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NASA NTRS1992

A test suite for magnetohydrodynamical simulations

A collection is presented of MHD problems that will provide researchers who have interests in modeling MHD phenomena with a battery of tests (a 'test suite') for calibrating their numerical algorithms. Use of these tests will provide a common reference for comparison of different numerical MHD algorithms. The test suite includes both 1D and 2D problems. Taken together, these problems test the abilities of a numerical method to propagate accurately all of the MHD wave families in moving and stationary media, to capture MHD shocks and contact discontinuities, and to model accurately Lorentz force terms in multiple dimensions. An example solution of each test problem is presented. Diagnostic convergence-testing procedures that provide a quantitative evaluation of MHD algorithms are demonstrated.

Stone, James M.↗

NASA NTRS2012

Solar Wind Charge Exchange During Geomagnetic Storms

On March 31st. 2001, a coronal mass ejection pushed the subsolar magnetopause to the vicinity of geosynchronous orbit at 6.6 RE. The NASA/GSFC Community Coordinated Modeling Center (CCMe) employed a global magnetohydrodynamic (MHD) model to simulate the solar wind-magnetosphere interaction during the peak of this geomagnetic storm. Robertson et aL then modeled the expected 50ft X-ray emission due to solar wind charge exchange with geocoronal neutrals in the dayside cusp and magnetosheath. The locations of the bow shock, magnetopause and cusps were clearly evident in their simulations. Another geomagnetic storm took place on July 14, 2000 (Bastille Day). We again modeled X-ray emission due to solar wind charge exchange, but this time as observed from a moving spacecraft. This paper discusses the impact of spacecraft location on observed X-ray emission and the degree to which the locations of the bow shock and magnetopause can be detected in images.

Robertson, Ina P.↗

DOE OSTI2024

An MPMD approach coupling electromagnetic continuum mechanics approximations in ALEGRA

In this work, two complementary approximations for describing aspects of continuum electromagnetics in moving media are discussed: electroquasistatic and magnetoquasistatic. Each has been implemented in the finite element shock code ALEGRA for modeling dynamic electromechanical phenomena on typical engineering time scales, with fully integrated circuit coupling. The approximations can be obtained by consistent asymptotic balancing of Maxwell’s equations relative to timescales associated with magnetic diffusion, charge relaxation, and electromagnetic wave propagation. In ALEGRA, the electroquasistatic approximation is used for ferroelectric (FE) modeling, while the magnetoquasistatic approximation is used for magnetohydrodynamic (MHD) modeling. In this paper we introduce for the first time a detailed derivation of a useful quasi-steady “low-R m ” variant of the MHD approximation applicable for cases, such as with detonators, where the thermodynamic pressure arising from Joule heating dominates over magnetic forces. An additional purpose of this paper is to present a coupling mode using Multiple Program-Multiple Data (MPMD) message passing communication that allows the user to run 3D FE problems together with 2D and/or 3D MHD problems with the respective simulation domains coupled through a common circuit equation. The MPMD coupling capability is used here to model the dynamic coupling of a notional ferroelectric generator with an RP-87 exploding bridgewire detonator. The simulated bridgewire heats up and bursts under current generated by simulated depoling of the ferroelectric generator, as a demonstration of the MPMD capability.

42 ENGINEERING↗

NASA NTRS1993

Structure of the dayside reconnection layer in resistive MHD and hybrid models

Numerical simulations were performed to investigate the structure of the reconnection layer at the dayside magnetopause. Two typical cases are examined in detail; both are asymmetric in magnetic field and plasma density. In case 1, the guide fields in the magnetosheath and in the magnetosphere are set at zero and thus the tangential magnetic fields on the two sides of the initial current sheet are exactly antiparallel. In case 2, the angle between the tangential magnetic fields on the two sides of the initial current sheet is 145 deg. The results obtained from a resistive MHD model and from a hybrid model are found to be different. In the MHD simulation of case 1, a 2-4 intermediate shock is found to bound the reconnection layer on the magnetosheath side, while an Alfven wave pulse bounds the reconnection layer on the magnetospheric side. In case 2, it is found that a time-dependent intermediate shock (TDIS) bounds the reconnection layer on the magnetosheath side, with a slow expansion wave propagating behind. With the MHD simulations, in the general case in which the tangential magnetic fields on the two sides of the initial current sheet are not exactly antiparallel, a rotational discontinuity across which the tangential magnetic field rotates, a large angle is found to bound the reconnection layer on the magnetosheath side.

Lin, Y.↗

NASA NTRS1999

Semiempirical Two-Dimensional Magnetohydrodynamic Model of the Solar Corona and Interplanetary Medium

We have developed a two-dimensional semiempirical MHD model of the solar corona and solar wind. The model uses empirically derived electron density profiles from white-light coronagraph data measured during the Skylub period and an empirically derived model of the magnetic field which is fitted to observed streamer topologies, which also come from the white-light coronagraph data The electron density model comes from that developed by Guhathakurta and coworkers. The electron density model is extended into interplanetary space by using electron densities derived from the Ulysses plasma instrument. The model also requires an estimate of the solar wind velocity as a function of heliographic latitude and radial component of the magnetic field at 1 AU, both of which can be provided by the Ulysses spacecraft. The model makes estimates as a function of radial distance and latitude of various fluid parameters of the plasma such as flow velocity V, effective temperature T(sub eff), and effective heat flux q(sub eff), which are derived from the equations of conservation of mass, momentum, and energy, respectively. The term effective indicates that wave contributions could be present. The model naturally provides the spiral pattern of the magnetic field far from the Sun and an estimate of the large-scale surface magnetic field at the Sun, which we estimate to be approx. 12 - 15 G. The magnetic field model shows that the large-scale surface magnetic field is dominated by an octupole term. The model is a steady state calculation which makes the assumption of azimuthal symmetry and solves the various conservation equations in the rotating frame of the Sun. The conservation equations are integrated along the magnetic field direction in the rotating frame of the Sun, thus providing a nearly self-consistent calculation of the fluid parameters. The model makes a minimum number of assumptions about the physics of the solar corona and solar wind and should provide a very accurate empirical description of the solar corona and solar wind Once estimates of mass density rho, flow velocity V, effective temperature T(sub eff), effective heat flux q(sub eff), and magnetic field B are computed from the model and waves are assumed unimportant, all other plasma parameters such as Mach number, Alfven speed, gyrofrequency, etc. can be derived as a function of radial distance and latitude from the Sun. The model can be used as a planning tool for such missions as Slar Probe and provide an empirical framework for theoretical models of the solar corona and solar wind The model will be used to construct a semiempirical MHD description of the steady state solar corona and solar wind using the SOHO Large Angle Spectrometric Coronagraph (LASCO) polarized brightness white-light coronagraph data, SOHO Extreme Ultraviolet Imaging Telescope data, and Ulysses plasma data.

Sittler, Edward C., Jr.↗

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 OSTI2024

Boundary condition effects on runaway electron mitigation coil modeling for the SPARC and DIII-D tokamaks

Abstract Extended-MHD modeling of planned Runaway Electron Mitigation Coils (REMC) for SPARC and DIII-D is performed with the NIMROD code. A coil has been designed for each machine, with the two differing in shape and location, but both having n = 1 symmetry (with n the toroidal mode number). Compared to previous modeling efforts, three improvements are made to the simulations boundary conditions. First a resistive wall model is used in place of an ideal wall. Second, the ThinCurr code is used to compute the time-dependent 3D fields used as magnetic boundary conditions for the simulations. Third, the simulation boundary is moved from the first-wall location to the Vacuum Vessel (VV), which extends the boundary past the location of the internal REMC. To remove the 3D coil from the simulation domain, an equivalent set of 3D fields is calculated at the VV boundary that produce approximately the same field distribution at the last closed flux surface assuming vacuum between the two. Each of these three boundary condition improvements leads to an improvement in the predicted performance of the REMC for both machines. The resistive wall alone primarily effects the resonance of the coil with the plasma after the TQ, affecting the q-profile evolution in the SPARC modeling, and allowing the applied spectrum to be modified in response to the plasma in the DIII-D modeling. The movement of the simulation boundary has the most significant effect on the RE confinement overall, including in the early stages, particularly for a DIII-D inner wall limited equilibrium, where the RE loss fraction increases from 90% to > 99%, with SPARC RE losses also occurring much earlier when the boundary is placed at the VV.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1994

Physics and evolution of constant opening angle jets using a quasi-one-dimensional magnetohydrodynamic model

We discuss the significance of the assumptions of infinite conductivity and time independence in the context of an ideal MHD model for constant opening angle jets. The model is developed by projecting the MHD equations onto the jet axis. We find that for initially sub-Alfvenic flows (i.e., flows emanating from active galactic nuclei and neutron stars) wind-type solutions exist only when the field lines at the origin are wound up in a direction opposite to the direction of rotation of the compact source. We discuss the possibility that the time evolution of these outflows may be a cycle between breeze- and wind-type solutions as a result of continuous changes in the boundary conditions at the origin due to accretion. We propose that such cycles may explain the apparent one-sideness of some jets, especially the ones for which we cannot use arguments of relativistic beaming. We examine the dependence of the wind-type solutions on the following parameters describing the outflow at the origin: the degree of winding of the field lines, the value of the gas pressure, the polytropic index, the strength of the magnetic field, the value of the rotational velocity, the gravitational potential of the compact object, and the injection velocity. We compare results with results obtained previously, and discuss briefly the qualitative features and physical interpretation of the solutions for outflows emanating from neutron stars and protostars.

Koupelis, Theodoros↗

NASA NTRS1983

Solar maximum mission: Ground support programs at the Harvard Radio Astronomy Station

Observations of the spectral characteristics of solar radio bursts were made with new dynamic spectrum analyzers of high sensitivity and high reliability, over the frequency range 25-580 MHz. The observations also covered the maximum period of the current solar cycle and the period of international cooperative programs designated as the Solar Maximum Year. Radio data on shock waves generated by solar flares were combined with optical data on coronal transients, taken with equipment on the SMM and other satellites, and then incorporated into computer models for the outward passage of fast-mode MHD shocks through the solar corona. The MHD models are non-linear, time-dependent and for the most recent models, quasi-three-dimensional. They examine the global response of the corona for different types of input pulses (thermal, magnetic, etc.) and for different magnetic topologies (for example, open and closed fields). Data on coronal shocks and high-velocity material ejected from solar flares have been interpreted in terms of a model consisting of three main velocity regimes.

Maxwell, A.↗

NASA NTRS2003

Modeling the Magnetic and Thermal Structure of Active Regions: 1st Year 1st Semi-Annual Progress Report

This report covers technical progress during the first six months of the first year of NASA SR&T contract "Modeling the Magnetic and Thermal Structure of Active Regions", NASW-03008, between NASA and Science Applications International Corporation, and covers the period January 14, 2003 to July 13, 2003. Under this contract SAIC has conducted research into theoretical modeling of the properties of active regions using the MHD model.

Mikic, Zoran↗

NASA NTRS2010

Dst Index in the 2008 GEM Modeling Challenge - Model Performance for Moderate and Strong Magnetic Storms

The GEM 2008 modeling challenge efforts are expanding beyond comparing in-situ measurements in the magnetosphere and ionosphere to include the computation of indices to be compared. The Dst index measures the largest deviations of the horizontal magnetic field at 4 equatorial magnetometers from the quiet-time background field and is commonly used to track the strength of the magnetic disturbance of the magnetosphere during storms. Models can calculate a proxy Dst index in various ways, including using the Dessler-Parker Sckopke relation and the energy of the ring current and Biot-Savart integration of electric currents in the magnetosphere. The GEM modeling challenge investigates 4 space weather events and we compare models available at CCMC against each other and the observed values of Ost. Models used include SWMF/BATSRUS, OpenGGCM, LFM, GUMICS (3D magnetosphere MHD models), Fok-RC, CRCM, RAM-SCB (kinetic drift models of the ring current), WINDMI (magnetosphere-ionosphere electric circuit model), and predictions based on an impulse response function (IRF) model and analytic coupling functions with inputs of solar wind data. In addition to the analysis of model-observation comparisons we look at the way Dst is computed in global magnetosphere models. The default value of Dst computed by the SWMF model is for Bz the Earth's center. In addition to this, we present results obtained at different locations on the Earth's surface. We choose equatorial locations at local noon, dusk (18:00 hours), midnight and dawn (6:00 hours). The different virtual observatory locations reveal the variation around the earth-centered Dst value resulting from the distribution of electric currents in the magnetosphere during different phases of a storm.

Rastaetter, Lutz↗

DOE OSTI2021

Development, Implementation, and Verification of Partially-Ionized Collisional Multifluid Plasma Models in Drekar

We consider the development of multifluid models for partially ionized multispecies plasmas. The models are composed of a standard set of five-moment fluid equations for each species plus a description of electromagnetics. The most general model considered utilizes a full set of fluid equations for each charge state of each atomic species, plus a set of fluid equations for electrons. The fluid equations are coupled through source terms describing electromagnetic coupling, ionization, recombination, charge exchange, and elastic scattering collisions in the low-density coronal limit. The form of each of these source terms is described in detail, and references for required rate coefficients are identified for a diverse range of atomic species. Initial efforts have been made to extend these models to incorporate some higher-density collisional effects, including ionization potential depression and three- body recombination. Some reductions of the general multifluid model are considered. First, a reduced multifluid model is derived which averages over all of the charge states (including neutrals) of each atomic species in the general multifluid model. The resulting model maintains full consistency with the general multifluid model from which it is derived by leveraging a quasi-steady-state collisional ionization equilibrium assumption to recover the ionization fractions required to make use of the general collision models. Further reductions are briefly considered to derive certain components of a single-fluid magnetohydrodynamics (MHD) model. In this case, a generalized Ohm's law is obtained, and the standard MHD resistivity is expressed in terms of the collisional models used in the general multifluid model. A number of numerical considerations required to obtain robust implementations of these multifluid models are discussed. First, an algebraic flux correction (AFC) stabilization approach for a continuous Galerkin finite element discretization of the multifluid system is described in which the characteristic speeds used in the stabilization of the fluid systems are synchronized across all species in the model. It is demonstrated that this synchronization is crucial in order to obtain a robust discretization of the multifluid system. Additionally, several different formulations are considered for describing the electromagnetics portion of the multifluid system using nodal continuous Galerkin finite element discretizations. The formulations considered include a parabolic divergence cleaning method and an implicit projection method for the traditional curl formulation of Maxwell's equations, a purely- hyperbolic potential-based formulation of Maxwell's equations, and a mixed hyperbolic-elliptic potential-based formulation of Maxwell's equations. Some advantages and disadvantages of each formulation are explored to compare solution robustness and the ease of use of each formulation. Numerical results are presented to demonstrate the accuracy and robustness of various components of our implementation. Analytic solutions for a spatially homogeneous damped plasma oscillation are derived in order to verify the implementation of the source terms for electromagnetic coupling and elastic collisions between fluid species. Ionization balance as a function of electron temperature is evaluated for several atomic species of interest by comparing to steady-state calculations using various sets of ionization and recombination rate coefficients. Several test problems in one and two spatial dimensions are used to demonstrate the accuracy and robustness of the discretization and stabilization approach for the fluid components of the multifluid system. This includes standard test problems for electrostatic and electromagnetic shock tubes in the two-fluid and ideal shock-MHD limits, a cylindrical diocotron instability, and the GEM challenge magnetic reconnection problem. A one-dimensional simplified prototype of an argon gas puff configuration as deployed on Sandia's Z-machine is used as a demonstration to exercise the full range of capabilities associated with the general multifluid model.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Two-temperature effects in Hall-MHD simulations of the HIT-SI experiment

A two-temperature Hall-magnetohydrodynamic (Hall-MHD) model, which evolves the electron and ion temperatures separately, is implemented in the PSI-Tet 3D MHD code and used to model plasma dynamics in the Helicity Injected Torus–Steady Inductive (HIT-SI) experiment. The two-temperature model is utilized for HIT-SI simulations in both the PSI-Tet and NIMROD codes at a number of different injector frequencies in the 14.5–68.5 kHz range. At all frequencies, the NIMROD two-temperature model results in increased toroidal current, lower chord-averaged density, higher average temperatures, outward radial shift of the current centroid, and axial symmetrization of the current centroid, relative to the single-temperature NIMROD simulations. The two-temperature PSI-Tet model illustrates similar trends, but at high frequency operation, it exhibits lower electron temperature, smaller toroidal current, and decreased axial symmetrization with respect to the single-temperature PSI-Tet model. With all models, average temperatures and toroidal currents increase with the injector frequency. Power balance and heat fluxes to the wall are calculated for the two-temperature PSI-Tet model and illustrate considerable viscous and compressive heating, particularly at high injector frequency. Parameter scans are also presented for artificial diffusivity, wall temperature, and density. Both artificial diffusivity and the density boundary condition significantly modify the plasma density profiles, leading to larger average temperatures, toroidal current, and relative density fluctuations at low densities. As a result, a low density simulation achieves sufficiently high current gain (G > 5) to generate significant volumes of closed flux lasting 1–2 injector periods.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS2023

Quantifying the Ability of Magnetohydrodynamic Models to Reproduce Observed Birkeland Current and Auroral Electrojet Magnitudes

Although global magnetohydrodynamic (MHD) models have increased in sophistication and are now at the forefront of modeling Space Weather, there is still no clear understanding of how well these models replicate the observed ionospheric current systems. Without a full understanding and treatment of the ionospheric current systems, global models will have significant shortcomings that will limit their use. In this study we focus on reproducing observed seasonal interhemispheric asymmetry in ionospheric currents using the Space Weather Modeling Framework (SWMF). We find that SWMF does reproduce the linear relationship between the electrojets and the FACs, despite the underestimation of the currents’ magnitudes. Quantitatively, we find that at best SWMF is only capturing approximately 60% of the observed current. We also investigate how varying F10.7 effects the ionospheric potential and currents during the summer and winter. We find that simulations ran with higher F10.7 result in lower ionospheric potentials. Additionally, we find that the models do not always replicate the expected behavior of the currents with varying F10.7. This work points to a needed improvement in ionospheric conductance models.

Tre'Shunda James↗

NASA NTRS2000

Acceleration of the Fast Solar Wind by Solitary Waves in Coronal Holes

The purpose of this investigation is to develop a new model for the acceleration of the fast solar wind by nonlinear, time-dependent multidimensional MHD simulations of waves in solar coronal holes. Preliminary computational studies indicate that solitary-like waves are generated in coronal holes nonlinearly by torsional Alfven waves. These waves in addition to thermal conduction may contribute considerably to the accelerate the solar wind. Specific goals of this proposal are to investigate the generation of nonlinear solitary-like waves and their effect on solar wind acceleration by numerical 2.5D MHD simulation of coronal holes with a broad range of plasma and wave parameters; to study the effect of random disturbances at the base of a solar coronal hole on the fast solar wind acceleration with a more advanced 2.5D MHD model and to compare the results with the available observations; to extend the study to a full 3D MHD simulation of fast solar wind acceleration with a more realistic model of a coronal hole and solar boundary conditions. The ultimate goal of the three year study is to model the fast solar wind in a coronal hole, based on realistic boundary conditions in a coronal hole near the Sun, and the coronal hole structure (i.e., density, temperature, and magnetic field geometry) that will become available from the recently launched SOHO spacecraft.

Ofman, Leon↗

NASA NTRS2001

Acceleration of the Fast Solar Wind by Solitary Waves in Coronal Holes

The purpose of this investigation is to develop a new model for the acceleration of the fast solar wind by nonlinear. time-dependent multidimensional MHD simulations of waves in solar coronal holes. Preliminary computational studies indicate that nonlinear waves are generated in coronal holes by torsional Alfv\'{e}n waves. These waves in addition to thermal conduction may contribute considerably to the accelerate the solar wind. Specific goals of this proposal are to investigate the generation of nonlinear solitary-like waves and their effect on solar wind acceleration by numerical 2.5D MHD simulation of coronal holes with a broad range of plasma and wave parameters; to study the effect of random disturbances at the base of a solar coronal hole on the fast solar wind acceleration with a more advanced 2.5D MHD model and to compare the results with the available observations; to extend the study to a full 3D MHD simulation of fast solar wind acceleration with a more realistic model of a coronal hole and solar boundary conditions. The ultimate goal of the three year study is to model the, fast solar wind in a coronal hole, based on realistic boundary conditions in a coronal hole near the Sun, and the coronal hole structure (i.e., density, temperature. and magnetic field geometry,) that will become available from the recently launched SOHO spacecraft.

Ofman, Leon↗

NASA NTRS1984

Modeling of energy buildup for a flare-productive region

A self-consistent MHD model of shearing magnetic loops is used to investigate magnetic energy buildup in active region AR 2372 (Boulder number), in the period of April 5-7, 1980. The magnetic field and sunspot motions in this region, derived using observational data obtained by the Marshall Space Flight Center Solar Observatory, suggest the initial boundary conditions for the model. It is found that the plasma parameters (i.e., density, temperature, and plasma flow velocity) do not change appreciably during the process of energy buildup as the magnetic loops are sheared. Thus, almost all of the added energy is stored in the magnetic field. Furthermore, it is shown that dynamical processes are not important during a slow buildup (i.e., for a shearing velocity less than 1 km/s). Finally, it is concluded that the amount of magnetic energy stored and the location of this stored magnetic energy depend on the initial magnetic field (whether potential or sheared) and the magnitude of the shearing motion.

Wu, S. T.↗

DOE OSTI2021

Modification of the magneto-hydrodynamic equilibrium by the lower-hybrid wave driven fast electrons on the TST-2 spherical tokamak

Presence of a large population of fast particles may qualitatively modify the tokamak equilibrium from the one that can be described by standard magneto-hydrodynamics (MHD). The kinetic modification of the MHD equilibrium was studied for a lower-hybrid (LH) wave driven plasma on the TST-2 spherical tokamak. The analysis was performed using an equilibrium reconstruction method based on an extended MHD model that considers a two-component plasma of bulk MHD fluid and kinetic fast electrons. Scrape-off-layer current appeared naturally in the extended MHD analysis because of the finite electron orbit excursion from the flux surfaces. This reduced the bulk pressure contribution to the toroidal current substantially. Furthermore, the resulting poloidal flux profile was more consistent with that inferred from the Thomson scattering measurement.

extended magneto-hydrodynamics↗