3D MHD Research Articles

Mean attractors and invariant measures of locally monotone and generally coercive SPDEs driven by superlinear noise

We study the global solvability, mean attractors and invariant measures for an abstract locally monotone and generally coercive SPDEs driven by infinite-dimensional superlinear noise defined in a dual space of intersection of finitely many Banach spaces. The main feature of this abstract system is that it covers a larger class of fundamental models which are included or not included previously. Under an extended locally monotone variational setting, we establish the global well-posedness, Itô's energy equality and existence of mean random attractors in some high-order Bochner spaces. The existence, uniqueness, support, (high-order and exponential) moment estimates, ergodicity, (pointwise and Wasserstein-type) exponentially mixing and asymptotic stability of invariant measures and evolution systems of measures are discussed for autonomous and nonautonomous stochastic equations. A stopping time technique is used to prove the convergence of solutions in probability in order to overcome the difficulty caused by the local monotonicity and superlinear growth of the coefficients. Our abstract results and unified methods are expected to be applied to various types of SPDEs like 2D Navier-Stokes equations, 2D MHD equations, 2D magnetic Bénard problem, Burgers type equations, 3D Leray α-model, convective Brinkman-Forchheimer equations, fractional (s,p)-Laplacian equations with monotone nonlinearities of polynomial growth of arbitrary order, and others.

Simulations of two-temperature jets in galaxy clusters

Context. Non-radiating protons in the radio lobes play an essential role in shaping the jet morphology, as demonstrated in recent radio and X-ray observations. However, since protons and electrons are not always in energy equilibrium due to weak Coulomb coupling, it is difficult to estimate the energy contribution of protons for the inflation of radio lobes. Aims. The focus of this study is to examine the effect of the variable model for electron heating by turbulence and shock waves on the thermal energy distribution of electrons and protons. Methods. We performed two-temperature three-dimensional magnetohydrodynamic (3D MHD) simulations of sub-relativistic jets in the galaxy cluster, while varying the jet magnetization parameters. Because the energy partition rate between electrons and protons in shock and turbulence is determined by plasma kinetic scale physics, our global simulations include electron instantaneous heating sub-grid models for shock waves and turbulence. Results. We find that most of the bulk kinetic energy of the jet is converted into the thermal energy of protons through both shocks and turbulence. Thus, protons are energetically dominant. Meanwhile, thermal electrons stored in the lobe evolve toward energy equipartition with magnetic energy through turbulent dissipation. We further estimated the radio power and the mechanical jet power of radio lobes following the same method used for radio and X-ray observations, then we compared these powers with that of the observed radio jets. The two-temperature model quantitatively explains the radiatively inefficient radio cavities, but it cannot reproduce the radiatively efficient cavity, even for strongly magnetized jets. This implies that a significant population of pair-plasma is needed to explain radiatively efficient radio cavities.

Dissecting Earth's Magnetosphere: 3D Energy Transport in a Simulation of a Real Storm Event

AbstractWe present new analysis methods of 3D MHD output data from the Space Weather Modeling Framework during a simulated storm event. Earth's magnetosphere is identified in the simulation domain and divided based on magnetic topology and the bounding magnetopause definition. Volume energy contents and surface energy fluxes are analyzed for each subregion to track the energy transport in the system as the driving solar wind conditions change. Two energy pathways are revealed, one external and one internal. The external pathway between the magnetosheath and magnetosphere has magnetic energy flux entering the lobes and escaping through the closed field region and is consistent with previous work and theory. The internal pathway, which has never been studied in this manner, reveals magnetically dominated energy recirculating between open and closed field lines. The energy enters the lobes across the dayside magnetospheric cusps and escapes the lobes through the nightside plasmasheet boundary layer. This internal circulation directly controls the energy content in the lobes and the partitioning of the total energy between lobes and closed field line regions. Qualitative analysis of four‐field junction neighborhoods indicate the internal circulation pathway is controlled via the reconnection X‐line(s), and by extension, the interplanetary magnetic field orientation. These results allow us to make clear and quantifiable arguments about the energy dynamics of Earth's magnetosphere, and the role of the lobes as an expandable reservoir that cannot retain energy for long periods of time but can grow and shrink in energy content due to mismatch between incoming and outgoing energy flux.

Heat and Mass Transfer on 3D MHD Flow of Casson Nanofluid in Presence of Arrhenius Activation Energy

Heat and Mass Transfer on 3D MHD Flow of Casson Nanofluid in Presence of Arrhenius Activation Energy

Influence of the interstellar magnetic field and 11-year cycle of solar activity on the heliopause nose location

Context. The heliosphere is formed by the interaction between the solar wind (SW) plasma emanating from the Sun and a magnetised component of local interstellar medium (LISM) inflowing on the Sun. A separation surface called the heliopause (HP) forms between the SW and the LISM. Aims. In this article, we define the nose of the HP and investigate the variations in its location. These result from a dependence on the intensity and direction of the interstellar magnetic field (ISMF), which is still not well known but has a significant impact on the movement of the HP nose, as we try to demonstrate in this paper. Methods. We used a parametric study method based on numerical simulations of various forms of the heliosphere using a time-dependent three-dimensional magnetohydrodynamic (3D MHD) model of the heliosphere. Results. The results confirm that the nose of the HP is always in a direction that is perpendicular to the maximum ISMF intensity directly behind the HP. The displacement of the HP nose depends on the direction and intensity of the ISMF, with the structure of the heliosphere and the shape of the HP depending on the 11-year cycle of solar activity. Conclusions. In the context of the planned space mission to send the Interstellar Probe (IP) to a distance of 1000 AU from the Sun, our study may shed light on the question as to which direction the IP should be sent. Further research is needed that introduces elements such as current sheet, reconnection, cosmic rays, instability, or turbulence into the models.

A Fundamental Mechanism of Solar Eruption Initiation in a Multipolar Magnetic Field

Recently, we established a fundamental mechanism of solar eruption initiation in which an eruption can be initiated from a bipolar field through magnetic reconnection in the current sheet (CS) that is formed slowly in the core field as driven by photospheric shearing motion. Here, using a series of fully 3D MHD simulations with a range of different photospheric magnetic flux distributions, we extended this fundamental mechanism to the quadrupolar magnetic field containing a null point above the core field, which is the basic configuration of the classical breakout model. As is commonly believed, in such a multipolar configuration, the reconnection triggered in the CS originated at the null point (namely, the breakout reconnection) plays the key role in eruption initiation by establishing a positive feedback loop between the breakout reconnection and the expansion of the core field. However, our simulation showed that the key to eruption initiation in such a multipolar configuration remains the slow formation of the CS in the sheared core, rather than the onset of fast breakout reconnection. The breakout reconnection only helps the formation of the core CS by letting the core field expand faster, but the eruption cannot occur when the bottom surface driving is stopped well before the core CS is formed, even though the fast reconnection has already been triggered in the breakout CS. This study clarified the role of breakout reconnection and confirmed formation of the core CS as the key to the eruption initiation in a multipolar magnetic field.

Unsteady 3D MHD Boundary Layer Stream for Non-Newtonian Power-Law Fluid Near Stagnation Point of Moving Surfaces

An unsteady three-dimensional MHD boundary layer is a fluid flow region near a surface where magnetic fields are present and interact with the fluid flow, causing it to become unsteady. This type of flow is commonly found in various astrophysical and technological applications, such as in plasmas and fusion reactors. The 3D nature of the flow introduces additional complexities to the flow dynamics, making the study and modeling of unsteady MHD boundary layers a challenging and active area of research. The unsteady boundary layer flow of fluid over a moving stagnation surface is theoretically examined in the current work with the impression of a magnetic field. The exact outcomes of the governing equations for the flow domain are obtained by utilizing the shooting phenomena. The specified analytical outcomes are also obtained for some cases. Detailed discussions of the parameters involved are confirmed both physically and graphically. Numerical results for both profiles are presented graphically. The study and modeling of unsteady 3D MHD boundary layers is imperative for a thorough understanding of various physical phenomena, improving the performance of technological systems, and advancing our knowledge of fluid dynamics.

Transition in particle transport under resonant magnetic perturbations in a tokamak

Nonlinear 3D MHD simulations and validations reveal that the hybrid particle-MHD transport is a key process for driving the pump-out in the presence of Resonant Magnetic Perturbations (RMPs) in the KSTAR tokamak. Particle transport and the resulting density pump-out by RMPs are shown to be composed of not only the classical flow convection near magnetic islands due to polarization but also the neoclassical ion diffusion across perturbed magnetic surfaces. The latter is known as the Neoclassical Toroidal Viscosity (NTV) and is integrated into nonlinear MHD simulations here for the first time, revealing that the two-stage pump-outs observed in KSTAR experiments are reproduced only with such integrated nonlinear MHD and transport evolution. Near-resonant responses, which have received less attention than the resonant response, play distinct roles in the pump-out along with the island formation. In addition, this modeling is used to investigate the pump-outs in double-null-like plasmas and numerically capture the effect of the double-null shape on the pump-outs, which may explain the difficulty of Edge Localized Mode (ELM) suppression access in double-like plasmas. This reveals new aspects of the impact toroidal geometry and mode coupling have on 3D physics and reveals the importance of near-resonant components in suppressing ELMs.

Secular outflows from 3D MHD hypermassive neutron star accretion disc systems

ABSTRACT Magnetized hypermassive neutron stars (HMNSs) have been proposed as a way for neutron star mergers to produce high electron fraction, high-velocity ejecta, as required by kilonova models to explain the observed light curve of GW170817. The HMNS drives outflows through neutrino energy deposition and mechanical oscillations, and raises the electron fraction of outflows through neutrino interactions before collapsing to a black hole (BH). Here, we perform 3D numerical simulations of HMNS–torus systems in ideal magnetohydrodynamics, using a leakage/absorption scheme for neutrino transport, the nuclear APR equation of state, and Newtonian self-gravity, with a pseudo-Newtonian potential added after BH formation. Due to the uncertainty in the HMNS collapse time, we choose two different parametrized times to induce collapse. We also explore two initial magnetic field geometries in the torus, and evolve the systems until the outflows diminish significantly ($\sim\!\! 1\!\! - \!\!2\ \mathrm{s}$). We find bluer, faster outflows as compared to equivalent BH–torus systems, producing M ∼ 10−3 M⊙ of ejecta with Ye ≥ 0.25 and v ≥ 0.25c by the simulation end. Approximately half the outflows are launched in disc winds at times $t\lesssim 500 \ \mathrm{ms}$, with a broad distribution of electron fractions and velocities, depending on the initial condition. The remaining outflows are thermally driven, characterized by lower velocities and electron fractions. Nucleosynthesis with tracer particles shows patterns resembling solar abundances in all models. Although outflows from our simulations do not match those inferred from two-component modelling of the GW170817 kilonova, self-consistent multidimensional detailed kilonova models are required to determine whether our outflows can power the blue kilonova.

Nonlinear verification of the resistive-wall boundary modules in the specyl and pixie3d magneto-hydrodynamic codes for fusion plasmas

A nonlinear verification benchmark is reported between the three-dimensional magneto-hydrodynamic (3D MHD) codes specyl [Cappello and Biskamp, Nucl. Fusion 36, 571 (1996)] and pixie3d [Chacón, Phys. Plasmas, 15, 056103 (2008)]. This work substantially extends a former successful verification study between the same two codes [Bonfiglio et al., Phys. Plasmas, 17, 082501 (2010)] and focuses on the verification of thin-shell resistive-wall boundary conditions, recently implemented in both codes. Such boundary conditions feature a thin resistive shell in contact with the plasma and an ideal wall placed at a finite distance, separated from the resistive shell by a vacuum region, along with a 3D boundary flow consistent with Ohm’s law. This setup allows the study of MHD modes that are influenced by the plasma magnetic boundary, such as external kink modes. The linear growth and nonlinear saturation of external kink modes are studied in both the tokamak and reversed-field pinch magnetic configurations, demonstrating excellent agreement between the two codes. For the tokamak, we present a comparison with analytical linear stability results for the external kink mode, demonstrating remarkable agreement between numerical and analytical growth rates.

3D MHD Radiation Flow of Unsteady Casson Fluid with Viscous Dissipation Effect

A numerical evaluation of the crucial physical properties of a 3D unsteady MHD flow along a stretching sheet for a Casson fluid in the presence of radiation and viscous dissipation has been carried out. Meanwhile, by applying similarity transformations, the nonlinear partial differential equations (PDEs) are transformed into a system of ordinary differential equations (ODEs). Furthermore, in the numerical solution of nonlinear ODEs, the shooting method along with Adams Moulton method of order four has been used. The obtained numerical results are computed with the help of FORTRAN. The tables and graphs describe the numerical results for different physical parameters which affect the velocity and temperature profiles.

Theoretical analysis of Arrhenius activation energy on 3D MHD nanofluid flow with convective boundary condition

Industry and space technology have significant issues managing heat energy and controlling mass dispersion. The purpose of this study is to develop motion caused by boundary layer thickness sheets that are increasingly being used in various engineering fields (civil engineering, mechanical, aeronautical, maritime processes and constructions). The activation energy is a critical factor in chemical reactions due to the existence of many applications in gas-cooled reactors, nuclear thermal rockets and liquid-fluoride reactors. This study presents the numerical analysis of activation energy on three dimensional (3D) nanofluid (NFs) motion via Stretching Surface (SS) with nonlinear thermal radiation effect. This is in contrast to the conventional slip condition, convective condition applied at surface. The governing basic equations are translated into nonlinear ODEs by suitable similarity transformations. The relevant boundary value problem was explored for a numerical solution for applying the MATLAB based on Runge–Kutta–Fehlberg (RKF) scheme via shooting technique. The major outcomes of current work have more concentration ([Formula: see text]) and Mass Transfer Rate ([Formula: see text]) for various numerical values of Activation Energy ([Formula: see text]). The present solutions determine very good correlation with the previously studied ones in a special case as predicted in the tables.

Global regularity of 2D MHD equations with almost Laplacian velocity dissipation

We obtain the global existence and global regularity for the 2D MHD equations with almost Laplacian velocity dissipation, which require the dissipative operators weaker than any power of the fractional Laplacian. The result can be regarded as a further improvement and generalization of previous works.

Numerical quantification of the wind properties of cool main sequence stars

ABSTRACT As a cool star evolves, it loses mass and angular momentum due to magnetized stellar winds that affect its rotational evolution. This change has consequences that range from the alteration of its activity to influences over the atmosphere of any orbiting planet. Despite their importance, observations constraining the properties of stellar winds in cool stars are extremely limited. Therefore, numerical simulations provide a valuable way to understand the structure and properties of these winds. In this work, we simulate the magnetized winds of 21 cool main-sequence stars (F-type to M-dwarfs) using a state-of-the-art 3D MHD code driven by observed large-scale magnetic field distributions. We perform a qualitative and quantitative characterization of our solutions, analysing the dependencies between the driving conditions (e.g. spectral type, rotation, and magnetic field strength) and the resulting stellar wind parameters (e.g. Alfvén surface size, mass-loss rate, angular momentum loss rate, and stellar wind speeds). We compare our models with the current observational knowledge on stellar winds in cool stars and explore the behaviour of the mass-loss rate as a function of the Rossby number. Furthermore, our 3D models encompass the entire classical Habitable Zones (HZ) of all the stars in our sample. This allows us to provide the stellar wind dynamic pressure at both edges of the HZ and analyse the variations of this parameter across spectral type and orbital inclination. The results here presented could serve to inform future studies of stellar wind-magnetosphere interactions and stellar wind erosion of planetary atmospheres via ion escape processes.

Convective heat and mass transfer rate on 3D Williamson nanofluid flow via linear stretching sheet with thermal radiation and heat absorption

A mathematical analysis is communicated to the thermal radiation and heat absorption effects on 3D MHD Williamson nanoliquid (NFs) motion via stretching sheet. The convective heat and mass boundary conditions are taken in sheet when liquid is motion. As a novelty, the effects of thermal radiation, heat absorption and heat and mass convection are incorporated. The aim is to develop heat transfer. Williamson NFs are most important source of heat absorption, it having many significant applications in “energy generation, HT, aircraft, missiles, electronic cooling systems, gas turbines” etc. The suitable similarity transformations have been utilized for reduce basic governing P.D. E’s into coupled nonlinear system of O.D. E’s. Obtained O.D. Es are calculated by help of R–K–F (“Runge–Kutta–Fehlberg”)4th order procedure with shooting technique in MATLAB programming. We noticed that, the skin friction coefficient is more effective in Williamson liquid motion when compared with NFs motion with higher numerical values of stretching ratio parameter, Williamson liquid motion is high when compared to NFs motion for large values of magnetic field. We compared with present results into previous results for various conditions. Finally, in the present result is good invention of previous results.

Regularity criteria for the 3D axisymmetric non-resistive MHD system

The main purpose of this paper is to study regularity criteria for a class of axisymmetric solutions to 3D incompressible non-resistive MHD system. We establish that strong solutions of this system can be smoothly extended beyond the possible blow-up time T if the horizontal angular component of the velocity in some mixed Lorentz spaces. Our result extends and generalizes the corresponding result of Wang and Guo.

The Global Well-posedness of Strong Solutions to 2D MHD Equations in Lei-Lin Space

The Global Well-posedness of Strong Solutions to 2D MHD Equations in Lei-Lin Space

MHD modeling of shattered pellet injection in JET

Nonlinear 3D MHD simulations of shattered-pellet injection (SPI) in JET show prototypical SPI-driven disruptions using the M3D-C1 and NIMROD extended-MHD codes. Initially, radiation-driven thermal quenches are accelerated by MHD activity as the pellet crosses rational surfaces, leading to a radiation spike, global stochasticization of the magnetic field, and a complete thermal quench. Eventually, current quenches, preceded by a current spike are seen as the Ohmic heating becomes equal to the radiative cooling. The results are qualitatively similar for both a single monolithic pellet, pencil-beam model, and a realistic shatter to represent the SPI plume. A scan in viscosity from 500 to 2000 m2 s−1 for MHD simulations finds that reducing viscosity increases MHD activity and decreases thermal quench time slightly. A realistic cloud of fragments modeling shows that mixed-D–Ne pellet travels deeper into the plasma core before the thermal quench. At the slow pellet speeds, the pellet is found to be moving slowly enough inward that even the 5% neon in the mixed pellet is enough to effectively radiate the thermal energy available. Radiation toroidal peaking is predicted to be at levels consistent with experimental observations and reduced as the pellet travels deeper into the plasma. These simulations lay the ground work for more-sophisticated validative and predictive modeling of SPI in JET using both M3D-C1 and NIMROD.

Validation and Testing of the CROBAR 3D Coronal Reconstruction Method with a MURaM Simulation

I report on validation and testing of a novel 3D reconstruction method than can obtain coronal plasma properties from a single snapshot perspective. I first reported on the method in 2021, and I have since named it the Coronal Reconstruction Onto B-Aligned Regions (CROBAR) method. The testing and validation are carried out with a cube from a MURaM 3D MHD simulation, which affords a coronal-like “ground truth” against which the reconstruction method can be applied and compared. I find that the method does quite well, recovering the “coronal veil”−like features recently reported from the MURaM simulations and allaying concerns that these features would thwart recovery of valid 3D coronal structure from a limited number of perspectives. I also find that a second perspective between ∼45° and 90° does significantly improve the reconstructions. Two distinct channels with soft-X-ray-like temperature response (peaking above 5 MK) would suffice for CROBAR’s optically thin observables A suite of AIA-like EUV passbads, with good coverage in the 3–8 MK range, is also well suited to CROBAR.

Super-Fermi acceleration in multiscale MHD reconnection

We investigate the Fermi acceleration of charged particles in 2D MHD anti-parallel plasmoid reconnection, finding a drastic enhancement in energization rate ε ̇ over a standard Fermi model of ε ̇ ∼ ε. The shrinking particle orbit width around a magnetic island due to E → × B → drift produces a ε ̇ ∥ ∼ ε ∥ 1 + 1 / 2 χ power law with χ ∼ 0.75. The increase in the maximum possible energy gain of a particle within a plasmoid due to the enhanced efficiency increases with the plasmoid size and is by multiple factors of 10 in the case of solar flares and much more for larger plasmas. Including the effects of the non-constant E → × B → drift rates leads to further variation in power law indices from ≳ 2 to ≲ 1, decreasing with plasmoid size at the time of injection. The implications for energetic particle spectra are discussed alongside applications to 3D plasmoid reconnection and the effects of a guide field.