drift instability is unstable at the leading edge of the shock foot, which is excited by the relative drift between the shock-reflected ions and the incident electrons. The electrostatic waves triggered by the electron cyclotron drift instability can scatter and heat the incident electrons, which facilitates their escape from the shock’s loss cone. These electrons are then reflected by the shock and energized by SDA. In this way, the acceleration efficiency of SDA at low-plasma-beta quasi-perpendicular shocks is highly enhanced.

A multi-dimensional, robust, and cell-centered finite-volume scheme for the ideal MHD equations

We present a new multi-dimensional, robust, and cell-centered finite-volume scheme for the ideal MHD equations. This scheme relies on relaxation and splitting techniques and can be easily used at high order. A fully conservative version is not entropy satisfying but is observed experimentally to be more robust than standard constrained transport schemes at low plasma beta. At very low plasma beta and high Alfvén number, we have designed an entropy-satisfying version that is not conservative for the magnetic field but preserves admissible states and we switch locally a-priori between the two versions depending on the regime of plasma beta and Alfvén number. This strategy is robust in a wide range of standard MHD test cases, all performed at second order with a classic MUSCL-Hancock scheme.

Effects of wave damping and finite perpendicular scale on three-dimensional Alfvén wave parametric decay in low-beta plasmas

Effects of wave damping and finite perpendicular scale on three-dimensional Alfvén wave parametric decay in low-beta plasmas

Complete quasilinear model for the acceleration-driven lower hybrid drift instability and a computational assessment of its validity.

A complete quasilinear model is derived for the electrostatic acceleration-driven lower hybrid drift instability in a uniform two-species low-beta plasma in which current is perpendicular to the background magnetic field. The model consists of coupled nonlinear velocity space diffusion equationsfor the volume-averaged ion and electron distribution functions. Each species' diffusion coefficient depends on a time-evolving spectral density of the electric-field energy per unit volume and a time-evolving dispersion relation. The dispersion relation is expressed analytically in integral form without the use of asymptotic limits and applies to arbitrary distribution functions, so long as they can be expressed as a function of one velocity coordinate, e.g., f(v_{y}) or f(v_{⊥}). The quasilinear model conserves energy and is complete in that it fully describes the evolution of the distribution functions, including resonant and nonresonant particle-wave interactions, while accounting for distribution-function-dependent mixed-complex frequencies. The quasilinear diffusion model is solved numerically and self-consistently using a Crank-Nicolson temporal discretization and a second-order finite-volume velocity-space discretization. Numerical solutions are compared to nonlinear fourth-order accurate continuum kinetic Vlasov-Poisson simulations. Evolution of electric-field energy, growth rates, distribution functions, and diffusion coefficients are shown to be in agreement with Vlasov simulations. The quasilinear model is shown to predict anomalous transport terms, like resistivity and heating, to within a factor of order unity. Discrepancies between the quasilinear model and Vlasov simulations are assessed and attributed primarily to lack of damping in the quasilinear description and to the use of unperturbed-orbit susceptibilities in the linear theory dispersion relation. The results illuminate the predictive accuracy of the quasilinear model, place approximate bounds on its validity, and provide much needed vetting of quasilinear theory's ability to predict the nonlinear state of a microturbulent plasma.

New Regime of Inertial Alfvén Wave Turbulence in the Auroral Ionosphere.

We investigate a new regime of inertial Alfvén wave turbulence observed in the very low beta plasma of the auroral ionosphere using electric and magnetic field measurements by the TRICE-2 sounding rocket. Combining the observed features of the electric and magnetic field frequency spectra with the linear properties of inertial Alfvén waves, we deduce the path of the anisotropic turbulent cascade through wave vector space. We find a critically balanced cascade through the magnetohydrodynamic scales of the inertial range down to the perpendicular scale of the plasma skin depth, followed by a parallel cascade to the ion inertial length. We infer damping of the cascade by a combination of proton cyclotron damping and electron Landau damping.

Observation of Kinetic Alfvén Waves inside an Interplanetary Coronal Mass Ejection Magnetic Cloud at 1 au

Recent advancements have significantly enhanced our grasp of interplanetary coronal mass ejections (ICMEs) in the heliosphere. These observations have uncovered complex kinematics and structural deformations in ICMEs, hinting at the possible generation of magnetohydrodynamic (MHD) and kinetic-scale waves. While MHD-scale waves in magnetic clouds have been explored, understanding the dynamics of kinetic-scale mode waves remains challenging. This article demonstrates the first in situ observation of kinetic Alfvén waves (KAWs) within an ICME’s magnetic cloud, notably near the heliospheric current sheet–ICME interaction region, close to the reconnection exhaust. Analysis indicates a distinctive negative bump in the estimated normalized magnetic helicity (σ m = −0.38) around the gyrofrequency spread, indicating a right-handed polarization of the wave. Furthermore, examination across flow angle (θ VB) within the frequency domain reveals a specific zone (90°–135°) showcasing negative helicity fluctuations, confirming the presence of KAWs. Moreover, we noted a significant rise in temperature anisotropy in the vicinity, indicating the role of KAWs in plasma heating. Identifying KAW challenges established notions about ordered magnetic clouds and raises questions about energy transfer processes within these structures. This finding opens the door to a deeper understanding of energy transfer mechanisms within traditionally nondissipative regions and invites further exploration of low-beta plasma heating and the interactions between waves and particles in magnetic clouds.

Kinetic numerical analysis of electromagnetic ion cyclotron instability in non-thermal Vasyliunas-Cairns distributed plasmas

Enhanced fluctuations driven by non-thermal features of particle-distributions are reported frequently in the variety of space plasma observations. In the rare-collisional plasmas, these amplified fluctuations scatter the particles in various direction and governs the dynamics of space plasma environments effectively. Electromagnetic ion cyclotron (EMIC) waves usually responsible for low frequency interplanetary magnetic field fluctuations. These are natural emissions in numerous natural environments of plasmas which usually operates underneath the ion/proton cyclotron frequencies. These are identified as left hand circular polarization (L-mode) with a propagation directed towards the ambient magnetic field. Various space missions and in situ measurements unveil the perpendicular temperature anisotropies of non-thermal populations of ions/protons i.e. in heliospheric regions and solar wind. These proton temperature anisotropies excite EMIC instability which in turn the pitch angle scatters the ions and restrained the anisotropy in certain ranges. In Vasyliunas-Cairns distributed hybrid non-thermal electromagnetic proton plasma, the transverse dielectric response function (TDERF) is calculated for L-mode. It is then numerically solved in order to show the impact of non-thermal populations due to non-thermal parameters α and κ on the dispersion and growth rates of EMIC instability in low and high plasma beta β regimes. Possible variation in the real oscillatory and imaginary frequencies spectrum is also analyzed with the variation in the values of other pertinent parameters i.e. temperature anisotropy τ and β. The parametric numerical analysis of the present work has relevance about that plasma phenomena of space regions where non-thermal distributed populations are prevalent.

Ion Kinetics of Plasma Interchange Reconnection in the Lower Solar Corona

The exploration of the inner heliosphere by the Parker Solar Probe has revealed a highly structured solar wind with ubiquitous deflections from the Parker spiral, known as switchbacks. Interchange reconnection (IR) may play an important role in generating these switchbacks, by forming unstable particle distributions that generate wave activity that in turn may evolve to such structures. IR occurs in very low-beta plasmas and in the presence of strong guiding fields. Although IR is unlikely to release enough energy to provide an important contribution to the heating and acceleration of the solar wind, it affects the way the solar wind is connected to its sources, connecting open field lines to regions of closed fields. This “switching on” provides a mechanism by which the plasma near coronal hole boundaries can mix with that trapped inside the closed loops. This mixing can lead to a new energy balance. It may significantly change the characteristics of the solar wind because this plasma is already preheated and can potentially have quite different density and particle distributions. It not only replenishes the solar wind, but also affects the electric field, which in turn affects the energy balance. This interpenetration is manifested by the formation of a bimodal ion distribution, with a core and a beam-like population. Such distributions are indeed frequently observed by the Parker Solar Probe. Here we provide a first step toward assessing the role of such processes in accelerating and heating the solar wind.

Reconnection in a pinch

A recently published analysis of current sheets has updated the classic Harris 1D static solution by considering multiple classes of charged particle trajectories in a generalized and dynamic current sheet. It uses a 1D PIC simulation to describe dynamic pinching and bifurcation of the current sheet. These 1D results strongly suggest that properties of the inflowing plasma, including the plasma beta, have an important effect on the equilibrium thickness of the pinched current sheet. Since 1D studies cannot describe magnetic reconnection, the time appears right to carry such 1D studies over to 2D or 3D simulations to explore current sheet thickness effects on reconnection. The Magnetospheric Multiscale Mission (MMS), with its well-resolved multipoint measurements of collisionless plasma and fields, has found that collisionless reconnection is accompanied by non-adiabatic motions of electrons that only occur in magnetic structures with a narrow scale comparable to electron inertial lengths (de). The recent 1D studies suggest that a plasma pinch to such scales may only occur for inflowing magnetized plasmas with relatively low plasma beta. We conclude that a parametric exploration of simulated and observed reconnection inflow conditions, particularly plasma beta, should shed light on the enablement of reconnection in collisionless plasmas.

Spectrum of kinetic-Alfvén-wave turbulence: intermittency or tearing mediation?

ABSTRACT We investigate the spectral properties of the electromagnetic fluctuations of sub-ion scale turbulence in weakly collisional, low-beta plasmas using a two-field isothermal gyrofluid model. The numerical results strongly support a description of the turbulence as a critically balanced Kolmogorov-like cascade of kinetic Alfvén wave fluctuations, as amended by previous studies to include intermittency effects. The measured universal index of the energy spectra from systems with different flux-unfreezing mechanisms excludes the role of tearing mediation in determining the spectra. The fluctuations remain isotropic in the plane perpendicular to the strong background magnetic fields as they cascade to smaller scales, which explains the absence of tearing mediation. The calculation of high-order, multipoint structure functions of magnetic fluctuations suggests that the intermittent structures have a quasi-2D, sheet-type morphology. These results are useful for explaining recent observations of the spectrum and structure of magnetic and density fluctuations in the solar wind at sub-proton scales, and are relevant for modelling the energy dissipation in a broad range of astrophysical systems.

Electron heating in kinetic-Alfvén-wave turbulence.

We report analytical and numerical investigations of subion-scale turbulence in low-beta plasmas using a rigorous reduced kinetic model. We show that efficient electron heating occurs and is primarily due to Landau damping of kinetic Alfvén waves, as opposed to Ohmic dissipation. This collisionless damping is facilitated by the local weakening of advective nonlinearities and the ensuing unimpeded phase mixing near intermittent current sheets, where free energy concentrates. The linearly damped energy of electromagnetic fluctuations at each scale explains the steepening of their energy spectrum with respect to a fluid model where such damping is excluded (i.e., a model that imposes an isothermal electron closure). The use of a Hermite polynomial representation to express the velocity-space dependence of the electron distribution function enables us to obtain an analytical, lowest-order solution for the Hermite moments of the distribution, which is borne out by numerical simulations.

Compressible Turbulence in the Near-Sun Solar Wind: Parker Solar Probe’s First Eight Perihelia

Many questions remain about the compressibility of solar wind turbulence with respect to its origins and properties. Low plasma beta (ratio of thermal to magnetic pressure) environments allow for the easier generation of compressible turbulence, enabling study of the relationship between density fluctuations and turbulent Mach number. Utilizing Parker Solar Probe plasma data, we examine the normalized proton density fluctuations as a function of turbulent Mach number M t conditioned on plasma beta and cross helicity. With consideration of statistical error in the parameters computed from in situ data, we find a general result that , consistent with both linear-wave theory and nearly incompressible turbulence in an inhomogeneous background field. We compare observational results conditioned on plasma beta and cross helicity with 3D magnetohydrodynamic simulations and observe rather significant similarities with respect to how those parameters affect the proportionality between density fluctuations and turbulent Mach number. This study further investigates the complexity of compressible turbulence as viewed by the density scaling relationship and may help better understand the compressible environment of the near-Sun solar wind.

On the relationship between the multi-region relaxed variational principle and resistive inner-layer theory

We show that the variational energy principle of the multi-region relaxed magnetohydrodynamic (MRxMHD) model can be used to predict finite-pressure linear tearing instabilities. In this model, the plasma volume is sliced into sub-volumes separated by ‘ideal interfaces’, and in each volume the magnetic field relaxes to a Taylor state, where the pressure gradient . The MRxMHD model is implemented in the Stepped-Pressure Equilibrium Code (SPEC) so that the equilibrium solution in each region is computed while preserving the force balance across the interfaces. As SPEC computes the Hessian matrix (a discretized stability matrix), the stability of an MRxMHD equilibrium can also be computed with SPEC. In this article, using SPEC, we investigate the effect of local pressure gradients and the in the vicinity of the resonant surface of a tearing mode. For low-beta plasma, we have been able to illustrate a relationship between the resistive singular-layer theory (Coppi et al 1966 Nucl. Fusion 6 101; Glasser et al 1975 Phys. Fluids 18 875–88) and the MRxMHD model. Within the singular layer, the volume-averaged magnetic helicity and the flux-averaged toroidal flux are shown to be the invariants for the linear tearing modes in SPEC simulations. Our technique to compute MRxMHD stability is first tested numerically in a cylindrical tokamak and its application in toroidal geometry is demonstrated. We demonstrate an agreement between the stability boundary obtained with SPEC simulation and the resistive inner-layer theories.

A drift-kinetic perturbed Lagrangian for low-frequency nonideal MHD applications

We find that the perturbed Lagrangian derived from the drift-kinetic equation in [Porcelli F et al 1994 Phys. Plasmas 1 470] is inconsistent with the ordering for the low-frequency large-scale magnetohydrodynamic (MHD). Here, we rederive the expression for the perturbed Lagrangian within the framework of nonideal MHD using the ordering system for the low-frequency large-scale MHD in a low-beta plasma. The obtained perturbed Lagrangian is consistent with Chen’s gyrokinetic theory [Chen L and Zonca F 2016 Rev. Mod. Phys. 88 015008], where the terms related to the field curvature and gradient are small quantities of higher order and thus negligible. As the perturbed Lagrangian has been widely used in the literature to calculate the plasma nonadiabatic response in low-frequency MHD applications, this finding may have a significant impact on the understanding of the kinetic driving and dissipative mechanisms of MHD instabilities and the plasma response to electromagnetic perturbations in fusion plasmas.

Particle-in-cell simulations of Alfvén wave parametric decay in a low-beta plasma

We study the parametric decay instability of parallel-propagating Alfvén waves in a low-beta plasma using one-dimensional fully kinetic simulations. We focus for the first time on the conversion of the energy stored in the initial Alfvén wave into particle internal energy, and on its partition between particle species. We show that compressible fluctuations generated by the decay of the pump wave into a secondary ion-acoustic mode and a reflected Alfvén wave contribute to the gain of internal energy via two distinct mechanisms. First, the ion-acoustic mode leads nonlinearly to proton trapping and proton phase-space mixing, in agreement with previous work based on hybrid simulations. Second, during the nonlinear stage, a compressible front of the fast type develops at the steepened edge of the backward Alfvén wave leading to a field-aligned proton beam propagating backwards at the Alfvén speed. We find that parametric decay heats preferentially protons, which gain approximately 50 % of the pump wave energy in the form of internal energy. However, we find that electrons are also energized and that they contribute to the total energy balance by gaining 10 % of the pump wave energy. By investigating energy partition and particle heating during parametric decay, our results contribute to the determination of the role of compressible and kinetic effects in wave-driven models of the solar wind.

On the Interpretation of the Scalings of Density Fluctuations from In Situ Solar Wind Observations: Insights from 3D Turbulence Simulations

Solar wind turbulence is often perceived as weakly compressible and the density fluctuations remain poorly understood both theoretically and observationally. Compressible magnetohydrodynamic simulations provide useful insights into the nature of density fluctuations. We discuss a few important effects related to 3D simulations of turbulence and in situ observations. The observed quantities such as the power spectrum and variance depend on the angle between the sampling trajectory and the mean magnetic field due to anisotropy of the turbulence. The anisotropy effect is stronger at smaller scales and lower plasma beta. Additionally, in situ measurements tend to exhibit a broad range of variations, even though they could be drawn from the same population with the defined averages, so a careful averaging may be needed to reveal the scaling relations between density variations and other turbulence quantities such as turbulent Mach number from observations.

Provably Positive Central Discontinuous Galerkin Schemes via Geometric Quasilinearization for Ideal MHD Equations

In the numerical simulation of ideal magnetohydrodynamics (MHD), keeping the pressure and density always positive is essential for both physical considerations and numerical stability. This is however a challenging task, due to the underlying relation between such a positivity-preserving (PP) property and the magnetic divergence-free (DF) constraint as well as the strong nonlinearity of the MHD equations. In this paper, we present the first rigorous PP analysis of the central discontinuous Galerkin (CDG) methods and construct arbitrarily high-order provably PP CDG schemes for ideal MHD. By the recently developed geometric quasilinearization (GQL) approach, our analysis reveals that the PP property of standard CDG methods is closely related to a discrete magnetic DF condition, whose form was unknown prior to our analysis and differs from that for the noncentral discontinuous Galerkin (DG) and finite volume methods in [K. Wu, SIAM J. Numer. Anal., 56 (2018), pp. 2124–2147]. The discovery of this relation lays the foundation for the design of our PP CDG schemes. In the one-dimensional (1D) case, the discrete DF condition is naturally satisfied, and we rigorously prove that the standard CDG method is PP under a condition that can be enforced easily with an existing PP limiter. However, in the multidimensional cases, the corresponding discrete DF condition is highly nontrivial, yet critical, and we analytically prove that the standard CDG method, even with the PP limiter, is not PP in general, as it generally fails to meet the discrete DF condition. We address this issue by carefully analyzing the structure of the discrete divergence terms and then constructing new locally DF CDG schemes for Godunov’s modified MHD equations with an additional source term. The key point is to find out the suitable discretization of the source term such that it exactly cancels out all the terms in the discovered discrete DF condition. Based on the GQL approach, we prove in theory the PP property of the new multidimensional CDG schemes under a CFL condition. The robustness and accuracy of the proposed PP CDG schemes are further validated by several demanding 1D, two-dimensional, and three-dimensional numerical MHD examples, including the high-speed jets and blast problems with very low plasma beta.

Proton and Helium Heating by Cascading Turbulence in a Low-beta Plasma

How ions are energized and heated is a fundamental problem in the study of energy dissipation in magnetized plasmas. In particular, the heating of heavy ions (including 4He2+, 3He2+, and others) has been a constant concern for understanding the microphysics of impulsive solar flares. In this article, via two-dimensional hybrid-kinetic particle-in-cell simulations, we study the heating of helium ions (4He2+) by turbulence driven by cascading waves launched at large scales from the left-handed polarized helium ion cyclotron wave branch of a multi-ion plasma composed of electrons, protons, and helium ions. We find significant parallel (to the background magnetic field) heating for both helium ions and protons due to the formation of beams and plateaus in their velocity distribution functions along the background magnetic field. The heating of helium ions in the direction perpendicular to the magnetic field starts with a lower rate than that in the parallel direction, but overtakes the parallel heating after a few hundreds of the proton gyro-periods due to cyclotron resonances with mainly obliquely propagating waves induced by the cascade of injected helium ion cyclotron waves at large scales. There is, however, little evidence for proton heating in the perpendicular direction due to the absence of left-handed polarized cyclotron waves near the proton cyclotron frequency. Our results are useful for understanding the preferential heating of 3He and other heavy ions in the 3He-rich solar energetic particle events, in which helium ions play a crucial role as a species of background ions regulating the kinetic plasma behavior.