Results for “resistive MHD” — Page 9

DOE OSTI2024

Generation of shear flows induced by AE / EPM in LHD plasma

The generation of shear flows (SFs) by Alfven Eigenmodes (AEs) and energetic particle modes (EPMs) have important effects on the operation of future nuclear fusion reactors, because SFs regulate the saturation of the AEs/EPMs, the transport of EPs and thermal plasma, as well as the formation of transport barriers among other consequences. The aim of this study is the analysis of SFs generation during the saturation phase of AEs and EPMs in LHD plasma. Experiments performed in the 23rd and 24th LHD experimental campaigns are dedicated to explore the destabilization of AEs/EPMs in discharges with different heating patterns, thermal plasma and magnetic field configurations. In particular, the shots 176490 and 179697 show the destabilization of MHD bursts and energetic-ion-driven resistive interchange modes (EIC), respectively. Charge exchange spectroscopy measurements in both discharges indicate that the generation of SFs by AE/EPM is uncorrelated with the perturbation induced by the neutral beam injector (NBI). Nonlinear simulations performed using the gyro-fluid code FAR3d show the generation of zonal structures, especially SFs, induced during the saturation phase of Toroidal Alfven Eigenmodes (TAEs) triggered in the MHD burst as well as by the 1/1 EIC in the bursting phase. The simulations indicate that SFs are caused by the radial electric fields powered by energy transfers from the unstable AE/EPM towards the thermal plasma. The strongest SFs are measured during the EIC bursting phase once the 1/1 EPM overlaps with nearby resonances at the plasma periphery. Likewise, the largest SFs during the MHD burst are observed once TAEs radially overlap in the inner-middle plasma region.

AE↗

NASA NTRS2014

Statistical Mechanics of Turbulent Dynamos

Incompressible magnetohydrodynamic (MHD) turbulence and magnetic dynamos, which occur in magnetofluids with large fluid and magnetic Reynolds numbers, will be discussed. When Reynolds numbers are large and energy decays slowly, the distribution of energy with respect to length scale becomes quasi-stationary and MHD turbulence can be described statistically. In the limit of infinite Reynolds numbers, viscosity and resistivity become zero and if these values are used in the MHD equations ab initio, a model system called ideal MHD turbulence results. This model system is typically confined in simple geometries with some form of homogeneous boundary conditions, allowing for velocity and magnetic field to be represented by orthogonal function expansions. One advantage to this is that the coefficients of the expansions form a set of nonlinearly interacting variables whose behavior can be described by equilibrium statistical mechanics, i.e., by a canonical ensemble theory based on the global invariants (energy, cross helicity and magnetic helicity) of ideal MHD turbulence. Another advantage is that truncated expansions provide a finite dynamical system whose time evolution can be numerically simulated to test the predictions of the associated statistical mechanics. If ensemble predictions are the same as time averages, then the system is said to be ergodic; if not, the system is nonergodic. Although it had been implicitly assumed in the early days of ideal MHD statistical theory development that these finite dynamical systems were ergodic, numerical simulations provided sufficient evidence that they were, in fact, nonergodic. Specifically, while canonical ensemble theory predicted that expansion coefficients would be (i) zero-mean random variables with (ii) energy that decreased with length scale, it was found that although (ii) was correct, (i) was not and the expected ergodicity was broken. The exact cause of this broken ergodicity was explained, after much investigation, by greatly extending the statistical theory of ideal MHD turbulence. The mathematical details of broken ergodicity, in fact, give a quantitative explanation of how coherent structure, dynamic alignment and force-free states appear in turbulent magnetofluids. The relevance of these ideal results to real MHD turbulence occurs because broken ergodicity is most manifest in the ideal case at the largest length scales and it is in these largest scales that a real magnetofluid has the least dissipation, i.e., most closely approaches the behavior of an ideal magnetofluid. Furthermore, the effects grow stronger when cross and magnetic helicities grow large with respect to energy, and this is exactly what occurs with time in a real magnetofluid, where it is called selective decay. The relevance of these results found in ideal MHD turbulence theory to the real world is that they provide at least a qualitative explanation of why confined turbulent magnetofluids, such as the liquid iron that fills the Earth's outer core, produce stationary, large-scale magnetic fields, i.e., the geomagnetic field. These results should also apply to other planets as well as to plasma confinement devices on Earth and in space, and the effects should be manifest if Reynolds numbers are high enough and there is enough time for stationarity to occur, at least approximately. In the presentation, details will be given for both theoretical and numerical results, and references will be provided.

Shebalin, John V.↗

NASA NTRS2014

MHD Turbulence and Magnetic Dynamos

Incompressible magnetohydrodynamic (MHD) turbulence and magnetic dynamos, which occur in magnetofluids with large fluid and magnetic Reynolds numbers, will be discussed. When Reynolds numbers are large and energy decays slowly, the distribution of energy with respect to length scale becomes quasi-stationary and MHD turbulence can be described statistically. In the limit of infinite Reynolds numbers, viscosity and resistivity become zero and if these values are used in the MHD equations ab initio, a model system called ideal MHD turbulence results. This model system is typically confined in simple geometries with some form of homogeneous boundary conditions, allowing for velocity and magnetic field to be represented by orthogonal function expansions. One advantage to this is that the coefficients of the expansions form a set of nonlinearly interacting variables whose behavior can be described by equilibrium statistical mechanics, i.e., by a canonical ensemble theory based on the global invariants (energy, cross helicity and magnetic helicity) of ideal MHD turbulence. Another advantage is that truncated expansions provide a finite dynamical system whose time evolution can be numerically simulated to test the predictions of the associated statistical mechanics. If ensemble predictions are the same as time averages, then the system is said to be ergodic; if not, the system is nonergodic. Although it had been implicitly assumed in the early days of ideal MHD statistical theory development that these finite dynamical systems were ergodic, numerical simulations provided sufficient evidence that they were, in fact, nonergodic. Specifically, while canonical ensemble theory predicted that expansion coefficients would be (i) zero-mean random variables with (ii) energy that decreased with length scale, it was found that although (ii) was correct, (i) was not and the expected ergodicity was broken. The exact cause of this broken ergodicity was explained, after much investigation, by greatly extending the statistical theory of ideal MHD turbulence. The mathematical details of broken ergodicity, in fact, give a quantitative explanation of how coherent structure, dynamic alignment and force-free states appear in turbulent magnetofluids. The relevance of these ideal results to real MHD turbulence occurs because broken ergodicity is most manifest in the ideal case at the largest length scales and it is in these largest scales that a real magnetofluid has the least dissipation, i.e., most closely approaches the behavior of an ideal magnetofluid. Furthermore, the effects grow stronger when cross and magnetic helicities grow large with respect to energy, and this is exactly what occurs with time in a real magnetofluid, where it is called selective decay. The relevance of these results found in ideal MHD turbulence theory to the real world is that they provide at least a qualitative explanation of why confined turbulent magnetofluids, such as the liquid iron that fills the Earth's outer core, produce stationary, large-scale magnetic fields, i.e., the geomagnetic field. These results should also apply to other planets as well as to plasma confinement devices on Earth and in space, and the effects should be manifest if Reynolds numbers are high enough and there is enough time for stationarity to occur, at least approximately. In the presentation, details will be given for both theoretical and numerical results, and references will be provided.

Shebalin, John V↗

NASA NTRS1993

Energy storage and dissipation in the magnetotail during substorms. I - Particle simulations. II - MHD simulations

2D electromagnetic particle simulations are used to investigate the dynamics of the tail during development of substorms under the influence of the pressure in the magnetospheric boundary layer and the dawn-to-dusk electric field. It is shown that pressure pulses result in thinning of the tail current sheet as the magnetic field becomes pinched near the region where the pressure pulse is applied. The pinching leads to the tailward flow of the current sheet plasma and the eventual formation and injection of a plasmoid. Surges in the dawn-to-dusk electric field cause plasma on the flanks to convect into the center of the current sheet, thereby thinning the current sheet. The pressure in the magnetospheric boundary laser is coupled to the dawn-to-dusk electric field through the conductivity of the tail. Changes in the predicted evolution of the magnetosphere during substorms due to changes in the resistivity are investigated under the assumption that MHD theory provides a suitable representation of the global or large-scale evolution of the magnetotail to changes in the solar wind and to reconnection at the dayside magnetopause. It is shown that the overall evolution of the magnetosphere is about the same for three different resistivity distributions with plasmoid formation and ejection in each case.

Winglee, R. M.↗

NASA NTRS1983

Reconnection rates, small scale structures and simulations

The study of reconnection in the context of one fluid, two dimensional magnetohydrodynamics (MHD), with spatially uniform constant density, viscosity and resistivity is though to retain most of the physics important in reconnection. Much of the existing reconnection literature makes use of this approach. This discussion focuses on attempts to determine the properties of reconnection solutions to MHD as precisely as possible without regard to the intrinsic limitations of the model.

Matthaeus, W. H.↗

DOE OSTI2026

MARS-Q modeling of low- n resistive kink-peeling modes and edge harmonic oscillations in DIII-D

Linear and quasilinear magnetohydrodynamic (MHD) modeling is carried out for two DIII-D discharges that both featured a transition from quiescent H-mode (QH) to wide-pedestal QH (WPQH). The MHD perturbations, associated with the edge harmonic oscillations (EHOs) observed during the QH-phase in both discharges, are identified as low-n (n is the toroidal mode number) resistive kink-peeling instabilities, with the ideal MHD counterpart remaining stable. The quasilinear model successfully simulates EHO-like perturbations during the QH phase in both discharges, confirming the experimental observations. A less intuitive finding is the EHO-like behavior involving the n = 2 perturbation, simulated for one of the discharges during the WPQH-phase. This result, while consistent with experimental observations, is obtained despite the fact that the initial perturbation is linearly stable. The eventual growth of the perturbation is solely due to nonlinear interaction between the MHD perturbation and the plasma toroidal flow. The occurrence of the EHO-like perturbation during the WPQH-phase is found to be sensitive to the initial profile of the plasma edge rotation. For DIII-D plasmas considered, the neoclassical toroidal viscosity, generated by three-dimensional low-n perturbations, is found to play a dominant role in modifying the edge flow during EHOs.

EHO↗

DOE OSTI2023

The theory of kinetic effects on resistive wall mode stability in tokamaks

Tokamak fusion plasmas benefit from high pressures but are then susceptible to modes of instability. These magnetohydrodynamic (MHD) modes are macroscopic distortions of the plasma, but certain collective motions of individual particles can provide stabilizing effects opposing them. The presence of a resistive wall slows the mode growth, converting a kink to a resistive wall mode (RWM). A kinetic MHD model includes Maxwell's equations, ideal MHD constraints, and kinetic effects included through the pressure tensor, calculated with the perturbed drift-kinetic distribution function of the particles. The kinetic stabilizing effects on the RWM arise through resonances between the plasma rotation and particle drift motions: precession, bounce, and transit. A match between particle motions and the mode allows efficient transfer of energy that would otherwise drive the growth of the mode, thus damping the growth. The first approach to calculating RWM stability is to write a set of equations for the complex mode frequency in terms of known quantities and then to solve the system. The “energy principle” approach, which has the advantage of clarity in distinguishing the various stabilizing and destabilizing effects, is to change the force balance equation into an equation in terms of changes of kinetic and potential energies, and then to write a dispersion relation for the mode frequency in terms of those quantities. These methods have been used in various benchmarked codes to calculate kinetic effects on RWM stability. Importantly, the theory has illuminated the important roles of plasma rotation, energetic particles, and collisions in RWM stability.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1985

Ohm's law for a current sheet

The paper derives an Ohm's law for single-particle motion in a current sheet, where the magnetic field reverses in direction across the sheet. The result is considerably different from the resistive Ohm's law often used in MHD studies of the geomagnetic tail. Single-particle analysis is extended to obtain a self-consistency relation for a current sheet which agrees with previous results. The results are applicable to the concept of reconnection in that the electric field parallel to the current is obtained for a one-dimensional current sheet with constant normal magnetic field. Dissipated energy goes directly into accelerating particles within the current sheet.

Lyons, L. R.↗

NASA NTRS1992

The evolution of line-tied coronal arcades including a converging footpoint motion

It has been demonstrated in the past that single, 2D coronal arcades are very unlikely driven unstable by a simple shear of the photospheric footpoints of the magnetic field lines. By means of 2D, time-dependent MHD simulations, evidence is presented that a resistive instability can result if in addition to the footpoint shear a slow motion of the footpoints toward the photospheric neutral line is included. The photospheric footpoint velocity in this model is nonsingular and the shear dominates everywhere. Starting from a planar potential field geometry for the arcade, it is found that after some time a current sheet is formed which is unstable with respect to the tearing instability. The time of its onset scales with the logarithm of the magnetic diffusivity assumed in the calculation. In its nonlinear phase, a quasi-stationary situation arises in the vicinity of the x-line with an almost constant reconnection rate. The height of the x-line above the photosphere and the distance of the separatrix footpoints remain almost constant in this phase, while the helical flux tube, formed above the neutral line, continuously grows in size.

Inhester, B.↗

NASA NTRS1980

The stability properties of cylindrical force-free fields - Effect of an external potential field

A large-scale potential field with an embedded smaller-scale force-free structure gradient x B equals alpha B is studied in cylindrical geometry. Cases in which alpha goes continuously from a constant value alpha 0 on the axis to zero at large r are considered. Such a choice of alpha (r) produces fields which are realistic (few field reversals) but not completely stable. The MHD-unstable wavenumber regime is found. Since the considered equilibrium field exhibits a certain amount of magnetic shear, resistive instabilities can arise. The growth rates of the tearing mode in the limited MHD-stable region of k space are calculated, showing time-scales much shorter than the resistive decay time.

Chiuderi, C.↗

NASA NTRS1977

Dissipative, forced turbulence in two-dimensional magnetohydrodynamics

The equations of motion of a turbulent two-dimensional MHD flow are solved in the presence of finite viscosity and resistivity for the case when external mechanical and/or magnetic forces act on the fluid, the goal of the study being to verify the existence of a MHD dynamo effect which is represented by a substantial back-transfer of mean square vector potential to the longest allowed Fourier wavelengths. The regime explored is that for which the mechanical and magnetic Reynolds numbers are in the range 100 to 1000. It is concluded that mechanical forcing terms alone cannot lead to dynamo action, but that dynamo action can result from either magnetic forcing terms or from both mechanical and magnetic forcing terms simultaneously.

Fyfe, D.↗

NASA NTRSDate not supplied

Effect of Plasma Sheaths on Earth Re-entry MHD Processes

The first study of the full coupling between the aerothermodynamics, the magnetohydrodynamics, and the plasma sheaths within earth entry flows is here per-formed. The problem tackled herein is representative of a force-generating MHD patch located between the plenum and the frustum of a capsule entering the earth’s atmosphere at Mach 34. The reactions are obtained from a modified 11-species Park chemical solver. The physical model fully couples the drift-diffusion model for the sheaths to the multispecies Navier-Stokes equations for the plasma flow. The Hall and ion slip effects are taken into consideration within the plasma flow and within the sheaths. Results obtained indicate that the cathode sheath can exert significant resistance to current flow and thus reduce the MHD-generated force by 40% or more. The effect of the sheath on the MHD force is found to be more pronounced at lower applied magnetic field.

Earth Re-entry↗

DOE OSTI2024

Extended-MHD simulations of disruption mitigation via massive gas injection in SPARC

Recent developments to the M3D-C1 code enable higher fidelity modeling of disruptions, and can be applied in the design verification of reactor-scale tokamaks. Among these new capabilities is a method to mesh conducting vessel structures such as coils and passive plates, packing of the toroidal mesh around gas injectors, as well as anisotropic resistivity inside the vessel structures. We present extended-magnetohydrodynamic (MHD) simulations of disruption mitigation via massive gas injection (MGI) in SPARC. The goal of this study is to inform the disruption mitigation layout of SPARC and aid in the design of an effective gas injector configuration. Fully three-dimensional simulations with M3D-C1 are carried out for various injector configurations with the primary goal of determining the effect of different MGI parameters on heat loads and vessel forces. The simulations include a model for impurity ionization, recombination, advection and radiation, as well as spatially resolved conducting structures around the plasma. A localized mixture of deuterium and neon with a small toroidal and poloidal width is injected in up to six locations. We demonstrate that M3D-C1 can model a rapid shutdown via MGI using narrow and more realistic gas plumes than in previous simulations. As a result of the q = 1 surface in the SPARC baseline case a sawtooth is observed early in the simulations. Despite the sawtooth and the onset of edge MHD instabilities, the impurity distribution remains localized around the injector locations, but enables a radiative shutdown of the plasma. We find that using the maximum of six gas injectors results in a lower peaking factor and leads to a more even distribution of radiation toroidally than using two injectors.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1995

Coronal heating by the resonant absorption of Alfven waves: Wavenumber scaling laws.

The importance of global modes in coronal loop heating is well established. In the present work the scaling of the global-mode resonant heating rate with the perturbation wavenumbers is studied with the numerical solution of the linearized time-dependent MHD equations for a full compressible, low-beta, resistive plasma using an implicit integration scheme. The numerical simulations demonstrate that the dissipation on inhomogeneties in the background Alfven speed occurs in narrow resonant layer with the highest heating rate at the global-mode frequency. The global-mode heating rate H (sub r) was found to scale as H (Sub r) approximately k (sub y) (exp 1.03) when k (sub z) = 0.1, and as H (sub r) approximately k (sub y) (exp -1.93) when k (sub z) = 0.75, where k (sub y) and k (sub z) are the wavenumbers in the perpendicular and parallel to the magnetic field directions, respectively, while the dependence of H (sub r) on k (sub z) is more complex. The quality factor Q of the MHD resonance cavity scales as Q approximately k (sub y) (exp -1.8) for k (sub z) = 0.75 and as Q approximately k (sub y) (exp -1.46) for k (sub z) = 0.1. The numerically determined heating rate scaling, the global-mode fequency, and the quality factor are in good agreement with the analytical linear theory. The magnitude of the perturbed velocities was found to decrease with k (sub y). Assuming typical coronal loop parameters (B (sub 0) = 100-200 G, upsilon (sub A) = 2000-4000 km/s), the Alfven waves can supply the required heating to a low-Q loops.

Ofman, L.↗

DOE OSTI2024

Effects of zero and reversed magnetic shear on resistive wall modes in a straight limiter tokamak with zero beta

Advanced tokamak scenarios often feature equilibriums with zero and reversed magnetic shear. To isolate and investigate their impacts on the resistive wall mode (RWM) instability analytically, we construct a series of cylindrical limiter equilibriums with different magnetic shear in the core and toward plasma edge, as a prototype of the configurations in advanced tokamak scenarios. Equilibriums with zero β are considered so that the analysis focuses on the current-driven RWMs. Analytical solutions for the n=1 resistive wall mode, derived from the reduced ideal magnetohydrodynamics (MHD) equations, consistently demonstrate key insights for both the core and the edge: the growth rate of RWMs is inversely proportional to the averaged magnetic shear when the safety factor at the edge (qa) is held constant. Specifically, an increase in positive averaged magnetic shear results in a decreased growth rate, whereas an increase in negative averaged magnetic shear leads to an increased growth rate. Furthermore, the influence of nqa on the mode's stability significantly surpasses the effects of magnetic shear changes previously discussed. These analytical calculation results provide a verification of NIMROD simulations.

Wan, Sui (ORCID:0009000464121677)↗

DOE OSTI2020

Final Report for Tech-X Corporations’s contribution to Enhancing Understanding of High Energy Density Plasmas from Wire Array and Solid Liner Implosions Using Fluid Modeling with Kinetic Closures

Recent results from experiments and simulation of magnetically driven pulsed power liners have explored the role of the early-time electrothermal instability in the evolution of the magneto-Rayleigh-Taylor instability. Our focus will be on understanding the development of such instabilities and the potential stabilization mechanisms via electron thermal conduction, viscosity, and large magnetic fields which we expect could play a significant role in supporting the success of the MagLIF program. Experiments have shown that studies of high-energy density plasmas from wire-array implosions require physics modeling that goes well beyond simple models such as ideal magnetohydrodynamics. The goal of this work is to provide increased understanding of these experiments by employing simulations with a multi-fluid extended-MHD model which uses kinetic closures for thermal conduction, resistivity and viscosity. We will use codes easily available to the wider research community, including university students, with a secondary goal of providing the community with well-benchmarked tools capable of advanced modeling of high-energy-density plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1993

Coronal heating by the resonant absorption of Alfven waves - Importance of the global mode and scaling laws

Numerical simulations of the MHD equations for a fully compressible, low-beta, resistive plasma are used to study the resonance absorption process for the heating of coronal active region loops. Comparisons with more approximate analytic models show that the major predictions of the analytic theories are, to a large extent, confirmed by the numerical computations. The simulations demonstrate that the dissipation occurs primarily in a thin resonance layer. Some of the analytically predicted features verified by the simulations are (a) the position of the resonance layer within the initial inhomogeneity; (b) the importance of the global mode for a large range of loop densities; (c) the dependence of the resonance layer thickness and the steady-state heating rate on the dissipation coefficient; and (d) the time required for the resonance layer to form. In contrast with some previous analytic and simulation results, the time for the loop to reach a steady state is found to be the phase-mixing time rather than a dissipation time. This disagreement is shown to result from neglect of the existence of the global mode in some of the earlier analyses. The resonant absorption process is also shown to behave similar to a classical driven harmonic oscillator.

Steinolfson, Richard S.↗

DOE OSTI2024

Role of electrostatic perturbation on kinetic resistive wall mode with application to spherical tokamak

Abstract A more complete non-perturbative magnetohydrodynamic (MHD)-kinetic hybrid formulation is developed by including the perturbed electrostatic potential δφ in the particle Lagrangian. The fluid-like counter-parts of the hybrid equations, in the Chew-Goldberger-Low high-frequency limit, are also derived and utilized to test the new toroidal implementation in the MARS-K code. Application of the updated non-perturbative hybrid model for a high- β spherical tokamak plasma in MAST finds that the perturbed electrostatic potential generally plays a minor role in the n = 1 ( n is the toroidal mode number) resistive wall mode instability. The effect of δφ is largely destabilizing, with the growth rate of the instability increased by several (up to 20) percent as compared to the case without including δφ . A similar relative change is also obtained for the kinetic-induced resonant field amplification effect at high- β in the MAST plasma considered. The updated capability of the MARS-K code allows quantitative exploration of drift kinetic effects on various MHD instabilities and the antenna-driven plasma response where the electrostatic perturbation, coupled to magnetic perturbations, may play important roles.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗