Magnetohydrodynamic Model Research Articles

Numerical and Experimental Investigation of Magnetohydrodynamic Effects on Radiative Heating During Superorbital Earth Reentry

Numerical predictions of radiative heat flux were performed on a representative Mars return (Earth reentry upon return from Mars) condition with a flight equivalent velocity of [Formula: see text], produced by the University of Queensland’s X2 expansion tube. The primary goal was to numerically evaluate the effect of an externally applied magnetic field on radiative heat flux to a scaled test model based on NASA’s Stardust vehicle. Numerical simulations used the Eilmer4 computational fluid dynamics (CFD) code coupled with NASA’s NEQAIR code for radiation calculations. A two-dimensional, axisymmetric magnetohydrodynamic (MHD) model was implemented in order to model MHD effects. The numerical results predicted a significant increase of 54% to stagnation point radiative heat flux when the magnet was used, and a smaller increase of 8% to afterbody radiative heat flux. An attempt was made to compare the numerical predictions to experimental measurements. A spherical permanent magnet fitted into the test model provided a stagnation point magnetic flux density of 0.68 T. A radiation gauge was developed consisting of a thin-film heat flux gauge placed behind an optical window, enabling isolation of the radiative heat flux component. Several challenges were encountered, including the absorbance calibration of the radiation gauges, chemical contamination of the test flow, and noisy measurements when the magnet was on. These prevented firm conclusions to be made and warrant further experiments to validate the CFD results.

Numerical analysis of double-fractional PDEs in MHD hybrid nanofluid blood flow with slip velocity, heat source, and radiation effects

Abstract The study of blood flow in cylindrical geometries resembling small arteries is crucial for advancing drug delivery systems, cardiovascular health, and treatment methods. However, Conventional models have failed to capture the complex memory effects and non-local behavior inherent in blood flow dynamics, which hinders their accuracy in predicting critical flow and heat transfer properties for medical applications. To overcome these limitations, this research introduces a novel fractional-order magnetohydrodynamic model for blood flow, incorporating a $ZnO$ and $Fe_3O_4$ hybrid nanofluid. The model uniquely integrates boundary slip velocity effects within the double fractional Maxwell model (DFMM) rheology framework and utilizes the dual fractional phase lag bioheat model (DFPLM) applied to a porous cylindrical structure. Fractional-order time derivatives in the thermal and momentum equations are formulated using the Caputo approach, with numerical solutions derived via finite difference methods leveraging L1 and L2 approximations for Caputo fractional derivatives. The study examines the effects of fractional orders, relaxation time, and phase lags for heat and temperature, along with parameters such as thermal radiation, wall slip velocity, and porosity. These factors are analyzed for their impact on velocity, temperature, skin friction, and the Nusselt number. Results indicate that the hybrid nanofluid enhances heat transfer compared to blood or mono-hybrid nanofluids, while also reducing skin friction. Furthermore, fractional-order models provide more reliable and realistic predictions under varying flow conditions. The DFMM shows smoother transitions in velocity and friction, while the DFPLM predicts higher temperatures and greater heat transfer enhancement compared to classical and single-phase lag models. By integrating fractional calculus, this model offers improved simulation of complex transport phenomena in small arteries, contributing to the development of more effective cardiovascular treatments.

Coronal mass ejection propagation in the dynamically coupled space weather tool: COCONUT + EUHFORIA

Numerical magnetohydrodynamics (MHD) models such as the European heliospheric forecasting information asset (EUHFORIA) have been developed to predict the arrival time of coronal mass ejections (CMEs) and accelerated high-energy particles. However, in EUHFORIA, transient magnetic structures are injected at 0.1 AU into a background solar wind created from a static solar wind model. This means the inserted CME model is completely independent of the coronal magnetic field and thus is missing all potential interactions between the CME and the solar wind in the corona. This paper aims to present the time-dependent coupling between the coronal model COolfluid COroNal UnsTructured (COCONUT) and the heliospheric forecasting tool EUHFORIA. This first attempt to couple these two simulations should allow us to follow directly the propagation of a flux rope from the Sun to Earth. We performed six COCONUT simulations where a flux rope is implemented at the solar surface using either the Titov-Démoulin CME model or the regularised Biot-Savart law (RBSL) CME model. At regular intervals, the magnetic field, velocity, temperature, and density of the 2D surface $R_ b odot $ were saved in boundary files. These series of coupling files were read in a modified version of EUHFORIA in order to progressively update its inner boundary. After presenting the early stage of the propagation in COCONUT, we examined how the disturbance of the solar corona created by the propagation of flux ropes is transmitted into EUHFORIA. In particular, we considered the thermodynamic and magnetic profiles at L1 and compared them with those obtained at the interface between the two models. We demonstrate that the properties of the heliospheric solar wind in EUHFORIA are consistent with those in COCONUT, acting as a direct extension of the coronal domain. Moreover, the disturbances initially created from the propagation of flux ropes in COCONUT continue to evolve from the corona in the heliosphere to Earth, with a smooth transition at the interface between the two simulations. Looking at the profile of magnetic field components at Earth and different distances from the Sun, we also find that the transient magnetic structures have a self-similar expansion in COCONUT and EUHFORIA. However, the amplitude of the profiles depends on the flux rope model used and its properties, thus emphasising the important role of the initial properties in solar source regions for accurately predicting the impact of CMEs. The dynamically coupled COCONUT plus EUHFORIA model chain constitutes a new space weather forecasting tool that can predict the characteristics of the flux-rope CMEs upon their arrival at L1.

A detailed investigation of particle energization mechanisms in models of collapsing magnetic traps

ABSTRACT In this paper, we provide a detailed investigation of the energization processes in two-dimensional, two and a half-dimensional, and three-dimensional collapsing magnetic trap models. Using kinematic magnetohydrodynamic models of collapsing magnetic traps, we examine the importance of Fermi acceleration in comparison with betatron acceleration in these models. We extend previous work by investigating particle orbits in two-dimensional models without and with a guide field component and from full three-dimensional models. We compare the outcomes for the different models and how they depend on the chosen initial conditions. While in the literature betatron acceleration has been emphasized as the major mechanism for particle energization in collapsing magnetic traps, we find that Fermi acceleration can play a significant role as well for particle orbits with suitable initial conditions.

Global Simulation of the Solar Wind: A Comparison with Parker Solar Probe Observations during 2018–2022

Global magnetohydrodynamic (MHD) models play an important role in the infrastructure of space weather forecasting. Validating such models commonly utilizes in situ solar wind measurements made near the Earth’s orbit. The purpose of this study is to test the performance of G3DMHD (a data driven, time-dependent, 3D MHD model of the solar wind) with Parker Solar Probe (PSP) measurements. Since its launch in 2018 August, PSP has traversed the inner heliosphere at different radial distances sunward of the Earth (the closest approach ∼13.3 R ⊙), thus providing a good opportunity to study evolution of the solar wind and to validate heliospheric models of the solar wind. The G3DMHD model simulation is driven by a sequence of maps of the photospheric field extrapolated to the assumed source surface (2.5 R ⊙) using the potential field model from 2018 to 2022, which covers the first 15 PSP orbits. The Pearson correlation coefficient (cc) and the mean absolute scaled error (MASE) are used as the metrics to evaluate the model performance. It is found that the model performs better for both magnetic intensity (cc = 0.75; MASE = 0.60) and the solar wind density (cc = 0.73; MASE = 0.50) than for the solar wind speed (cc = 0.15; MASE = 1.29) and temperature (cc = 0.28; MASE = 1.14). This is due primarily to lack of accurate boundary conditions. The well-known underestimate of the magnetic field in solar minimum years is also present. Assuming that the radial magnetic field becomes uniformly distributed with latitude at or below 18 R ⊙ (the inner boundary of the computation domain), the agreement in the magnetic intensity significantly improves (cc = 0.83; MASE = 0.49).

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

Context. 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. Aims. 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. Methods. 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. Results. 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%) and only a small part to the magnetic energy (about 5%). 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.

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

Context. 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. Aims. 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). Methods. 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. Results. 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. Conclusions. 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.

Evolution characteristics of shock wave in microsecond-scale underwater electrical wire explosion

The underwater electrical wire explosion (UEWE) is a physical phenomenon initiated by the rapid injection of electrical energy, triggering an explosive event. UEWE offers advantages in energy conversion efficiency, repeatability, and controllability, making it valuable in various industrial applications. Building upon established zero-dimensional (0D) and one-dimensional (1D) models, this paper proposes an enhanced 0D-1D coupled cold-start model to describe the plasma channel expansion and subsequent shock wave (SW) propagation characteristics. The model comprises two submodules: a 0D magnetohydrodynamics model that describes plasma channel boundary expansion during the explosion, and a 1D hydrodynamics model using an artificial viscosity algorithm to depict SW propagation. The constructed numerical model facilitates investigation of plasma characteristics, SW propagation behavior, and energy conversion efficiency throughout the UEWE process. Additionally, the influences of wire dimensions and discharge frequency on these characteristics were analyzed. The results indicate that SW propagation characteristics are primarily governed by thermal pressure variations within the wire and that different wire dimensions markedly affect SW amplitude, attenuation, and impulse. The efficiency of electrical-to-SW energy conversion remains relatively low; however, thicker and shorter wires can enhance SW amplitude and improve conversion efficiency. Higher discharge frequencies produce greater impact forces and impulses near the explosion site, while also improving energy conversion rates. This study offers a theoretical basis and technical guidance for prospective engineering applications.

The evolution of coronal shock wave properties and their relation with solar energetic particles

Context. Shock waves driven by fast and wide coronal mass ejections (CMEs) are considered to be very efficient particle accelerators and are involved in the production of solar energetic particle (SEP) events. These events cause space weather phenomena by disturbing the near-Earth radiation environment. In past studies, we analysed statistically the relation between the maximum intensity of energetic electrons and protons and the properties of coronal shocks inferred at the point of magnetic connectivity. The present study focuses on a gradual SEP event measured by STEREO-A and -B on 11 October 2013. This event had the interesting properties that it (1) occurred in isolation with very low background particle intensities measured before the event, (2) was associated with a clear onset of SEPs measured in situ allowing detailed timing analyses, and (3) was associated with a fast CME event that was magnetically connected with STEREO-A and -B. These three properties allowed us to investigate at a high cadence the temporal connection between the rapidly evolving shock properties and the SEPs measured in situ. Aims. The aim of the present study is to investigate the relative roles of fundamental shock parameters such as the compression ratio, Mach number and geometry, in the intensity and composition of the associated SEP event measured in situ. Methods. We used shock reconstruction techniques and multi-viewpoint imaging data obtained by the STEREO-A and -B, SOHO, and SDO spacecraft to determine the kinematic evolution of the expanding shock wave. We then exploited 3D magneto-hydrodynamic modelling to model the geometry and Mach number of the shock wave along an ensemble of magnetic field lines connected to STEREO-A and -B, also estimating the uncertainties of the shock parameters. Using a velocity dispersion analysis of the available SEP data we time-shifted the SEP time series and analysed the relations between observed SEP properties and the modelled shock properties. We also studied the energy dependence of these relations. Results. We find a very good temporal agreement between the formation of the modelled shock wave and the estimated release times for both electrons and protons. The simultaneous release of protons and electrons suggests a common acceleration process. This early phase is marked at both STEREOs by elevated electron-to-proton ratios that coincide with the highly quasi-perpendicular phase of the shock. These findings suggest that the rapid evolution of the shock as it transits from the low to the high corona modifies the conditions under which particles are accelerated. We discuss these findings in terms of basic geometry and acceleration processes.

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.

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.

Magnetic interaction of stellar coronal mass ejections with close-in exoplanets: implication on planetary mass-loss and Ly α transits

ABSTRACT Coronal mass ejections (CMEs) erupting from the host star are expected to affect the atmospheric erosion processes of planets. For planets with a magnetosphere, the embedded magnetic field in the CMEs is thought to be the most important parameter to affect planetary mass-loss. In this work, we investigate the effect of different magnetic field structures of stellar CMEs on the atmosphere of a hot Jupiter with a dipolar magnetosphere. We use a time-dependent 3D radiative magnetohydrodynamic (MHD) atmospheric escape model that self-consistently models the outflow from hot Jupiter’s magnetosphere and its interaction with stellar CMEs. For our study, we consider three configurations of magnetic field embedded in CMEs – (a) northward $B_z$ component, (b) southward $B_z$ component, and (c) radial component. We find that both the CMEs with northward $B_z$ and southward $B_z$ increase the planetary mass-loss rate when the CME arrives from the stellar side, with the mass-loss rate remaining higher for the CME with northward $B_z$ until it arrives on the opposite side. The largest magnetopause is found for the CME with a southward $B_z$ component. During the passage of a CME, the planetary magnetosphere goes through three distinct changes – (1) compressed magnetosphere, (2) enlarged magnetosphere, and (3) relaxed magnetosphere for all three CME configurations. The computed synthetic Ly $\alpha$ transit absorption generally increases when the CME is in interaction with the planet for all magnetic configurations but the maximum Ly $\alpha$ absorption is found for the case of radial CME with the most compressed magnetosphere.

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.

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.