Magnetohydrodynamic Model Research Articles

Super-Intense Geomagnetic Storm on 10-11 May 2024: Possible Mechanisms and Impacts.

One of the most intense geomagnetic storms of recent times occurred on 10-11 May 2024. With a peak negative excursion of Sym-H below -500nT, this storm is the second largest of the space era. Solar wind energy transferred through radiation and mass coupling affected the entire Geospace. Our study revealed that the dayside magnetopause was compressed below the geostationary orbit (6.6 RE) for continuously ∼6hr due to strong Solar Wind Dynamic Pressure (SWDP). Tremendous compression pushed the bow-shock also to below the geostationary orbit for a few minutes. Magnetohydrodynamic models suggest that the magnetopause location could be as low as 3.3RE. We show that a unique combination of high SWDP (≥15nPa) with an intense eastward interplanetary electric field (IEFY≥2.5mV/m) within a super-dense Interplanetary Coronal Mass Ejection lasted for 409min-is the key factor that led to the strong ring current at much closer to the Earth causing such an intense storm. Severe electrodynamic disturbances led to a strong positive ionospheric storm with more than 100% increase in dayside ionospheric Total Electron Content (TEC), affecting GPS positioning/navigation. Further, an HF radio blackout was found to occur in the 2-12MHz frequency band due to strong D- and E-region ionization resulting from a solar flare prior to this storm.

CESE Schemes for Solar Wind Plasma MHD Dynamics

Magnetohydrodynamic (MHD) numerical simulation has emerged as a pivotal tool in space physics research, witnessing significant advancements. This methodology offers invaluable insights into diverse space physical phenomena based on solving the fundamental MHD equations. Various numerical methods are utilized to approximate the MHD equations. Among these, the space–time conservation element and solution element (CESE) method stands out as an effective computational approach. Unlike traditional numerical schemes, the CESE method significantly enhances accuracy, even at the same base point. The concurrent discretization of space and time for conserved variables inherently achieves higher-order accuracy in both dimensions, without the need for intricate higher-order time discretization processes, which are often challenging in other methods. Additionally, this scheme can be readily extended to multidimensional cases, without relying on operator splitting or direction alternation. This paper primarily delves into the remarkable progress of CESE MHD models and their applications in studying solar wind, solar eruption activities, and the Earth’s magnetosphere. We aim to illuminate potential avenues for future solar–interplanetary CESE MHD models and their applications. Furthermore, we hope that the discussions presented in this review will spark new research endeavors in this dynamic field.

Investigating explosive events in a 3D quiet-Sun model: Transition region and coronal response

Transition region explosive events are characterized by the non-Gaussian profiles of the emission lines that form at transition region temperatures, and they are believed to be manifestations of small-scale reconnection events in the transition region. Traditionally, the enhanced emission at the line wings is interpreted as bi-directional outflows generated by the reconnection of oppositely directed magnetic fields. We investigate whether the 2D picture also holds in a more realistic setup of a 3D radiation magnetohydrodynamic (MHD) quiet-Sun model. We also compare the thermal responses in the transition region and corona of different events. We took a 3D self-consistent quiet-Sun model extending from the upper convection zone to the lower corona calculated using the MURaM code. We first synthesized the Si iv line profiles from the model and then located the profiles which show signatures of bi-directional flows. These tend to appear along network lanes, and most do not reach coronal temperatures. We isolated two hot events (around 1 MK) and one cool event (order of 0.1 MK) and examined the magnetic field evolution in and around these selected events. Furthermore, we investigated why some explosive events reach coronal temperatures, while most remain cool. We also examined the emission of these events as seen in the 174 AA passband of the Extreme Ultraviolet Imager (EUI) on board Solar Orbiter and all coronal passbands of the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO). The field lines around two events reconnect at small angles (i.e., they undergo component reconnection). The third case is associated with the relaxation of a highly twisted flux rope. All three events reveal signatures in the synthesized EUI 174 AA images. The intensity variations in two events are dominated by variations of the coronal emissions, while the cool component seen in the respective channel contributes significantly to the intensity variation in one case. In comparison, one hot event is embedded in regions with higher magnetic field strength and heating rates while the densities are comparable, and the other hot event is heated to coronal temperatures mainly because of the low density. Small-scale heating events seen in the extreme-ultraviolet (EUV) channels of AIA or EUI might be hot or cool. Our results imply that the major difference between the events in which coronal counterparts dominate or not is the amount of converted magnetic energy and/or density in and around the reconnection region.

Measurements of the solar coronal magnetic field based on coronal seismology with propagating Alfvénic waves: forward modeling

Abstract Recent observations have demonstrated the capability of mapping the solar coronal magnetic field using the technique of coronal seismology based on the ubiquitous propagating Alfv'{e}nic/kink waves through imaging spectroscopy. We established a magnetohydrodynamic (MHD) model of a gravitationally stratified open magnetic flux tube, exciting kink waves propagating upwards along the tube. Forward modeling was performed to synthesize the Fe \textsc{xiii} 1074.7 and 1079.8 nm spectral line profiles, which were then used to determine the wave phase speed, plasma density, and magnetic field with seismology method. A comparison between the seismologically inferred results and the corresponding input values verifies the reliability of the seismology method. In addition, we also identified some factors that could lead to errors during magnetic field measurements. Our results may serve as a valuable reference for current and future coronal magnetic field measurements based on observations of propagating kink waves.

Cross-field Diffusion Effects on Particle Transport in a Solar Coronal Flux Rope

Solar energetic particles associated with solar flares and coronal mass ejections (CMEs) are key agents of space weather phenomena, posing severe threats to spacecraft and astronauts. Recent observations by Parker Solar Probe indicate that the magnetic flux ropes of a CME can trap energetic particles and act as barriers, preventing other particles from crossing. In this Letter, we introduce the novel COCONUT+PARADISE model to investigate the confinement of energetic particles within a flux rope and the effects of cross-field diffusion (CFD) on particle transport in the solar corona, particularly in the presence of a CME. Using the global magnetohydrodynamic coronal model COolfluid COroNal UnsTructured (COCONUT), we generate background configurations containing a CME modeled as a Titov–Démoulin flux rope (TDFR). We then utilize the particle transport code PArticle Radiation Asset Directed at Interplanetary Space Exploration (PARADISE) to inject monoenergetic 100 keV protons inside one of the TDFR legs near its footpoint and evolve the particles through the COCONUT backgrounds. To study CFD, we employ two different approaches regarding the perpendicular proton mean free path (MFP): a constant MFP and a Larmor radius-dependent MFP. We contrast these results with those obtained without CFD. While particles remain fully trapped within the TDFR without CFD, we find that even relatively small perpendicular MFP values allow particles on the outer layers to escape. In contrast, the initially interior trapped particles stay largely confined. Finally, we highlight how our model and this Letter's results are relevant for future research on particle acceleration and transport in an extended domain encompassing both the corona and inner heliosphere.

The IMF Clock Angle Effect on the Tail Cross Section of the Martian Magnetic Pileup Boundary and Bow Shock

Using a three-dimensional global magnetohydrodynamic (MHD) simulation model, we investigate the effects of different interplanetary magnetic field (IMF) clock angles on the tail configuration of the Martian magnetic pileup boundary (MPB) and bow shock (BS). The study reveals the following: (1) The cross sections of the tail MPB and BS are approximately elliptical. The MPB tail cross section generally elongates in the direction of the IMF clock angle, whereas the BS tail cross section is roughly elongated perpendicular to the IMF clock angle direction. (2) An IMF with a northward component can cause the tail cross section of the MPB to shift slightly to the south when the intense crustal magnetic fields are located on the dayside. (3) As the tail distance from Mars increases, the eccentricity of the cross section ellipses of both the MPB and BS tail increases, as well as the major and minor axes. Additionally, the major and minor axes of the tail MPB’s cross section ellipses begin to decrease at the far magnetotail, suggesting that the Martian MPB tail might be a closed structure on the nightside.

Spectropolarimetric Inversion in Four Dimensions with Deep Learning (SPIn4D). I. Overview, Magnetohydrodynamic Modeling, and Stokes Profile Synthesis

The National Science Foundation’s Daniel K. Inouye Solar Telescope (DKIST) will provide high-resolution, multiline spectropolarimetric observations that are poised to revolutionize our understanding of the Sun. Given the massive data volume, novel inference techniques are required to unlock its full potential. Here, we provide an overview of our “SPIn4D” project, which aims to develop deep convolutional neural networks (CNNs) for estimating the physical properties of the solar photosphere from DKIST spectropolarimetric observations. We describe the magnetohydrodynamic (MHD) modeling and the Stokes profile synthesis pipeline that produce the simulated output and input data, respectively. These data will be used to train a set of CNNs that can rapidly infer the four-dimensional MHD state vectors by exploiting the spatiotemporally coherent patterns in the Stokes profile time series. Specifically, our radiative MHD model simulates the small-scale dynamo actions that are prevalent in quiet-Sun and plage regions. Six cases with different mean magnetic fields have been explored; each case covers six solar-hours, totaling 109 TB in data volume. The simulation domain covers at least 25 × 25 × 8 Mm, with 16 × 16 × 12 km spatial resolution, extending from the upper convection zone up to the temperature minimum region. The outputs are stored at a 40 s cadence. We forward model the Stokes profile of two sets of Fe i lines at 630 and 1565 nm, which will be simultaneously observed by DKIST and can better constrain the parameter variations along the line of sight. The MHD model output and the synthetic Stokes profiles are publicly available, with 13.7 TB in the initial release.

Turbulent plasma flow, its energies, and structures: Velocity vortices, magnetic field cocoons, and plasmoids

Turbulent flows are believed to be present in the solar corona, especially in connection with solar flares and coronal mass ejections. They are supposed to be very effective processes in energy transportation and can contribute to the heating of the solar corona. We study turbulence in reconnection outflows associated with flares and coronal mass ejections. We simulated the generation and evolution of the turbulent plasma flow and investigated its energies and formed plasma velocity and magnetic field structures. For the numerical simulations, we adopted a three-dimensional (3D) magnetohydrodynamic (MHD) model, in which we solved a full set of the 3D time-dependent resistive and compressible MHD equations using the Lare3d numerical code. We numerically studied turbulence in the plasma flow in the model with the plasma parameters that could simulate processes in the magnetic reconnection outflows in solar flares. Starting from a non-turbulent plasma flow in the energetically closed system, we studied the evolution of the kinetic, internal, and magnetic energies during the turbulence generation. We found that most of the kinetic energy is transformed into the plasma heating (about $95 <!PCT!>$) and only a small part to the magnetic energy (about $5 <!PCT!>$). The turbulence in the system evolves to the saturation stage with the power-law index of the kinetic density spectrum, $-5/3$. Magnetic energy is also saturated due to its dissipation and reconnection in small and complex magnetic field structures. We show examples of the structures formed in studied turbulent flow: velocity vortices, magnetic field cocoons, and plasmoids.

Computational Technology for Shell Models of Magnetohydrodynamic Turbulence Constructing

The paper discusses the computational technology for constructing one type of small-scale magnetohydrodynamic turbulence models – shell models. Any such model is a system of ordinary quadratic nonlinear differential equations with constant coefficients. Each phase variable is interpreted in absolute value as a measure of the intensity of one of the fields of the turbulent system in a certain range of spatial scales (scale shell). The equations of any shell model must have several quadratic invariants, which are analogues of conservation laws in ideal magnetohydrodynamics. The derivation of the model equations consists in obtaining such expressions for constant coefficients for which the predetermined quadratic expressions will indeed be invariants. Derivation of these expressions «manually» is quite cumbersome and the likelihood of errors in formula transformations is high. This is especially true for non-local models in which large-scale shells that are distant in size can interact. The novelty and originality of the work lie in the fact that the authors proposed a computational technology that allows one to automate the process of deriving equations for shell models. The technology was implemented using computer algebra methods, which made it possible to obtain parametric classes of models in which the invariance of given quadratic forms is carried out absolutely accurately – in formula form. The determination of the parameter values in the resulting parametric class of models is further carried out by agreement with the measures of the interaction of shells in the model with the probabilities of their interaction in a real physical system. The idea of the described technology and its implementation belong to the authors. Some of its elements were published by the authors earlier, but in this work, for the first time, its systematic description is given for models with complex phase variables and agreement of measures of interaction of shells with probabilities. There have been no similar works by other authors previously. The technology allows you to quickly and accurately generate equations for new non-local turbulence shell models and can be useful to researchers involved in modeling turbulent systems.

The effect of data-driving and relaxation models on magnetic flux rope evolution and stability

Understanding the flux rope eruptivity and effects of data driving in modelling solar eruptions is crucial for correctly applying different models and interpreting their results. We aim to investigate these by analysing the fully data-driven modelled eruption of the active regions (ARs) 12473 and AR11176, as well as preforming relaxation runs for AR12473 (found to be eruptive) where the driving is switched off systematically at different time steps. We intend to analyse the behaviour and evolution of fundamental quantities that are essential for understanding the eruptivity of magnetic flux ropes (MFRs). The data-driven simulations were carried out with the time-dependent magnetofrictional model (TMFM) for AR12473 and AR11176. For the relaxation runs, we employed the magnetofrictional method (MFM) and a zero-beta magnetohydrodynamic (MHD) model to investigate how significant the differences between the two relaxation procedures are when started from the same initial conditions. In total, 22 simulations were studied. To determine the eruptivity of the MFRs, we calculated and analysed characteristic geometric properties such as the cross-section, MFR height, and physical stability parameters such as MFR twist and the decay index. Furthermore, for the eruptive cases, we investigated the effect of sustained driving beyond the point of eruptivity on the MFR properties and evolution. We find that the fully driven AR12473 MFR is eruptive, while the AR11176 MFR is not. For the relaxation runs, we find that the MFM MFRs are eruptive when the driving is stopped around the flare time or later, while the MHD MFRs show eruptive behaviour even if the driving is switched off one and a half days before the flare occurs. We also find that characteristic MFR properties can vary greatly even for the eruptive cases of different relaxation simulations. The results suggest that data driving can significantly influence the evolution of the eruption, with differences appearing even when the relaxation time is set to later stages of the simulation when the MFRs have already entered an eruptive phase. Moreover, the relaxation model affects the results significantly, as highlighted by the differences between the MFM and MHD MFRs, showing that eruptivity in MHD does not directly translate to eruptivity in the MFM, despite the same initial conditions. Finally, if the exact critical values of instability parameters are unknown, tracking the evolution of typical MFR properties can be a powerful tool for determining MFR eruptivity.

Dawn‐Dusk Asymmetry of the Magnetopause Distance Under the Parker Spiral Configuration of the IMF

AbstractThe dawn‐dusk asymmetry of the magnetopause radial distance under the Parker (and ortho‐Parker) configuration of the interplanetary magnetic field (IMF) is investigated. An extensive data set of about 50,000 magnetopause crossings identified in the data from the THEMIS A‐E, Magion 4, Geotail, and Interball‐1 satellites is used for this purpose. It is shown that the magnetopause radial distances are larger at the side where the IMF is quasi‐parallel to the bow shock normal than at the side where IMF is quasi‐perpendicular to the bow shock normal. The effect is more significant at the flanks than close to the subsolar point. This introduces a significant asymmetry of the magnetopause shape, with the difference in the magnetopause radial distances being as large as about one Earth radius beyond the terminator. The experimental results are confirmed by a global magnetohydrodynamic (MHD) model, demonstrating that the asymmetry can be explained by MHD effects, without considering foreshock transients. This MHD model is further used to investigate the evolution of individual pressure components across the magnetopause and contrast them in quasi‐parallel and quasi‐perpendicular cases.

The arcing and post-arc breakdown characteristics of SF6 generator circuit breaker based on magnetohydrodynamic model

The arcing and post-arc breakdown characteristics of SF6 generator circuit breaker based on magnetohydrodynamic model

Two-dimensional cylindrical magnetosonic shock waves in a relativistic degenerated plasma

Abstract In this paper, the characteristics of two-dimensional magnetosonic (MS) shock waves have been studied in a nonplanar relativistic degenerate collisional magnetoplasma whose constituents are non-degenerate warm ions and relativistic degenerated electrons. Employing fluid model equations for such plasma along with Maxwell equations, a set of magnetohydrodynamic (MHD) model equations is obtained. Based on the newly obtained MHD equations, a Burgers–Kadomstev–Petviashvili (Burger–KP) equation (which describes shock wave structures) is derived in cylindrical geometry using the reductive perturbation technique. The considered plasma system was investigated under the impacts of spin-magnetization, relativistic degeneracy, cylindrical geometry, and dissipation. Numerical results revealed that the relativistic degeneracy, dissipation, and electron spin-magnetization as well as nonplanar geometry significantly altered the MS shock wave properties. Interestingly, it is found that there is a change in the shock nature and emergence of new structures due to the influences of both transverse perturbation and cylindrical geometry. The implications of our investigation may be applicable to dense astrophysical environments, particularly neutron stars, and white dwarfs at which the relativistic degenerated electrons are existed.

Structure Formation Through Magnetohydrodynamical Instabilities in Primordial Disks

The shear flow instabilities under the presence of magnetic fields in the primordial disk can greatly facilitate the formation of density structures that serve as seeds prior to the onset of the gravitational Jeans instability. We evaluate the effects of the Parker, magnetorotational and kinematic dynamo instabilities by comparing the properties of these instabilities. We calculate the mass spectra of coagulated density structures by the above mechanism in the radial direction for an axisymmetric magnetohydrodynamic (MHD) torus equilibrium and power density profile models. Our local three-dimensional MHD simulation indicates that the coupling of the Parker and magnetorotational instability creates spiral arms and gas blobs in an accretion disk, reinforcing the theory and model. Such a mechanism for the early structure formation may be tested in a laboratory. The recent progress in experiments involving shear flows in rotating tokamak, field reversed configuration (FRC) and laser plasmas may become a key element to advance in nonlinear studies.

Observation of magnetic islands in tokamak plasmas during the suppression of edge-localized modes

AbstractIn tokamaks, a leading platform for fusion energy, periodic filamentary plasma eruptions known as edge-localized modes occur in plasmas with high-energy confinement and steep pressure profiles at the plasma edge. These edge-localized modes could damage the tokamak wall but can be suppressed using small three-dimensional magnetic perturbations. Here we demonstrate that these magnetic perturbations can change the magnetic topology just inside the steep gradient region of the plasma edge. We identify signatures of a magnetic island, and their observation is linked to the suppression of edge-localized modes. We compare high-resolution measurements of perturbed magnetic surfaces with predictions from ideal magnetohydrodynamic theory where the magnetic topology is preserved. Although ideal magnetohydrodynamics adequately describes the measurements in plasmas exhibiting edge-localized modes, it proves insufficient for plasmas where these modes are suppressed. Nonlinear resistive magnetohydrodynamic modelling supports this observation. Our study experimentally confirms the predicted role of magnetic islands in inhibiting the occurrence of edge-localized modes. This will be beneficial for physics-based predictions in future fusion devices to control these modes.

Current Sheet Broadening due to Turbulence in Three-dimensional Collisionless Reconnection

The present study has investigated the statistical distribution of the current sheet width across the reconnection diffusion region by means of the 3D particle-in-cell simulations. The 3D reconnection layers are unstable to the flow shear instabilities, which results in electromagnetic (EM) turbulence generating effective magnetic dissipation around the x-line. The simulations are performed for several ion-to-electron mass ratios and computational domain sizes, which determine the fastest-growing mode in each simulation run. When the turbulence is weak, the current sheet width increases with the turbulence intensity, following a theoretical curve independent of the mass ratio and domain size. However, when the turbulence is stronger, the width saturates at a low level around 2 times the local electron inertia length, i.e., much smaller than the ion kinetic scales. It is found that the intense inductive electric field due to the EM turbulence is partly canceled out by the eddy viscous effect. As a result, the reconnection electric field is almost unchanged during the quasi-steady phase, regardless of the turbulence intensity. The result implies that the magnetohydrodynamic turbulence models are unlikely to be applicable to the reconnection diffusion region.

Magnetic connectivity from the Sun to the Earth with MHD models. I. Impact of the magnetic modelling on connectivity validation

The magnetic connectivity between the Sun and the Earth is crucial to our understanding of the solar wind and space weather events. However, establishing this connectivity is challenging because of the lack of direct observations, which explains the need for reliable simulations. The method most often used to make such measurements over the last few years is the two-step ballistic method, but it has many free parameters that can affect the final result. Thus, we want to provide a connectivity method based on self-consistent magnetohydrodynamics (MHD) models. To this end, we combined the COCONUT coronal model with the EUHFORIA heliospheric model to compute the magnetic field lines from the Earth to the Sun. We then developed a way to quantify both the spatial and temporal uncertainty associated with this computation. To validate our method, we selected four cases already studied in the literature and associated with high-speed-stream events coming from unambiguous coronal holes visible on the disk. We always find a partial overlap with the assumed CH of origin. The extent of this overlap is 19<!PCT!> for event 1, 100<!PCT!> for event 2, 45<!PCT!> for event 3, and 100<!PCT!> for event 4. We looked at the polarity at Earth over the full Carrington rotation to better understand these results. We find that, on average, MHD simulations provide a very good polarity estimation, showing 69<!PCT!> agreement with real data for event 1, 36<!PCT!> for event 2, 68<!PCT!> for event 3, and 69<!PCT!> for event 4. For events 1 and 3, we can then explain the mixed results by the spatial and temporal uncertainty. An interesting result is that, for MHD models, minimum-activity cases appear to be more challenging because of the multiple recurrent crossings of the HCS, while maximum-activity cases appear easier because of the latitudinal extent of the HCS. A similar result was also found with Parker Solar Probe data in another study. We demonstrate that it is possible to use MHD models to compute magnetic connectivity and that this approach provides results of equal quality to those from the two-step ballistic method, with additional possibilities for improvements as the models integrate more critical physics.

A holographic model of magnetohydrodynamics with fortuitous SO(3) symmetry

We study magnetohydrodynamics using holography. The gravity model is closely related to the STU supergravity in five dimensions and admits an analytical black brane solution carrying the conserved charge dual to the magnetic 1-form symmetry of the magnetohydrodynamic system. The black brane solution features a fortuitous SO(3) symmetry, providing a new symmetry principle for describing the magnetohydrodynamics. Since the bulk theory contains multiple 2-form gauge fields, the resistivity becomes matrix-valued. We find that the antisymmetric part of the resistivity matrix exhibits novel features depending on the UV cut-off of the theory. We also compute the shear and bulk viscosities and find that the bulk viscosity is proportional to the shear viscosity. Remarkably, the proportionality constant is exactly what is required for conformality, despite the zeroth-order energy-momentum tensor not being trace-free.

Deterministic and stochastic geometric mechanics for Hall magnetohydrodynamics

We derive new models of stochastic Hall magnetohydrodynamics (MHD) by applying Lie group symmetry reduction in a stochastic Euler–Poincaré variational principle. The resulting new theory of stochastic Hall MHD has potential applications for uncertainty quantification and data assimilation in space plasma (space weather), planetary science and solar physics. The stochastic geometric mechanics approach we take here produces coordinate-free results that may then be applied in a variety of spatial configurations.

Study of arc and magnetic field parameters under delayed breaking condition of DB-DC VCB

Taking the mechanical double-break DC vacuum circuit breaker (DB DC VCB) as the research object, the magnetic field and temperature field distribution between the breaks and the plasma characteristics under the working condition of gap difference caused by actuator dispersion are investigated to explore the difference in arc characteristics between the two breaks. Based on the system of Maxwell and magnetohydrodynamic (MHD) equations, a non-simultaneous breaking model of the DB DC VCB is established, and parameters such as magnetic flux density, plasma velocity, inter-contact pressure, and ion and electron temperatures are calculated. The simulation results show that the cathode surface field emission effect is stronger in the small gap break (delayed breaking break). Besides, in the small gap break, the arc temperature is higher, the rate of decrease of temperature is lower, the electron velocity is higher, the magnetic flux density is lower, the regulatory ability of the magnetic field is weaker, and the plasma diffusion speed is slower. In the arc ignition stage, the arc aggregation state duration of the small gap break is longer than that of the normal break, which means the arc in the small gap break gets diffused and arc energy dissipation becomes harder. Therefore, the arc energy density of the delayed breaking break is greater, the arc morphology transition time is longer, the residual particle concentration after arc extinguishing is higher, and the probability of re-strike breakdown increases with the increase in gap difference. Improving the synchronization of the actuator could improve the breaking ability of the DB DC VCB. Index terms—plasma arc, double-break direct current vacuum circuit breaker (DB-DC VCB), transverse magnetic field (TMF), magnetohydrodynamic (MHD) model.