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This report consists of two published papers, 'Computation of Magnetohydrodynamic Flows Using an Iterative PNS Algorithm' and 'Numerical Simulation of Turbulent MHD Flows Using an Iterative PNS Algorithm'.
The effect of resistive, Hall, and viscous terms on the flow structure compared with compressible ideal MHD is studied numerically for a one-fluid non-ideal MHD model. The goal of the present study is to shed some light on the emerging area of non-ideal MHD modeling and simulation. Numerical experiments are performed on a hypersonic blunt body flow with future application to plasma aerodynamics flow control in reentry vehicles. Numerical experiments are also performed on a magnetized time-developing mixing layer with possible application to magnetic/turbulence mixing.
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.
Energetic O+ ions (tens of keV) rapidly increase in the inner magnetosphere and contribute significantly to the ring current during substorms. Previously, two source regions of the energetic O+ ions have been proposed. The first one is the dayside polar region. Ions from the dayside polar region are transported to the lobe; then they are injected to the nightside plasma sheet during substorm expansion phase. The second one is the nightside aurora region. After the substorm onset, energetic O+ ions are extracted from the ionosphere with the auroral acceleration processes, and the O+ ions are directly supplied to the nightside plasma sheet. We investigated the relative importance of these two regions on supplying the energetic O+ ions in the inner magnetosphere. We performed a test particle simulation in global MHD electromagnetic fields. We obtained the following results. (1) During the substorm growth phase, O+ ions at tens of eV are extracted from the dayside polar region, resulting in the enhancement of the warm O+ ions (hundreds of eV) in the lobe. After the substorm onset, the warm O+ ions are nonadiabatically accelerated to tens of keV and injected to the inner magnetosphere. These O+ ions contribute to most of the O+ ring current. (2) O+ ions at less than a few keVs are supplied from the nightside aurora region to the plasma sheet. However, their contribution to the O+ ring current remains small. From the results, we concluded that the main source of the energetic O+ ions is the dayside polar region.
Here, we introduce a novel experimental platform for the study of the Richtmyer–Meshkov instability in a cylindrically converging geometry using a magnetically driven cylindrical piston. Magnetically driven solid liner implosions are used to launch a shock into a liquid deuterium working fluid and, ultimately, into an on-axis rod with a pre-imposed perturbation. The shock front trajectory is tracked through the working fluid and up to the point of impacting the rod through the use of on axis photonic Doppler velocimetry. This configuration allows for precise characterization of the shock state as it impacts the perturbed rod interface. Monochromatic x-ray radiography is used to measure the post-shock interface evolution and rod density profile. The ALEGRA MHD model is used to simulate the dynamics of the experiment in one dimension. We show that late in time the perturbation growth becomes non-linear as evidenced by the observation of high-order harmonics, up to n = 5. Two dimensional simulations performed using a combination of the GORGON MHD code and the xRAGE radiation hydrodynamics code suggest that the late time non-linear growth is modified by convergence effects as the bubbles and spikes experience differences in the pressure of the background flow.
Broken ergodicity (BE) occurs in Fourier method numerical simulations of ideal, homogeneous, incompressible magnetohydrodynamic (MHD) turbulence. Although naive statistical theory predicts that Fourier coefficients of fluid velocity and magnetic field are zero-mean random variables, numerical simulations clearly show that low-wave-number coefficients have non-zero mean values that can be very large compared to the associated standard deviation. In other words, large-scale coherent structure (i.e., broken ergodicity) in homogeneous MHD turbulence can spontaneously grow out of random initial conditions. Eigenanalysis of the modal covariance matrices in the probability density functions of ideal statistical theory leads to a theoretical explanation of observed BE in homogeneous MHD turbulence. Since dissipation is minimal at the largest scales, BE is also relevant for resistive magnetofluids, as evidenced in numerical simulations. Here, we move beyond model magnetofluids confined by periodic boxes to examine BE in rotating magnetofluids in spherical domains using spherical harmonic expansions along with suitable boundary conditions. We present theoretical results for 3-D and 2-D spherical models and also present computational results from dynamical simulations of 2-D MHD turbulence on a rotating spherical surface. MHD turbulence on a 2-D sphere is affected by Coriolus forces, while MHD turbulence on a 2-D plane is not, so that 2-D spherical models are a useful (and simpler) intermediate stage on the path to understanding the much more complex 3-D spherical case.
The Mini-Magnetospheric Plasma Propulsion (M2P2), originally proposed by Winglee et al. [2000] predicts that a 15-km standoff distance (or 20-km cross-sectional dimension) of the magnetic bubble will provide for sufficient momentum transfer from the solar wind to accelerate a spacecraft to the unprecedented speeds of 50-80 km/s after an acceleration period of about three months. Such velocities will enable travel out of the solar system in period of about seven years-almost an order of magnitude improvement over present chemical based propulsion systems. However, for the parameters of the simulation of Winglee et al. [2000], a fluid model for the interaction of M2P2 with the solar wind is not valid. It is assumed in the MHD fluid model, normally applied to planetary magnetospheres, that the characteristic scale-size is much greater than the Larmor radius and ion skin depth of the solar wind. In the case of M2P2, the size of the magnetic bubble is actually less than or, comparable to, the scale of these characteristic parameters. Therefore, a kinetic approach, which addresses the small-scale physical mechanisms, must be used. We have adopted a two-component approach to determining a preliminary estimate of the momentum transfer to the plasma sail. The first component is a self-consistent MHD simulation of the small-scale expansion phase of the magnetic bubble. The fluid treatment is valid to roughly 5 km from the source and the steady-state MHD solution at the 5 km boundary was then used as initial conditions for the hybrid simulation. The hybrid simulations showed that the momentum transfer to the innermost regions of the plasma sail is negligible.
The generation of runaway electrons (REs) during disruptions poses a significant challenge for the operation of tokamaks. The production of these high-energy electrons can cause substantial damage, particularly when the plasma current is high, making it a critical concern for ITER. For the high-temperature plasmas anticipated in ITER, the primary generation of REs may be dominated by the hot tail mechanism, which consists of the acceleration of hot electrons from the pre-disruption population which have not yet thermalized with the bulk following the rapid cooling of the plasma. To account for the significant 3D effects on RE production, a hot tail modeling framework has been developed within the non-linear 3D extended MHD code JOREK. This paper presents the structure of this framework, which is based on test electrons evolving in MHD fields. The verification of the method shows good agreement with the reference DREAM code for 0D test cases, as well as for axisymmetric simulations of 15 MA ITER H-mode disruption scenarios. Furthermore, a proof-of-principle application to a DIII-D case demonstrates the framework’s capability to capture for the first time the hot tail generation in 3D MHD simulations in realistic geometry. Preliminary results suggest that the production of REs is significantly reduced by stochastic losses.
This is the final report for the DOE award DE-SC0021657, titled “Validation of Simulation Models for Wall-Connected Scrape off Layer Currents during MHD Activity in the HBT-EP Tokamak” for the period September 1, 2020 – April 30, 2025. This award is part of a broader collaborative project, which supported training of a PhD student at Columbia University under the joint supervision of Dr. Levesque and Dr. Hansen (on award DE-SC0021325). The award supported research into computational models for plasma and 3D conducting structures in the vicinity relevant to tokamak disruptions and other mode activity (eg. RWMs) using the NIMROD and PSI-Tet codes. Additional detail on progress in support of these tasks is provided below.
This is the final report for the DOE award DE-SC0021325, titled “Validation of Simulation Models for Wall-Connected Scrape off Layer Currents during MHD Activity in the HBT-EP Tokamak” for the period September 1, 2020 – May 31, 2023. This award is part of a broader collaborative project, which supported training of a PhD student at Columbia University under the joint supervision of Dr. Hansen and Columbia project members. The award supported research into computational models for plasma and 3D conducting structures in the vicinity relevant to tokamak disruptions and other mode activity (eg. RWMs) using the NIMROD, and PSI-Tet, codes.
This is a selective, somewhat editorialized assessment, based on a literature survey, of computer simulation as it exists today in magnetospheric physics. Both large (MHD) and small scale dynamical simulations are described and considered from the perspective of what they are trying to do and with what success. Several specific problem areas where simulations are being carried out are called for commentary: global magnetospheric structure, magnetotail and magnetopause reconnection, Kelvin-Helmholtz instability, hydrodynamic expansion of ionospheric ions, electric double layers, heavy ion heating, and auroral kilometric radiation. It is concluded that simulation is a necessary tool for understanding magnetospheric physics and that significant progress has been made in simulation development. However, results should be evaluated knowing that many factors, some real and physical, others structural, may contribute to such output. A plea is made for greater intercalibration among different simulators working in parallel areas, so that facts can be distinguished from artifacts.
The aim of this study is to analyze the effect of the neutral beam injector (NBI) operation regime on the saturation phase of the Alfven Eigenmodes (AEs) in DIII-D plasma. Here, the analysis is done using the linear and nonlinear versions of the gyro-fluid code FAR3d. A set of parametric analyses are performed modifying the nonlinear simulation EP $β$ (NBI injection power), EP energy (NBI voltage) and the radial location of the EP density profile gradient (NBI radial deposition). The analysis indicates a transition from the soft (local plasma relaxation) to the hard MHD (global plasma relaxation) limit if the simulation EP $β$ $\unicode{x2A7E}$ $0.02$, leading to bursting MHD activity caused by radial AEs overlapping. MHD bursts cause an enhancement of the EP transport showing ballistic-like features as avalanche-like events. Simulations in the soft MHD limit show an increment of the EP density gradient as the EP $β$ increases. On the other hand, there is a gradient upper limit in the hard MHD limit, consistent with the critical-gradient behavior. AEs induce shear flows and zonal current leading to the deformation of the flux surfaces and the safety factor profile, respectively, particularly strong for the simulation in the hard MHD limit. Simulations in the hard MHD regime show a decrease of the AE frequency in the saturation phase; this is caused by the destabilization of a transitional mode between a $9/3-10/3$ TAE and a $9/3$ RSAE that may explain the AE frequency down-sweeping observed in some DIII-D discharges. Reducing the EP energy in the nonlinear simulations leads to a weakening of the plasma perturbation. On the other hand, increasing the EP energy causes the opposite effect. Nonlinear simulations of off-axis NBI profiles indicate a lower plasma perturbation as the EP density gradient is located further away from the magnetic axis.
A statistical theory of geodynamo action is developed, using a mathematical model of the geodynamo as a rotating outer core containing an ideal (i.e., no dissipation), incompressible, turbulent, convecting magnetofluid. On the concentric inner and outer spherical bounding surfaces the normal components of the velocity, magnetic field, vorticity and electric current are zero, as is the temperature fluctuation. This allows the use of a set of Galerkin expansion functions that are common to both velocity and magnetic field, as well as vorticity, current and the temperature fluctuation. The resulting dynamical system, based on the Boussinesq form of the magnetohydrodynamic (MHD) equations, represents MHD turbulence in a spherical domain. These basic equations (minus the temperature equation) and boundary conditions have been used previously in numerical simulations of forced, decaying MHD turbulence inside a sphere [1,2]. Here, the ideal case is studied through statistical analysis and leads to a prediction that an ideal coherent structure will be found in the form of a large-scale quasistationary magnetic field that results from broken ergodicity, an effect that has been previously studied both analytically and numerically for homogeneous MHD turbulence [3,4]. The axial dipole component becomes prominent when there is a relatively large magnetic helicity (proportional to the global correlation of magnetic vector potential and magnetic field) and a stationary, nonzero cross helicity (proportional to the global correlation of velocity and magnetic field). The expected angle of the dipole moment vector with respect to the rotation axis is found to decrease to a minimum as the average cross helicity increases for a fixed value of magnetic helicity and then to increase again when average cross helicity approaches its maximum possible value. Only a relatively small value of cross helicity is needed to produce a dipole moment vector that is aligned at approx.10deg with the rotation axis.
One of the main goals of this project to understand the origin of density fluctuations in the solar winds, as revealed by the NASA’s Flagship satellite Parker Solar Probe (PSP) measurements, which motivates us to simulate and analyze magnetohydrodynamic (MHD) turbulence in the compressible regime. To achieve this goal, we have developed a set of sophisticated turbulence driving methods to study how MHD turbulence will develop under different time-correlated fluctuations at large-scales. Another key advance is that we have developed a new 3+1 (three spatial plus time domain) 4D FFT analysis of simulation data-cubes so that we can perform the spatio-temporal spectrum and mode decomposition studies on MHD turbulence.
This project adapts and applies the gyrokinetic Eulerian code COGENT to an emerging area of highly-magnetized Z-pinch plasma systems. Simulation efforts for these plasmas currently use either magneto-hydrodynamic (MHD) fluid codes, which suffer from fidelity being restricted to narrow plasma conditions, or fully kinetic particle-in-cell (PIC) methods, which suffer from the run-time needed to resolve the very small spatial and temporal scales required for the plasma conditions. The progress with achieving detailed theoretical understanding of Z-pinch plasma systems can be greatly expedited using some combination of gyrokinetic and drift-ordered MHD models, developed in the tokamak community and implemented in the COGENT code. These formulations are applicable to a much larger parameter space than standard MHD models, while providing a substantial speed-up in run-time over fully kinetic codes. In particular, the gyrokinetic formalism is successfully applied to a flow-stabilized Z pinch (FSZP) system – a promising fusion concept where a sheared axial flow is used to provide stability against large-scale ideal-MHD modes. Results of gyrokinetic simulations with COGENT agree well with those from fully kinetic simulations, while requiring ~500x less run-time.
Abstract A coupling between two distinctly different codes—one magnetohydrodynamic (MHD) and another kinetic—is achieved and applied for simulation of runaway electron (RE) production. The 3D initial value MHD code NIMROD simulates a DIII-D pure neon shattered pellet injection plasma quench including the propagation and ablation of the fragments, ionization and recombination of the impurities, and the radiated and transported energies. The field data from NIMROD is then used by the bounce-averaged Fokker–Planck Collisional QuasiLinear 3D (CQL3D) kinetic code to simulate the production of REs and their radial transport. The coupling procedure involves mapping of data between different grids and adjustment of the NIMROD toroidal electric field when REs appear. It is shown that without the radial transport, a large RE current is generated, up to 30% of the pre-pellet ohmic current. However, when the radial transport is included in CQL3D, the RE current is reduced to undetectable level, consistent with experiment. Various forms of the radial diffusion are surveyed to determine conditions when the fast electrons would not have time to be accelerated to relativistic energies before they are lost to chamber wall.
Numerical simulations of merging compact objects and their remnants form the theoretical foundation for gravitational wave and multimessenger astronomy. While Cartesian-coordinate-based adaptive mesh refinement is commonly used for simulations, spherical-like coordinates are more suitable for nearly spherical remnants and azimuthal flows due to lower numerical dissipation in the evolution of fluid angular momentum, as well as requiring fewer numbers of computational cells. However, the use of spherical coordinates to numerically solve hyperbolic partial differential equations can result in severe Courant-Friedrichs-Lewy (CFL) stability condition time step limitations, which can make simulations prohibitively expensive. This paper addresses this issue for the numerical solution of coupled spacetime and general relativistic magnetohydrodynamics evolutions by introducing a double fast Fourier transform (FFT) filter and implementing it within the fully message passing interface (mpi)-parallelized sphericalnr framework in the einstein toolkit. In conclusion, we demonstrate the effectiveness and robustness of the filtering algorithm by applying it to a number of challenging code tests, and show that it passes these tests effectively, demonstrating convergence while also increasing the time step significantly compared to unfiltered simulations.
Stability of edge-localized modes (ELMs) in spherical tokamaks is explored using the extended MHD model. Linear NIMROD simulations have been performed for three NSTX discharges 132543, 132588, and 141133, to investigate the role of resistivity, diffusivity, and shear flows on the onset of ELMs. The first discharge represents the wide pedestal regime and the later two discharges represent ELM-free enhanced pedestal H-mode. We first present the effect of toroidal rotation shear and find a flow shear destabilizing effect in these NSTX discharges. Simulations are also extended to include the two-fluid and ion gyroviscosity effects. Simulations show that the flow shear can shift the mode spectrum and alter the critical condition of ELM onset. We also uncover that ELM onset prediction in spherical tokamaks requires effects beyond MHD, in particular gyroviscosity and diamagnetic terms could stabilize Peeling-Ballooning modes consistent with the experimental observation of ELM-free regimes in NSTX. The findings give new insight into the nature of the interplay between resistivity, flows, and diamagnetic stabilization in ELM suppression and have potential applications to ELM control schemes in NSTX-U and next-generation spherical tokamaks. This study identifies the essential physical effects that must be included in future predictive and validation simulations.