MHD Model Research Articles

Global Strong Solution to the Cauchy Problem of One-dimensional Viscous Two-fluid MHD Model

Global Strong Solution to the Cauchy Problem of One-dimensional Viscous Two-fluid MHD Model

Investigation of the poloidal magnetic flux at the PF-3 plasma focus within the framework of the program of laboratory simulation of astrophysical jets

Astrophysical jets are collimated plasma outflows observed in diverse astrophysical settings covering seven decades of spatial scale and twenty decades of power, which, nevertheless, share many common features. This similarity over wide range of scales indicates a common core of physics underlying this phenomenon, leading to considerable interest in observational, theoretical and numerical studies. Laboratory astrophysics experiments for simulating astrophysical jets are premised on this common core of physics responsible for multi-scale similarity of jets remaining valid down to laboratory spatial scales of millimeters. Jets formed after the disassembly of the non-cylindrical z-pinch formed in a plasma focus installation have recently been subjects of observational studies. They offer an important complementarity to the main lines of investigations in two respects. Firstly, the multi-faceted role of gravity, radiation, nuclear reactions and related astrophysics is eliminated retaining only a rapid implosion of a compact plasma object in a magnetohydrodynamic environment as a common feature. Secondly, observations can be made using techniques of laboratory plasma diagnostics. In this paper, we report preliminary results regarding presence of poloidal magnetic flux associated with the jets lasting long after the pinch disassembly. This is significant in the context of uncertainty regarding the origin of poloidal magnetic field postulated in several MHD models of astrophysical jet phenomena. Evidence indicating presence of a radial component of electric field suggests existence of plasma rotation as well. These results suggest that more refined experiments can provide insights into the astrophysical jetting phenomena not available from observational astronomy techniques.

Effects of Injected Current Streams on MHD Equilibrium Reconstruction of Local Helicity Injection Plasmas in a Spherical Tokamak

Open field line currents are intrinsic to DC helicity injection plasma startup and pose a challenge for inferring the plasma equilibrium with standard reconstruction analysis. Local helicity injection (LHI) is a type of DC helicity injection which uses small, modular current sources to drive force-free current along helical field lines to produce tokamak plasmas. MHD modeling and magnetic measurements during LHI indicate the injected current streams remain coherent as helical structures on the outboard edge of a core toroidal plasma that is tokamak-like in a toroidally averaged sense. To extract core plasma equilibrium properties, external magnetic diagnostics corrected for contributions from the injected current streams are fitted by a standard Grad-Shafranov equilibrium code. An iterative approach for estimating and subtracting the stream contributions from the diagnostic signals is described and applied to a model equilibrium database to reduce systematic errors introduced by the streams. Convergence is usually attained with 2 to 4 iterations, with derived equilibrium parameters matching the prescribed axisymmetric core values to within estimated experimental uncertainties. Accurate recovery of core parameters occurs when the ratio of the net toroidal windup current from the streams to the core plasma current is less than 0.2, which is typically satisfied in most experiments.

MHD simulations of astrophysical and laboratory jets under different magnetic field configurations

This paper presents the results of MHD simulations of astrophysical and laboratory supersonic jets under a superposition of poloidal (Br, Bz) and toroidal (Bϕ) magnetic fields. It is shown that the escaping matter is quickly collimated by the magnetic field. A shock wave of an elongated shape is formed, which moves from the target to the boundary of the chamber, leaving behind a stable flow. A periodic shock wave structure is observed inside the main conical expanding shock wave. It is shown that the toroidal component of the magnetic field remains in the region throughout the entire calculation and plays a role in the collimation of the flow. The poloidal magnetic field decreases in the region of the jet cone, but remains in the simulation region throughout the calculation and also participates in flow collimation. Thus, both components Bz and Bϕ take part in the collimation of the flow by the magnetic field. The width of the jet and the opening angle of the cone Ɵ depend on the magnitude of the magnetic field induction. As the field increases, the jet becomes narrower and the cone angle decreases. Initially, we do not specify the rotation of the jet Ω. However, due to the presence of the Bϕ field, the substance acquires angular velocity and twists along the z axis. The simulation results are in agreement with laboratory jets arising in the experiment at the Neodymium laser installation, and with the previously obtained results of MHD modeling of jet formation separately, in poloidal or toroidal magnetic field.

Comprehensive Comparison of Two Global Multi‐Species MHD Models of Mars

AbstractUnderstanding the interaction between Mars and the solar wind is crucial for comprehending the atmospheric evolution and climate change on Mars. To gain a comprehensive understanding of the Martian plasma environment, global numerical simulations are essential in addition to spacecraft observations. However, there are still discrepancies among different simulation models. This study investigates how these discrepancies stem from the considered physical processes and numerical implementations. We compare two global multispecies MHD models: the “Sun model” based on the BATS‐R‐US code and the “Sakata model” based on a newly developed multifluid model MAESTRO. By employing the same typical upstream conditions and the same neutral atmosphere for current Mars, along with similar numerical implementations such as inner boundary conditions, we obtain simulation results that exhibit unprecedented agreement between the two models. The dayside results are nearly identical, especially along the subsolar line, indicating the robustness of MHD models to predict dayside interaction under given upstream conditions and ionosphere assumptions. The escape rates of planetary ions are also in good agreement. However, discrepancies remain in the terminator and nightside regions. Detailed numerical implementations, including inner boundary conditions, magnetic field divergence control methods, and radial resolutions, are shown to influence certain aspects of the results greatly, such as magnetotail configuration and ion diffusion.

Dust-evacuated Zones near Massive Stars: Consequences of Dust Dynamics on Star-forming Regions

Stars form within dense cores composed of both gas and dust within molecular clouds. However, despite the crucial role that dust plays in the star formation process, its dynamics is frequently overlooked, with the common assumption being a constant, spatially uniform dust-to-gas ratio and grain size spectrum. In this study, we introduce a set of radiation-dust-magnetohydrodynamic simulations of star-forming molecular clouds from the STARFORGE project. These simulations expand upon the earlier radiation MHD models, which included cooling, individual star formation, and feedback. Notably, they explicitly address the dynamics of dust grains, considering radiation, drag, and Lorentz forces acting on a diverse size spectrum of live dust grains. We find that once stars exceed a certain mass threshold (∼2 M ⊙), their emitted radiation can evacuate dust grains from their vicinity, giving rise to a dust-suppressed zone of size ∼100 au. This removal of dust, which interacts with gas through cooling, chemistry, drag, and radiative transfer, alters the gas properties in the region. Commencing during the early accretion stages and preceding the main-sequence phase, this process results in a mass-dependent depletion in the accreted dust-to-gas (ADG) mass ratio within both the circumstellar disk and the star. We predict that massive stars (≳10 M ⊙) would exhibit ADG ratios that are approximately 1 order of magnitude lower than that of their parent clouds. Consequently, stars, their disks, and circumstellar environments would display notable deviations in the abundances of elements commonly associated with dust grains, such as carbon and oxygen.

Coronal magnetic field and emission properties of small-scale bright and faint loops in the quiet Sun

Context. The present study provides statistical information on the coronal magnetic field and intensity properties of small-scale bright and faint loops in the quiet Sun. Aims. We aim to quantitatively investigate the morphological and topological properties of the coronal magnetic field in bright and faint small-scale loops, with the former known as coronal bright points (CBPs). Methods. We analyse 126 small-scale loops of all sizes using quasi-temporal imaging and line-of-sight magnetic field observations. These observations are taken by the Atmospheric Imaging Assembly (AIA) in the Fe XII 193 Å channel and the Helioseismic Magnetic Imager (HMI) on board the Solar Dynamics Observatory. We employ a recently developed automatic tool that uses a linear magneto-hydro-static (LMHS) model to compute the magnetic field in the solar atmosphere and automatically match individual magnetic field lines with small-scale loops. Results. For most of the loops, we automatically obtain an excellent agreement of the magnetic field lines from the LMHS model and the loops seen in the AIA 193 Å channel. One stand-out result is that the magnetic field is non-potential. We obtain the typical ranges of loop heights, lengths, intensities, mean magnetic field strength along the loops and at loop tops, and magnetic field strength at loop footpoints. We investigate the relationship between all those parameters. We find that loops below the classic chromospheric height of 1.5 Mm are flatter, suggesting that non-magnetic forces (one of which is the plasma pressure) play an important role below this height. We find a strong correlation (Pearson coefficient of 0.9) between loop heights and lengths. An anti-correlation is found between the magnetic field strength at loop tops and loop heights and lengths. The average intensity along the loops correlates stronger with the average magnetic field along the loops than with the field strength at loop tops. Conclusions. The latter correlation indicates that the energy release in the loops is more likely linked to the average magnetic field along the loops than the field strength on the loop tops. In other words, the energy is probably released all along the loops, but not just at the loop top. This result is consistent with a recent benchmarking radiative 3D MHD model.

The Impact of the 8–10 March 2012 Geomagnetic Storm on Inner Zone Protons as Measured by Van Allen Probes

AbstractThe Relativistic Electron Proton Telescope (REPT) instrument on the Van Allen Probes observed a double‐peaked inner zone proton population throughout the 7 year lifetime of the mission. M. Hudson et al. (2023) showed that a strong SEP event accompanied by a CME‐shock in early March 2012 provided the Solar Energetic Proton (SEP) source for the higher L trapped proton population, which then diffused radially inward to be observed by REPT at . The study followed trajectories of SEP protons launched isotropically from a sphere at 7 Re for 2.5 hr in fields calculated by the LFM‐RCM global MHD model, which includes electric fields needed to model the transport and trapping of the protons by the shock, and then a radial diffusion simulation was run for 2 years using the result from the test‐particle simulation as the initial condition. The simulation result was compared with REPT measurement in November 2013 and showed reasonable agreement. However, the simulation overestimated the Phase Space Density by a factor of four due to lack of field line curvature scattering during the storm in the model. In this study, a test‐particle simulation is performed for 2 days following the injection and trapping of protons in March 2012 using TS05 fields to simulate the field line curvature scattering of the trapped SEP due to the buildup of the ring current during the geomagnetic storm. The resulting sample distribution was then weighted using the flux at the end of the two‐hour MHD‐test particle simulation. A radial diffusion simulation is then run using the initial profile that included the loss effect, with improved comparison with REPT measurements after 2 years.

Modelling non-radially propagating coronal mass ejections and forecasting the time of their arrival at Earth

We present the study of two solar eruptive events observed on December 7 2020 and October 28 2021. Both events were associated with full halo coronal mass ejections (CMEs) and flares. These events were chosen because they show a strong non-radial direction of propagation in the low corona and their main propagation direction observed in the inner heliosphere is not fully aligned with the Sun-Earth line. This characteristic makes them suitable for our study, which aims to inspect how the non-radial direction of propagation in the low corona affects the time of CMEs’ arrival at Earth. We reconstructed the CMEs using SOHO/LASCO and STEREO/COR observations and modelled them with the 3D MHD model EUHFORIA and the cone model for CMEs. In order to compare the accuracy of forecasting the CME and the CME-driven shock arrival time at Earth obtained from different methods, we also used so-called type II bursts, radio signatures of associated shocks, to find the velocities of the CME-driven shocks and forecast the time of their arrival at Earth. Additionally, we estimated the CME arrival time using the 2D CME velocity obtained from the white light images. Our results show that the lowest accuracy of estimated CME Earth arrival times is found when the 2D CME velocity is used (time difference between observed and modelled arrival time, Δt ≈ −29 h and −39 h, for the two studied events, respectively). The velocity of the type II radio bursts provides somewhat better – but still not very accurate – results (Δt ≈ +21 h and −29 h, for the two studied events, respectively). Employing, as an input to EUHFORIA, the CME parameters obtained from the graduated cylindrical shell (GCS) fittings at consequently increasing heights, results in a strongly improved accuracy of the modelled CME and shock arrival time; Δt changes from 20 h to 10 min in the case of the first event, and from 12 h to 30 min in the case of the second one. This improvement shows that when we increased the heights of the GCS reconstruction we accounted for the change in the propagation direction of the studied CMEs, which allowed us to accurately model the CME flank encounter at Earth. Our results show the great importance of the change in the direction of propagation of the CME in the low corona when modelling CMEs and estimating the time of their arrival at Earth.

Three-dimensional transient modeling and simulation of high-current multi-component vacuum arc under transverse magnetic field

This paper established a three-dimensional transient MHD model of a high-current multi-component vacuum arc under a transverse magnetic field (TMF) to simulate the dynamic characteristics of plasma parameters in the uniform motion mode of a contracted arc under lower TMF. The model considered the ionization–recombination process among the multi-components and used the P1 model to calculate the thermal radiation losses. The simulation results show that the ion number density of The TMF arc is on the order 1024 m−3, and when the plasma temperature reaches 4.3 eV, the effects of thermal radiation cannot be ignored. The majority of the plasma from the cathode and anode undergo acceleration and then deceleration before finally intersecting at the center of the arc, creating an extreme value of the density and the pressure, where a large amount of kinetic energy is converted into internal energy. The arc will be bent and deflected under the action of the ampere force, and the deflection of Cu3+ is especially obvious. The TMF affects the collision strength of the jet in the intersection area and, thus, affects the ion density, in which the change of Cu2+ is dominant. The ionization–recombination process of ions is mainly determined by the electron temperature, which is affected by the arc current. As the current decreases, Cu1+ increases and Cu2+ and Cu3+ decrease, and the change in ionization rate is the main reason for the change in the proportion of each ionic component; the heat flux density to the anode and cathode is on the order of 1010 W/m2, which heats the front of the arc and ensures the stable movement of the arc. Meanwhile, due to the high ion number density, the ion heat flux accounts for the main part of the heat flux, and the anode exhibits a higher proportion of ion heat flux.

Non-linear MHD modelling of transients in tokamaks: a review of recent advances with the JOREK code

Abstract Transient MHD events like edge localized modes (ELMs) or disruptions are a concern for magnetic confinement fusion power plants. Research with the MHD code JOREK towards understanding control of such instabilities is reviewed here. Experimental validation for unmitigated vertical displacement events (VDEs) progressed. The mechanism of vertical force mitigation by impurity injection was identified. Two-way eddy current coupling to CARIDDI was completed. Shattered pellet injection (SPI) was simulated in JET, KSTAR and ASDEX Upgrade (AUG) and ITER. Benign runaway electron (RE) beam termination in JET and ITER was studied. Coupling of kinetic REs to the MHD is ongoing and a virtual RE synchrotron radiation diagnostic was developed. Regarding pedestal physics, regimes devoid of large ELMs in AUG were simulated and predictive JT60-SA simulations are ongoing. For ELM suppression by resonant magnetic perturbations (RMPs), AUG, ITER and EAST simulations were performed. A free boundary RMP model was validated against experiments. Evidence for penetrated magnetic islands at the pedestal top based on AUG experiments and simulations was found. Simulations of the naturally ELM-free quiescent H-mode (QH) in AUG and HL-3 show external kink mode formation prevents pedestal build-up towards an ELM within windows of the edge safety factor. With kinetic neutral particles, high field side high density (HFSHD) formation in ITER was simulated and with kinetic impurities, tungsten transport in AUG RMP plasmas was studied. To capture turbulent transport, electro-static full-f PiC models for ion temperature gradient (ITG) and trapped electron modes (TEM) were established and benchmarked. Application to RMP plasmas shows enhanced turbulence in comparison to unperturbed states. Energetic particle (EP) interactions with MHD were studied. Flux-pumping that prevents the safety factor on axis from dropping below unity was simulated. First non-linear stellarator applications include current relaxation in l=2 stellarators, while verification for advanced stellarators progresses.

Nonlinear MHD modeling of neon doped shattered pellet injection with JOREK and its comparison to experiments in KSTAR

Abstract 3D nonlinear MHD simulations of neon-doped single shattered pellet injection (SPI) conducted with the JOREK code reveal rich physics during SPI-induced disruptions in KSTAR. In the early phase, pressure-driven modes dominate, and the perturbation of the plasma current is largely consistent with the perturbation of the Pfirsch–Schlüter current. As shards reach the q = 1 surface, resistive current perturbations by helical electron cooling start to dominate, and the electron temperature in the core begins to collapse with convective mixing of the density driven by the internal 1 / 1 kink mode. The confinement of the plasma is later completely destroyed as a cold bubble convects into the core via quasi-interchange mode. Comparisons with available experimental data demonstrate qualitative agreements between JOREK results and experiments, and possible reasons for deviations are discussed.

From eruption to post-flare rain: A 2.5D MHD model

From eruption to post-flare rain: A 2.5D MHD model

Global Environmental Constraints on Magnetic Reconnection at the Magnetopause From In Situ Measurements

AbstractProgress in locating the X‐line on the magnetopause beyond the atypical due south interplanetary magnetic field (IMF) condition is hampered by the fact that the global plasma and field spatial distributions constraining where reconnection could develop on the magnetopause are poorly known. This work presents global maps of the magnetic shear, current density and reconnection rate, on the global dayside magnetopause, reconstructed from two decades of measurements from Cluster, Double Star, THEMIS and MMS missions. These maps, generated for various IMF and dipole tilt angles, offer a unique comparison point for models and observations. The magnetic shear obtained from vacuum magnetostatic draping is shown to be inconsistent with observed shear maps for IMF cone angles in 12.5° ± 2.5° ≤ |θco| ≤ 45° ± 5°. Modeled maximum magnetic shear lines fail to incline toward the equator as the IMF clock angle increases, in contrast to those from observations and MHD models. Reconnection rate and current density maps are closer together than they are from the shear maps, but this similarity vanishes for increasingly radial IMF orientations. The X‐lines maximizing the magnetic shear are the only ones to sharply turns toward and follow the anti‐parallel ridge at high latitude. We show the behavior of X‐lines with varying IMF clock and dipole tilt angles to be different as the IMF cone angle varies. Finally, we discuss a fundamental disagreement between X‐lines maximizing a given quantity on the magnetopause and predictions of local X‐line orientations.

The Effect of the Interplanetary Magnetic Field Clock Angle and the Latitude Location of the Intense Crustal Magnetic Field on the Ion Escape at Mars: An MHD Simulation Study

AbstractIn this paper, using a three‐dimensional multifluid MHD model, we studied the effects of the interplanetary magnetic field (IMF) clock angle and the latitude position of the intense crustal magnetic field (ICMF) on the escape of ions O+, , and at Mars. The main results are as follows: (a) The IMF clock angle affects the ion escape at Mars. When the ICMF is on the dayside, the ion escape rate reaches a maximum at the IMF clock angles close to 60°–90° and a minimum at the IMF clock angles close to 120°–150°, because the ICMF can change the topology of the magnetic field and affect the interaction between the solar wind and Mars. The difference between the maximum and minimum ion escape rates due to the IMF clock angle can reach over 50%. (b) Compared with the −ESW hemisphere, the escape flux of and in the +ESW hemisphere is more significant. However, O+ generally has a larger escape flux in the −ESW hemisphere. The different results in the ±ESW hemispheres might be due to the larger distribution of the hot oxygen corona, which changes the flow pattern of O+. (c) The latitude location of the ICMF can also affect the ion escape. When the ICMF is on the dayside, as the subsolar point varies from 25°S to 25°N, that is, the intense crustal magnetic field position keeps shifting southward, the ion escape rate shows a gradual increase.

Observations and Model of Subauroral Sporadic E Layer Irregularities Driven by Turning Shears and Dynamic Instability

AbstractObservations of coherent scatter from patchy sporadic E layers in the subauroral zone made with a 30‐MHz coherent scatter radar imager are presented. The quasiperiodic (QP) echoes are similar to what has been observed at middle latitudes but with some differences. The echoes arise from bands of scatterers aligned mainly northwest to southeast and propagating to the southwest. A notable difference from observations at middle latitudes is the appearance of secondary irregularities or braids oriented obliquely to the primary bands and propagating mainly northward along them. We present a spectral simulation of the patchy layers that describes neutral atmospheric dynamics with the incompressible Navier Stokes equations and plasma dynamics with an extended MHD model. The simulation is initialized with turning shears in the form of an Ekman spiral. Ekman‐type instability deforms the sporadic E layer through compressible and incompressible motion. The layer ultimately exhibits both the QP bands and the braids, consequences mainly of primary and secondary neutral dynamic instability. Vorticity due to dynamic instability is an important source of structuring in the sporadic E layer.

Going Beyond the MHD Approximation: Physics-based Numerical Solution of the CGL Equations

We present a new numerical model for solving the Chew–Goldberger–Low system of equations describing a bi-Maxwellian plasma in a magnetic field. Heliospheric and geospace environments are often observed to be in an anisotropic state with distinctly different parallel and perpendicular pressure components. The Chew–Goldberger–Low (CGL) system represents the simplest leading order correction to the common isotropic MHD model that still allows the incorporation of the latter’s most desirable features. However, the CGL system presents several numerical challenges: the system is not in conservation form, the source terms are stiff, and unlike MHD, it is prone to a loss of hyperbolicity if the parallel and perpendicular pressures become too different. The usual cure is to bring the parallel and perpendicular pressures closer to one another, but that has usually been done in an ad hoc manner. We present a physics-informed method of pressure relaxation based on the idea of pitch-angle scattering that keeps the numerical system hyperbolic and naturally leads to zero anisotropy in the limit of very large plasma beta. Numerical codes based on the CGL equations can, therefore, be made to function robustly for any magnetic field strength, including the limit where the magnetic field approaches zero. The capabilities of our new algorithm are demonstrated using several stringent test problems that provide a comparison of the CGL equations in the weakly and strongly collisional limits. This includes a test problem that mimics the interaction of a shock with a magnetospheric environment in 2D.

Time Sequence of Magnetospheric Responses to a Southward IMF Turning

AbstractWe use MHD simulations to study the time sequence of magnetospheric responses to a synthetic event with a southward interplanetary magnetic field (IMF) turning. The onset of dayside magnetopause reconnection launches a weak rarefaction wave and sunward flow in the equatorial magnetosphere simultaneously with a tailward flow through the polar cap. This convection results in the accumulation of magnetic flux in the tail lobes and thinning of the tail current layer which provides favorable conditions for the onset of nightside reconnection. The onset of nightside reconnection about 40 min later closes the Dungey convection cycle, resulting in a second increase in the sunward flow in the equatorial plane. Variations of the magnetopause standoff distance as well as the size of the polar cap (PC) may indicate the onsets of the dayside and nightside reconnections. We compare the results of two MHD models and discuss their differences.

Calculation of toroidal Alfvén eigenmode mode structure in general axisymmetric toroidal geometry

A workflow is developed based on the ideal MHD model to investigate the linear physics of various Alfvén eigenmodes in general axisymmetric toroidal geometry by solving the coupled shear Alfvén wave (SAW) and ion sound wave (ISW) equations in ballooning space. The model equations are solved by the FALCON code in the singular layer, and the corresponding solutions are then taken as the boundary conditions for calculating parallel mode structures in the whole ballooning space. As an application of the code, the frequencies and mode structures of toroidal Alfvén eigenmode (TAE) are calculated in the reference equilibria of the Divertor Tokamak Test facility with positive and negative triangularities, respectively. As typical result for reactor relevant plasma conditions, which are strongly triangular in the outer core region where magnetic shear is of order unity, we show that the triangularity effect on TAE is generally small. Furthermore, by properly handling the boundary conditions, we demonstrate finite TAE damping due to coupling with the local acoustic continuum and find that the damping rate is small for typical plasma parameters.

Challenges in Forecasting the Evolution of a Distorted CME Observed During the First Close Solar Orbiter Perihelion

Coronal Mass Ejections (CMEs), drivers of the most severe Space Weather disturbances, are often assumed to evolve self-similarly during their propagation. However, open magnetic field structures in the corona, leading to higher-speed streams in the ambient solar wind, can be source of strong distortions of the CME front. In this paper, we investigate a distorted and Earth-directed CME observed on 2022 March 25 combining three remote sensing with three in situ observatories at different heliocentric distances (from 0.5 to 1 au). Near quadrature observations by Solar Orbiter and the Solar Terrestrial Relations Observatory revealed a distortion of the CME front in both latitude and longitude, with Solar Orbiter observations showing an Earth-directed latitudinal distortion as low as ≈6 R ⊙. Near-Earth extreme-ultraviolet observations indicated the distortion was caused by interaction with faster wind from a nearby equatorial coronal hole. To evaluate the effect of the distortion on the CME's propagation, we adopted a three-point-of-view graduated cylindrical shell (GCS) fitting approach. For the first time, the GCS results are combined with an additional heliospheric single-viewpoint that looks further out in the heliosphere, revealing a deceleration in the CME before reaching ≈100 R ⊙. The CME geometry and velocity determined by this enhanced GCS are used to initialize a drag-based model and a WSA-Enlil MHD model. The estimated times of arrival are compared with in situ data at different heliocentric distances and, despite the complexity of the event, the error in the arrival times at each spacecraft results much lower (≈4 hr error) than the typical errors in literature (≈8–10 hr).