Excitation of a magnetohydrodynamic wave guide in a coaxial line
Excitation of magnetohydrodynamic wave guide in coaxial line
MAGNETOHYDRODYNAMIC WAVE↗
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Theory of magnetohydrodynamic wave scattering at the end of a wave guide
Theory of magnetohydrodynamic wave scattering at end of wave guide
MAGNETOHYDRODYNAMIC WAVE↗
Turbulent magnetohydrodynamic flows in prismatic and cylindrical pipes
Turbulent magnetohydrodynamic flows in prismatic and cylindrical pipes
MAGNETOHYDRODYNAMIC FLOW↗
On the one-dimensional magnetohydrodynamic flow in an annulus
One-dimensional magnetohydrodynamic flow in annulus
ONE-DIMENSIONAL FLOW↗
Magnetohydrodynamic plasma calculations
Computer simulations of magnetohydrodynamic plasma devices
PLASMA PHYSICS↗
A Simple GPU-Accelerated Two-Dimensional MUSCL-Hancock Solver for Ideal Magnetohydrodynamics
We describe our experience using NVIDIA's CUDA (Compute Unified Device Architecture) C programming environment to implement a two-dimensional second-order MUSCL-Hancock ideal magnetohydrodynamics (MHD) solver on a GTX 480 Graphics Processing Unit (GPU). Taking a simple approach in which the MHD variables are stored exclusively in the global memory of the GTX 480 and accessed in a cache-friendly manner (without further optimizing memory access by, for example, staging data in the GPU's faster shared memory), we achieved a maximum speed-up of approx. = 126 for a sq 1024 grid relative to the sequential C code running on a single Intel Nehalem (2.8 GHz) core. This speedup is consistent with simple estimates based on the known floating point performance, memory throughput and parallel processing capacity of the GTX 480.
graphics processing units↗
The Event Horizon General Relativistic Magnetohydrodynamic Code Comparison Project
Recent developments in compact object astrophysics, especially the discovery of merging neutron stars by LIGO, the imaging of the black hole in M87 by the Event Horizon Telescope, and high- precision astrometry of the Galactic Center at close to the event horizon scale by the GRAVITY experiment motivate the development of numerical source models that solve the equations of general relativistic magnetohydrodynamics (GRMHD). Here we compare GRMHD solutions for the evolution of a magnetized accretion flow where turbulence is promoted by the magnetorotational instability from a set of nine GRMHD codes: Athena++, BHAC, Cosmos++, ECHO, H-AMR, iharm3D, HARM-Noble, IllinoisGRMHD, and KORAL. Agreement among the codes improves as resolution increases, as measured by a consistently applied, specially developed set of code performance metrics. We conclude that the community of GRMHD codes is mature, capable, and consistent on these test problems.
relativistic processes↗
New Magnetohydrodynamic (MHD) Lift Concept for More Efficient Missions to Mars and Neptune
The potential for using an applied magnetic field to augment the aerodynamic lift and drag of a hypersonic vehicle entering Neptune or Mars was studied. The study was conducted to assess whether magnetohydrodynamics (MHD)could boost aerodynamic lift and/or drag for aerocapture of a spacecraft into planetary orbit. MHD seemed well suited to create Lorentz forces during aerocapture when the flow is most ionized and conductive. Neptune and Mars were selected since larger payloads and faster trip times to each planet may substantially increase scientific and exploration opportunities. The results of the systems analysis presented herein suggest that a single MHD effector located off-centerline creates steering forces equaling whole-body aerodynamic forces and suggests a ground-breaking opportunity for new mission classes. The magnetic field required to produce these large forces is around 1 Tesla (T) having a mass roughly the same amount as the ballast used for recent Mars lander missions.
Aerocapture↗
Impact of Magnetohydrodynamic (MHD) Induced Drag on High Ballistic Coefficient Aerocapture at Neptune
This paper presents analyses illustrating the benefits of magnetohydrodynamic (MHD) drag force control for a capsule performing aerocapture at Neptune relative to the same capsule utilizing conventional aerodynamic-only control across a range of design and flight conditions. MHD technology utilizes an onboard mag-net to create a magnetic field that interacts with the ionized plasma surrounding the capsule at hypersonic velocities, thus creating an electron current and inducing a Lorentz force used to increase capsule drag. The study assumes a 4.57-meterMars Science Laboratory (MSL) 70-degree sphere-cone capsule aerodynamic shape arrives hyperbolically at Neptune and aerocaptures into a synchronous Tri-ton orbit (3986 km x 430,000 km orbit inclined 157 degrees) that offers repeated flyby opportunities. Hyperbolic arrival velocity and the capsule entry mass (i.e., ballistic coefficient) are varied over a wide range of values to study the impact of these variables on key flight performance and sizing parameters. Results show reduced heat rates, heat loads, and thermal protection system mass for MHD cases at all conditions, with the benefit of MHD relative to conventional aerodynamic-only options increasing as ballistic coefficient increases, suggesting the payoff for MHD is significantly better for high-mass entry system design concepts with high ballistic coefficients.
Entry Descent and Landing↗
A Full-Induction Magnetohydrodynamics Solver for Liquid Metal Fusion Blankets in Vertex-CFD
Multiphysics modeling of liquid metal fusion blankets, which produce tritium and convert energy of neutrons created via fusion reactions into heat, is crucial for predicting performance, ensuring structural integrity, and optimizing energy production. While traditional blanket modeling of liquid metal flows during normal steady operating conditions commonly employs the inductionless approximation of the magnetohydrodynamics (MHD) equations, transient scenarios, when the plasma-confining magnetic field varies on millisecond time scales, require a full-induction MHD approach that dynamically evolves the magnetic field via the time-dependent induction equation. This paper presents the formulation, implementation, and initial verification of a full-induction MHD solver integrated within the open-source Vertex-CFD framework, which aims to achieve tight multiphysics coupling, a flexible software design enabling easy extension and addition of physics models, and performance portability across computing platforms. The solver utilizes finite element spatial discretization, implicit Runge–Kutta time integration, and an inexact Newton method to solve the resulting discrete nonlinear system, leveraging Trilinos packages for efficient computation. Verification against selected benchmark problems demonstrates accuracy and robustness of the solver. Furthermore, when the solver is applied to an idealized blanket model in 2.5D and full 3D, results obtained with Vertex-CFD are in good agreement with recently published quasi-2D simulations. These findings establish a computational foundation for future simulations of transient MHD phenomena in liquid metal blankets with Vertex-CFD, and open avenues for future extensions and performance optimizations.
Endeve, Eirik [ORNL] (ORCID:0000000312519507)↗
A constrained-transport embedded boundary method for compressible resistive magnetohydrodynamics
Motivated by the increased interest in pulsed-power magneto-inertial fusion devices in recent years, we present a method for implementing an arbitrarily shaped embedded boundary on a Cartesian mesh while solving the equations of compressible resistive magnetohydrodynamics. The method is built around a finite volume formulation of the equations in which a Riemann solver is used to compute fluxes on the faces between grid cells, and a face-centered constrained transport formulation of the induction equation. The small time step problem associated with the cut cells is avoided by always computing fluxes on the faces and edges of the Cartesian mesh. We extend the method to model a moving interface between two materials with different properties using a ghost-fluid approach, and show some preliminary results including shock-wave-driven and magnetically-driven dynamical compressions of magnetohydrostatic equilibria. In conclusion, we present a thorough verification of the method and show that it converges at second order in the absence of discontinuities, and at first order with a discontinuity in material properties.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
On reduced modelling of the modulational dynamics in magnetohydrodynamics
This paper explores structure formation in two-dimensional magnetohydrodynamic (MHD) turbulence as a modulational instability (MI) of turbulent fluctuations. We focus on the early stages of structure formation and consider simple backgrounds that allow for a tractable model of the MI while retaining the full chain of modulational harmonics. This approach allows us to systematically examine the validity of popular closures such as the quasilinear approximation and other low-order truncations. We find that, although such simple closures can provide quantitatively accurate approximations of the MI growth rates in some regimes, they can fail to capture the modulational dynamics in adjacent regimes even qualitatively, falsely predicting MI when the system is actually stable. We find that this discrepancy is due to the excitation of propagating spectral waves (PSWs) which can ballistically transport energy along the modulational spectrum, unimpeded until dissipative scales, thereby breaking the feedback loops that would otherwise sustain MIs. The PSWs can be self-maintained as global modes with real frequencies and drain energy from the primary structure at a constant rate until the primary structure is depleted. To describe these waves within a reduced model, we propose an approximate spectral closure that captures them and MIs on the same footing. We also find that introducing corrections to ideal MHD, conservative or dissipative, can suppress PSWs and reinstate the accuracy of the quasilinear approximation. In this sense, ideal MHD is a ‘singular’ system that is particularly sensitive to the accuracy of the closure within mean-field models.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
ARC physics basis–magnetohydrodynamics
ARC is designed to produce 400 MW of net electricity and prove the commercial feasibility of a fusion power plant. In order to achieve this goal ARC has to operate with optimal core performance in a stationary scenario that minimises wear on the first wall and divertor. This requires avoiding or mitigating magnetohydrodynamic (MHD) instabilities which have the potential to not only degrade the plasma core but also lead to deleterious transient heat loads on plasma facing components. Therefore, this work aims at characterising the MHD stability of the high performance ARC scenario and inform the design of error field correction coils. Firstly, simulations of vertical displacement events show that an in-vessel coil is not needed and instead the poloidal shaping coils can be used to control vertical stability. These simulations also inform the demands on the corresponding coil power supplies. Stability analysis of the ideal kink mode with or without a conducting wall and kinetic effects suggests that the ARC baseline scenario operates deeply in the stable region. Using RDCON, tearing modes at the 𝑚/𝑛 =2/1 and 3/2 surfaces (with poloidal mode number 𝑚, and toroidal mode number 𝑛) are shown to be linearly stable, and including thermal transport effects in the rational surfaces lead to further stabilisation. However, other transient plasma instabilities can seed neoclassical tearing modes (NTMs). The marginally stable width of NTMs in ARC strongly depends on the internal inductance and can fall below 0.1% of the normalised poloidal flux. Furthermore, an empirical cross-machine model of the 𝑛 =1 error field leading to a disruption predicts a critical error field larger than SPARC but smaller than ITER. Three-dimensional coils can be designed with the Generalised Purturbed Equilbium Code based on a simple model that calculates the maximum correctable error field that is limited by the neoclassical toroidal viscosity torque. Broad scans of different coil geometries identify a set of 2 rows of off-midplane coils to be a suitable solution. It is also determined that such a set of three-dimensional coils is capable of correcting 𝑛 =2 error fields to some degree and creating strong enough 𝑛 =2 or 𝑛 =3 edge resonant perturbation fields for the suppression of edge-localised modes at reasonable coil currents. The final design of the first ARC will be further informed by results from SPARC.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Magnetohydrodynamic simulations preliminarily predict the habitability and radio emission of TRAPPIST-1e
TRAPPIST-1e, an Earth-sized exoplanet in the habitable zone of the nearby M dwarf TRAPPIST-1, may experience magnetospheric responses that vary with stellar space weather, which could potentially influence both its habitability and radio emissions. Our objective is to investigate how different Earth-like magnetospheric configurations of TRAPPIST-1e – specifically variations in dipolar magnetic field strength and axial tilt – respond to diverse stellar space weather conditions, including events analogous to coronal mass ejections (CMEs), and to assess their implications for potential habitability and expected radio emissions. We conducted 3D magnetohydrodynamic simulations of the TRAPPIST-1e system using the PLUTO code in spherical coordinates. The planetary magnetic field was modelled as dipolar, with equatorial strengths from Earth-like to several times stronger. The dipole axis spans a representative range of axial tilts. We investigate four stellar wind environments, from sub-Alfvénic flow to CME-like disturbances. Planetary shielding was quantified based on the magnetopause standoff distance, and radio powers were estimated via empirical scaling laws. Our simulations show that both shielding and radio power depend strongly on the magnetic configuration. Stronger fields increase protection, while larger tilts reduce it. Radio power increases with both field strength and tilt across all wind regimes. An Earth-like magnetic field can provide effective shielding even under intense CMEs, whereas high tilts require stronger fields. Predicted radio powers reach ~10 20 erg s −1 during CMEs, making bursts from close-in, magnetised planets more detectable. However, for TRAPPIST-1e, the maximum cyclotron frequency lies below the Earth’s ionospheric cutoff (~10 MHz), making ground-based detection currently infeasible.
Sun: magnetic fields↗
Three-dimensional plasmoid-mediated reconnection and turbulence in Hall magnetohydrodynamics
Plasmoid instability accelerates reconnection in collisional plasmas by transforming a laminar reconnection layer into numerous plasmoids connected by secondary current sheets in two dimensions (2D) and by fostering self-generated turbulent reconnection in three dimensions (3D). In large-scale astrophysical and space systems, plasmoid instability likely initiates in the collisional regime but may transition into the collisionless regime as the fragmentation of the current sheet progresses toward kinetic scales. Hall magnetohydrodynamics (MHD) models are widely regarded as a simplified yet effective representation of the transition from collisional to collisionless reconnection. However, plasmoid instability in 2D Hall MHD simulations often leads to a single-X-line reconnection configuration, which significantly differs from fully kinetic particle-in-cell simulation results. This study shows that single-X-line reconnection is less likely to occur in 3D compared to 2D. Moreover, depending on the Lundquist number and the ratio between the system size and the kinetic scale, Hall MHD can also realize 3D self-generated turbulent reconnection. We analyze the features of the self-generated turbulent state, including the energy power spectra and the scale dependence of turbulent eddy anisotropy.
Physics↗
Nonlinear magnetohydrodynamic modeling of ideal ballooning modes in high- β Wendelstein 7-X plasmas
We present nonlinear magnetohydrodynamic (MHD) simulations of high- β Wendelstein 7-X plasmas using the stellarator extension of the M3D- C 1 code, building on the recent work that shows benign saturation of ideal ballooning modes above the designed β limit in the standard configuration [Zhou et al., Phys. Rev. Lett. 133, 135102 (2024)]. First, we examine the results' sensitivity to the parallel thermal conductivity. It is found that while an increased parallel conductivity reduces the linear growth rate, the saturated pressure profile is barely affected. Second, we consider the dependence on the profile shape. It is shown that an equilibrium with a peaked pressure profile and lower β is subject to more significant change than a broad profile with higher β and a larger growth rate, suggesting that benign saturation, or nonlinear stability, is not guaranteed and not dictated by linear growth. Third, we study the influence of the magnetic configuration, with the equilibrium rotational transform varied by adjusting the planar coil current. With similar growth rates, similar magnitudes of profile change are found regardless of the presence of a low-order resonance, which implies that the saturation mechanism is not specific to a resonant or non-resonant mode. These results indicate that MHD stability should still be treated seriously in stellarator operation and design, for which nonlinear modeling using tools like M3D- C 1 can play an instrumental role.
Zhou, Yao [Shanghai Jiao Tong University (China)] ↗
Expansion-driven Weibel instability in magnetohydrodynamics: Linear theory for static systems
The Weibel dispersion relation is obtained in the magnetohydrodynamic (MHD) approximation by including a tensor expression for temperature. MHD gives an upper cutoff wavenumber for Weibel growth identical to kinetic theory if the electron drift velocity is included in the evolution of the electron temperature. MHD overestimates growth rates compared to kinetic theory and gives maximum growth at larger wavenumbers, but it only leads to divergent results as temperature anisotropy tends to infinity. Thermal conduction in MHD lowers the growth rates and shifts maximum growth to smaller wavenumbers, but flux-limited or nonlocal thermal conduction is found to significantly limit these effects. The results are used as a first step in evaluating the potential of MHD to simulate expansion-driven Weibel instability, which occurs due to the temperature tensor only cooling in the direction of expansion. Finally, the small temperature anisotropy found in expansion-driven Weibel instability means that MHD could be an adequate model because growth rates are much less than the electron plasma frequency, and wavelengths are much greater than the Debye length.
Davies, J. R. [Univ. of Rochester, NY (United Stat↗
Numerical investigation of two-dimensional buoyancy-driven eddies in liquid metal magnetohydrodynamic flows in breeding blankets *
Abstract Lead–lithium flows are key features in the design of tokamak breeding blanket concepts such as the dual-coolant lead–lithium (DCLL). Since they flow under magnetic fields, they are affected by magnetohydrodynamic (MHD) effects. The neutron flux originating in the tokamak plasma heats the breeding blanket channels in a non-uniform manner, inducing buoyancy forces in the liquid metal. Buoyancy may become a source of quasi-two-dimensional (Q2D) turbulence, and the appearance of eddies may affect the transport of heat and tritium across the blanket. Blankets characterized by high-speed liquid metal flows (such as DCLL) will need ceramic insulating walls to reduce the MHD-related pressure drop in the channels. In our simulations, we have used the Q2D model proposed by Sommeria and Moreau (SM82) which is especially suitable for modeling electrically insulating channel flows. On top of that, we have modelled buoyancy forces in the momentum equation using the Oberbeck–Boussinesq approximation. In this work, we include a validation of the implemented Q2D model in buoyancy-driven cases and identify a thermohydraulic configuration that promotes the generation of eddies and the accumulation of tritium. We also show the results provided by our post-processing tool based on the bi-dimensional fast Fourier transform for eddy detection and characterization. We complete our investigation by performing an initial assessment of how eddies can accumulate tritium in the breeding blanket. We conclude by discussing the relevance of preventing accumulation of tritium within the blanket and suggest a possible solution.
Suarez, Daniel (ORCID:0000000251740100)↗