MHD Model Research Articles

A resistive MHD model and simulation on plasma flow evolution in the presence of resonant magnetic perturbation in a tokamak

Nonaxisymmetric magnetic fields such as the intrinsic error field and the externally applied resonant magnetic perturbation (RMP) in a tokamak are known to influence the plasma momentum transport and flow evolution through plasma response, which itself strongly depends on the plasma flow as well. The nonlinear interaction between plasma response and flow has been previously modeled in the conventional error field theory with the “no-slip” condition, which has been recently extended to allow the “free-slip” condition. In this work, we further target this specific process and numerically simulate the nonlinear plasma response and flow evolution in the presence of a single-helicity RMP in a circular-shaped model tokamak configuration, based on the full resistive MHD model in the initial-value code NIMROD. Time evolution of the parallel (to k) flow or “slip frequency” profile and its asymptotic steady state obtained from the NIMROD simulations are compared with both conventional and extended nonlinear response theories. Here, k is the wave vector of the propagating island. Good agreement with the extended theory with free-slip condition has been achieved for the parallel flow profile evolution in response to RMP in all resistive regimes, whereas the difference from the conventional theory with the no-slip condition tends to diminish as the plasma resistivity approaches zero.

Doppler-velocity Drifts Detected in a Solar Prominence

We analyzed multiline observations of a quiescent prominence from the slit spectrograph located at the Ondřejov Observatory. Dopplergrams and integrated intensity maps of the whole prominence were obtained from observations in six spectral lines: Ca ii H, Hϵ, Hβ, He i D3, Hα, and Ca ii IR. By combining integrated intensity maps with non-LTE radiative-transfer modeling, we carefully identified areas in an optically thin regime. The comparison of the Doppler-velocity maps and scatterplots from different lines shows the existence of differences in the velocity of ions and neutrals called velocity drift. The drift is of a local nature, present mostly at prominence edges in the area with a large velocity gradient, as can be tentatively expected based on multifluid MHD models. We could not explore the time evolution of the drift, since our data set consists of a single scan only. Our paper brings another contribution to a rather controversial problem of the detection of multifluid effects in solar prominences.

A Mixed Finite Element Method for Stationary Magneto-Heat Coupling System with Variable Coefficients.

In this article, a mixed finite element method for thermally coupled, stationary incompressible MHD problems with physical parameters dependent on temperature in the Lipschitz domain is considered. Due to the variable coefficients of the MHD model, the nonlinearity of the system is increased. A stationary discrete scheme based on the coefficients dependent temperature is proposed, in which the magnetic equation is approximated by Nédélec edge elements, and the thermal and Navier–Stokes equations are approximated by the mixed finite elements. We rigorously establish the optimal error estimates for velocity, pressure, temperature, magnetic induction and Lagrange multiplier with the hypothesis of a low regularity for the exact solution. Finally, a numerical experiment is provided to illustrate the performance and convergence rates of our numerical scheme.

Ulysses Flyby in the Heliosphere: Comparison of the Solar Wind Model with Observational Data

A model capable of reproducing a set of solar wind parameters along the virtual spacecraft orbit out of an ecliptic plane has been developed. In the framework of a quasi-stationary axisymmetric self-consistent MHD model the spatial distributions of magnetic field and plasma characteristics at distances from 20 to 1200 Solar radii at almost all solar latitudes could be obtained and analyzed. This model takes into account the Sun’s magnetic field evolution during the solar cycle, when the dominant dipole magnetic field is replaced by the quadrupole one. Self-consistent solutions for solar wind characteristics were obtained, depending on the phase of the solar cycle. To verify the model, its results are compared with the observed characteristics of solar wind along the Ulysses trajectory during its flyby around the Sun from 1990 to 2009. It is shown that the results of numerical simulation are generally consistent with the observational data obtained by the Ulysses spacecraft. A comparison of the model and experimental data confirms that the model can adequately describe the solar wind parameters and can be used for heliospheric studies at different phases of the solar activity cycle, as well as in a wide range of latitudinal angles and distances to the Sun.

Additional Evidence for a Pulsar Wind Nebula in the Heart of SN 1987A from Multiepoch X-Ray Data and MHD Modeling

Since the day of its explosion, supernova (SN) 1987A has been closely monitored to study its evolution and to detect its central compact relic. In fact, the formation of a neutron star is strongly supported by the detection of neutrinos from the SN. However, besides the detection in the Atacama Large Millimeter/submillimeter Array (ALMA) data of a feature that is compatible with the emission arising from a protopulsar wind nebula (PWN), the only hint of the existence of such an elusive compact object is provided by the detection of hard emission in NuSTAR data up to ∼20 keV. We report on the simultaneous analysis of multiepoch observations of SN 1987A performed with Chandra, XMM-Newton, and NuSTAR. We also compare the observations with a state-of-the-art three-dimensional magnetohydrodynamic simulation of SN 1987A. A heavily absorbed power law, consistent with the emission from a PWN embedded in the heart of SN 1987A, is needed to properly describe the high-energy part of the observed spectra. The spectral parameters of the best-fit power law are in agreement with the previous estimate, and exclude diffusive shock acceleration as a possible mechanism responsible for the observed nonthermal emission. The information extracted from our analysis is used to infer the physical characteristics of the pulsar and the broadband emission from its nebula, in agreement with the ALMA data. Analysis of the synthetic spectra also shows that, in the near future, the main contribution to the Fe K emission line will originate in the outermost shocked ejecta of SN 1987A.

JOREK3D: An extension of the JOREK nonlinear MHD code to stellarators

Although the basic concept of a stellarator was known since the early days of fusion research, advances in computational technology have enabled the modeling of increasingly complicated devices, leading up to the construction of Wendelstein 7-X, which has recently shown promising results. This recent success has revived interest in the nonlinear 3D MHD modeling of stellarators in order to better understand their performance and operational limits. This study reports on the extension of the JOREK code to 3D geometries and on the first stellarator simulations carried out with it. The first simple simulations shown here address the classic Wendelstein 7-A stellarator using a reduced MHD model previously derived by us. The results demonstrate that stable full MHD equilibria are preserved in the reduced model: the flux surfaces do not move throughout the simulation and closely match the flux surfaces of the full MHD equilibrium. Furthermore, both tearing and ballooning modes were simulated, and the linear growth rates measured in JOREK are in reasonable agreement with the growth rates from the CASTOR3D linear MHD code.

Kinetic Simulations of Instabilities and Particle Acceleration in Cylindrical Magnetized Relativistic Jets

Relativistic magnetized jets, such as those from AGN, GRBs, and XRBs, are susceptible to current- and pressure-driven MHD instabilities that can lead to particle acceleration and nonthermal radiation. Here, we investigate the development of these instabilities through 3D kinetic simulations of cylindrically symmetric equilibria involving toroidal magnetic fields with electron–positron pair plasma. Generalizing recent treatments by Alves et al. and Davelaar et al., we consider a range of initial structures in which the force due to toroidal magnetic field is balanced by a combination of forces due to axial magnetic field and gas pressure. We argue that the particle energy limit identified by Alves et al. is due to the finite duration of the fast magnetic dissipation phase. We find a rather minor role of electric fields parallel to the local magnetic fields in particle acceleration. In all investigated cases, a kink mode arises in the central core region with a growth timescale consistent with the predictions of linearized MHD models. In the case of a gas-pressure-balanced (Z-pinch) profile, we identify a weak local pinch mode well outside the jet core. We argue that pressure-driven modes are important for relativistic jets, in regions where sufficient gas pressure is produced by other dissipation mechanisms.

Numerical modeling of pedestal stability and broadband turbulence of wide-pedestal QH-mode plasmas on DIII-D

The wide-pedestal quiescent high confinement mode discovered on DIII-D in recent years is a stationary and quiescent H-mode (QH-mode) with the pedestal width exceeding EPED prediction by at least 25%. Its characteristics, such as low rotation, high energy confinement and edge localized mode-free operation, make it an attractive operation mode for future reactors. Linear and nonlinear simulations using BOUT++ reduced two fluid MHD models and awere carried out to investigate the bursty broadband turbulence often observed in the edge of wide-pedestal QH-mode plasmas. Two kinds of MHD-scale instabilities in different spatial locations within the pedestal were found in the simulations: one mild peeling–ballooning (PB) mode (γ PB < 0.04ω A) located near the minimum in E r well propagating in ion diamagnetic drift direction; and one drift-Alfvén wave locates at smaller radius compared to E r well propagating in the electron diamagnetic drift direction and unstable only when the parallel electron dynamics is included in the simulation. The coupling between drift wave and shear Alfvén wave provides a possible cause of the experimentally observed local profile flattening in the upper-pedestal. The rotation direction, mode location, as well as the wavenumber of these two modes from BOUT++ simulations agree reasonably well with the experimental measurements, while the lack of quantitative agreement is likely due to the lack of trapped electron physics in current fluid model. This work presents improved physics understanding of the pedestal stability and turbulence dynamics for wide-pedestal QH-mode.

Free convection to cool a hot square block by embedding in center of a chamber by nanofluid and magnetohydrodynamic

Hot block is observed in numerous industries and applications that can being an electronic component, solid matrix, battery, etc. In the present 2D simulation, a uniform magnetic field (MHD model) in the x-direction was utilized to affect the free convection of nanofluid water- A l 2 O 3 for aim of improvement and control the heat transfer and flow characterizations. The used geometry consisted of square chamber and hot block embedded in center of square chamber. The walls of the hot block and chamber performed as hot and cold sources led to create buoyancy force. This study investigated for Varity inclined angles of hot block ( 0 < η < 45 ), Rayleigh numbers ( 10 2 < R a < 10 4 ) and Hartmann numbers ( 0 < H a < 40 ) when the volume fraction of suspension was φ = 0.04 . Also, the effects of the mentioned parameters were studied on the streamlines, temperature contours, average Nusselt number. Observations showed that Adding magnetic field increased the heat transfer rate by 200% At low Rayleigh numbers, but it reduced the heat transfer rate 48% At high Rayleigh numbers.

Ion temperature effects on plasma flow in the magnetic mirror configuration

Effects of finite ion temperature on the plasma flow in the converging–diverging magnetic field, the magnetic mirror, or equivalently, magnetic nozzle configuration are studied using a quasineutral paraxial two-fluid MHD model with isothermal electrons and warm magnetized ions. The ion acceleration was studied with an emphasis on the role of the singularity at the sonic point transition. It is shown that the regularity of the sonic point defines a global solution describing plasma acceleration from subsonic to supersonic velocity. Stationary accelerating solutions were obtained and compared with the time dependent dynamics, confirming that the solutions of the time-dependent equations converge to the stationary solutions and, therefore, are stable. The effects of the ion pressure anisotropy were analyzed using the Chew–Golberger–Low model and its generalization. It is shown that the mirror force (manifested by the perpendicular ion pressure) enhances plasma acceleration. The role of ionization and charge exchange on plasma flow acceleration have been investigated.

Estimation of stagnation performance metrics in magnetized liner inertial fusion experiments using Bayesian data assimilation

We present a new analysis methodology that allows for the self-consistent integration of multiple diagnostics including nuclear measurements, x-ray imaging, and x-ray power detectors to determine the primary stagnation parameters, such as temperature, pressure, stagnation volume, and mix fraction in magnetized liner inertial fusion (MagLIF) experiments. The analysis uses a simplified model of the stagnation plasma in conjunction with a Bayesian inference framework to determine the most probable configuration that describes the experimental observations while simultaneously revealing the principal uncertainties in the analysis. We validate the approach by using a range of tests including analytic and three-dimensional MHD models. An ensemble of MagLIF experiments is analyzed, and the generalized Lawson criterion χ is estimated for all experiments.

Convergence analysis of a fully discrete finite element method for thermally coupled incompressible MHD problems with temperature-dependent coefficients

In this paper, we study a fully discrete finite element scheme of thermally coupled incompressible magnetohydrodynamic with temperature-dependent coefficients in Lipschitz domain. The variable coefficients in the MHD system and possible nonconvex domain may cause nonsmooth solutions. We propose a fully discrete Euler semi-implicit scheme with the magnetic equation approximated by Nédélec edge elements to capture the physical solutions. The fully discrete scheme only needs to solve one linear system at each time step and is unconditionally stable. Utilizing the stability of the numerical scheme and the compactness method, the existence of weak solution to the thermally coupled MHD model in three dimensions is established. Furthermore, the uniqueness of weak solution and the convergence of the proposed numerical method are also rigorously derived. Under the hypothesis of a low regularity for the exact solution, we rigorously establish the error estimates for the velocity, temperature and magnetic induction unconditionally in the sense that the time step is independent of the spacial mesh size.

Microwave Perspective on Magnetic Breakout Eruption

Microwave maps may provide critical information on the flux rope interaction and the breakout eruption if their polarization is measured with high precision. We demonstrate this diagnostic capability using the 17 GHz maps from the Nobeyama Radioheliograph (NoRH) of a circular ribbon flare SOL2014-12-17T04:51. The EUV images from SDO/AIA and the coronal magnetic field extrapolated from the HMI magnetogram are also used to support the interpretation of the microwave data. The most obvious evidence for the breakout eruption comes from the sign change of the microwave polarization over the AR at heliographic coordinates S20E09, indicating change of the overlying fields from a closed fan structure to a spine-like structure. Another important piece of evidence comes from the spatial and temporal variations of quasi-periodic pulsations (QPP) detected at the 17 GHz. The QPP was more obvious in one loop leg before the eruption and later moved to the spine field region on and after the flare. This indicates that the oscillatory power is transferred from an interacting flux rope to the outer spine, along which the reconnection launches torsional Alfvén waves, in good agreement with MHD model predictions for breakout eruption. In the practical viewpoint, these two diagnostics work because microwave observations are free of saturation even in strong flaring regions.

Statistical Analysis of the Distribution and Evolution of Mirror Structures in the Martian Magnetosheath

The mirror-mode structures in the Martian magnetosheath that were observed by Mars Atmosphere and Volatile Evolution during 2015–2018 are analyzed statistically. It is found that most mirror-mode events occurred close to the bow shock. Morphological categorization based on skewness of the magnetic field shows that ∼46.57% of the observed mirror-mode events are peak-like, ∼40.25% are wave-like, and ∼13.18% are dip-like. The mirror-mode structures mostly saturate in a very short time after their formation near the bow shock, which is a result of the high temperature anisotropy and high plasma beta at this location. Carried downstream by the magnetosheath flow, the mirror-mode structures remain in nonlinear saturation states. Meanwhile, the dayside magnetosheath plasma largely deviates from marginal stability, which is a state commonly that is expected in the terrestrial magnetosheath. By flowline tracing in an MHD model, it is found the mirror structures can be divided into two groups: ∼80% of the events that are observed near the bow shock evolve less than 10 s in plasma with high temperature anisotropy and high plasma beta value, keeping in saturated states; the other 20% of the events evolve following a similar process to that at the Earth, undergoing morphology transition in response to the local plasma conditions. However, the dayside magnetosheath is largely in an unstable condition, which prevents the mirror-mode structures from fully evolving into the decaying phase. Our results suggest that energy dispassion through wave-particle interaction might not be sufficient to remove the free energy that is introduced by the solar wind–Mars interaction.

Do We Need to Consider Electrons' Kinetic Effects to Properly Model a Planetary Magnetosphere: The Case of Mercury

AbstractThe magnetosphere of Mercury is studied using an implicit full particle‐in‐cell simulation (PIC). We use a hybrid simulation where ions are full particles and electrons are considered as a fluid to start a PIC simulation where electrons are also particles and follow their distribution function. This approach allows us to estimate the changes introduced by the electron kinetic physics. We find that the overall macroscopic state of the magnetosphere of Mercury is little affected, but several physical processes are significantly modified in the full PIC simulation: the foreshock region is more active with more intense shock reformation, the Kelvin‐Helmholtz rippling effects on the nightside magnetopause are sharper, and the magnetotail current sheet becomes thinner than those predicted by the hybrid simulation. The greatest effect of the electron physics comes from the processes of particle energization. Both species, not just the electrons, are found to gain more energy when kinetic electron processes are included. The region with the most energetic plasma is found on the dusk side of the tail where magnetic flux ropes are formed due to reconnection. We find that the ion and electron energization is associated with the regions of reconnection and the development of kinetic instabilities caused by counter‐streaming electron populations. The resulting electron distributions are highly non Maxwellian, a process that neither MHD nor hybrid models can describe.

Preferential Acceleration of Heavy Ions in a Spontaneously Fragmenting Flare Current Sheet

Abstract We study the ion acceleration in a mesoscale, spontaneously fragmenting flare current sheet (SFCS) characterized by the presence of a plasmoid cascade. The main subject of our investigation is to determine whether and how plasmoid cascades at intermediate scales in a fragmented current sheet of a solar flare can impact the (preferential) acceleration of specific ions. The time evolution of the SFCS is obtained from high-resolution 2.5D MHD simulations. The ion trajectories (in the background fields resulting from the MHD model), energies, and pitch angles are calculated using a relativistic test-particle code based on the half-acceleration–rotation–half-acceleration method. For light ions, the main acceleration effects of electromagnetic fields within the SFCS are analyzed using the guiding center approximation. We identify regions with the most-efficient ion acceleration within the SFCS, the accelerator efficiency, and spectra of the accelerated ions. The influence of the charge-to-mass ratio on ion behavior is also studied and resulting ion abundances are compared with observational data. The main ion acceleration takes place in the regions with a strong polarization term, which is part of the first-order Fermi acceleration. Because the term is mass dependent, heavier ions undergo preferential acceleration. The ion energy spectra, abundance-enhancement factors, and differential fluxes, obtained from the model, exhibit power-law profiles, in agreement with observed solar energetic particle events. Nonetheless, the obtained slopes for the abundance-enhancement factor do not exactly match the observed data. The computed slopes and profiles are not sensitive to changes in the initial plasma temperature.

Nuclear Reaction Sensitivity in Magnetohydrodynamically Driven Supernovae

Abstract The weak r-process offers an explanation of the formation of lighter heavy elements 36 ≤ Z ≤ 47 in ultra-metal-poor stars. Magnetohydrodynamically driven supernovae are thought to be a robust astronomical site of the weak r-process and recently gave a good description of the observational abundance pattern of an extremely metal-poor star. However, the characteristics of nuclear reactions in the MHD nucleosynthesis are not as clear as in another site, that of core-collapse supernovae. In this paper, the trajectories of the MHD model are implemented into SkyNet network calculations. By varying the reaction rates of each type, the (α,n) reactions are much more active than other types of reactions, such as (n,γ), (p,γ), (n,p), and (α,p). A further detailed sensitivity study investigates the (α,n) reactions and lists the most influential ones over the whole range, and the impactful reactions on each element from Sr to Ag are tabulated.

Comparing results of real-scale time MHD modeling with observational data for first flare M 1.9 in AR 10365

Abstract As shown in the first results of MHD simulations in the real scale of time, above the active region (AR) 10365, during the first flare M 1.9 (05/26/2003 05:34) at a height of 16–18 mm (lower corona), a singular line of magnetic field appears. The local maximum of the current density is situated on this singular line. The magnetic field in the vicinity of this singular line is the superposition of an X-type magnetic configuration and a divergent magnetic field. The accumulation of magnetic energy for solar flare with current sheet creation takes place near this singular line due to magnetic field deformation by disturbances in the X-type configuration in spite of the presence of overlaid diverging magnetic configuration. The magnetic configuration is so complicated that the singular line can be found only by using specially developed graphical system of search. The position of singular line coincides with position of source of flare radio emission at the frequency 17 GHz above AR 10365 measured by Nobeyama Radioheliograph (NoRH). Also, MHD simulation shows appearance of the singular line, in the vicinity of which X-type configuration dominates. However, apparently due to small disturbance, propagating from the photosphere, sufficient magnetic energy was not accumulated in this configuration, so the NoRH does not show the flare source of emission at the frequency 17 GHz in the place, where this singular line is situated.

On Linearly Unstable Steady States of an MHD Model of an Incompressible Polymeric Fluid in the Case of Absolute Conductivity

On Linearly Unstable Steady States of an MHD Model of an Incompressible Polymeric Fluid in the Case of Absolute Conductivity

Time-discretization of a plasma-neutral MHD model with a semi-implicit leapfrog algorithm

The semi-implicit leapfrog time-discretization is a workhorse algorithm for initial-value MHD codes to bridge between vastly separated time scales. Inclusion of atomic interactions with neutrals breaks the functional structure of the MHD equations that exploited by the leapfrog. We address how to best integrate atomic physics into the semi-implicit leapfrog. Following the Crank-Nicolson method, one approach is to time-center the atomic interactions in the linear solver and use a Newton method to include the nonlinear contributions. Alternatively, another family of methods are based on operator-splitting the terms associated with the atomic interactions using a Strang-splitting technique. These methods naturally break equations into constituent ODE and PDE parts and preserve the structure exploited by the semi-implicit leapfrog. We study the accuracy and efficiency of these methods through a battery of 0D and 1D cases and show that a second-order-in-time Douglas-Rachford inspired coupling between the ODE and PDE advances is effective in reducing the time-discretization error to be comparable to that of Crank-Nicolson with Newton iteration of the nonlinear terms. Splitting ODE and PDE parts results in independent matrix solves for each field which reduces the computational cost considerably and provides parallelization over species relative to Crank-Nicolson.