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DOE OSTI2021

Near-field models and simulations of pellet ablation in tokamaks

Here, detailed numerical studies of the ablation of a single neon pellet in the plasma disruption mitigation parameter space have been performed. Simulations were carried out using FronTier, a hydrodynamic/low magnetic Reynolds number MHD code with explicit tracking of material interfaces. FronTier's physics models resolve the pellet surface ablation and the formation of a dense, cold cloud of ablated material, the deposition of energy from hot plasma electrons, the expansion of the ablation cloud along magnetic field lines, and the radiation losses. A local thermodynamic equilibrium model based on Saha equations has been used to resolve atomic processes in the cloud and Redlich–Kwong corrections to the ideal gas equation of state for cold and dense gases, which have been used near the pellet surface. The FronTier pellet code is a next generation of the code described. It has been validated against the semi-analytic improved neutral gas shielding model in the 1D spherically symmetric approximation. Main results include quantification of the influence of atomic processes and Redlich–Kwong corrections on the pellet ablation in spherically symmetric approximation and verification of analytic scaling laws in a broad range of pellet and plasma parameters. Using axially symmetric MHD simulations, the properties of ablation channels and the reduction of pellet ablation rates in magnetic fields of increasing strength have been studied. While the main emphasis has been given to neon pellets for the plasma disruption mitigation, selected results on deuterium fueling pellets have also been presented.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1974

Closed cycle MHD power generation experiments in the NASA Lewis facility

Discussion of the performance improvements achieved through some modifications made in the closed cycle MHD facility. These modifications include a redesign of the MHD duct interior, addition of mixing bars, increased electrical isolation, and experimentation with various cesium seed vaporization and injection techniques. Uniform Faraday and Hall voltage profiles were obtained, and the Faraday open circuit voltage varied from 90 to 100% of the ideal uBh.

Sovie, R. J.↗

NASA NTRS2010

Multi-Scale Modeling of Global of Magnetospheric Dynamics

To understand the role of magnetic reconnection in global evolution of magnetosphere and to place spacecraft observations into global context it is essential to perform global simulations with physically motivated model of dissipation that is capable to reproduce reconnection rates predicted by kinetic models. In our efforts to bridge the gap between small scale kinetic modeling and global simulations we introduced an approach that allows to quantify the interaction between large-scale global magnetospheric dynamics and microphysical processes in diffusion regions near reconnection sites. We utilized the high resolution global MHD code BATSRUS and incorporate primary mechanism controlling the dissipation in the vicinity of reconnection sites in terms of kinetic corrections to induction and energy equations. One of the key elements of the multiscale modeling of magnetic reconnection is identification of reconnection sites and boundaries of surrounding diffusion regions where non-MHD corrections are required. Reconnection site search in the equatorial plane implemented in our previous studies is extended to cusp and magnetopause reconnection, as well as for magnetotail reconnection in realistic asymmetric configurations. The role of feedback between the non-ideal effects in diffusion regions and global magnetosphere structure and dynamics will be discussed.

Kuznetsova, M. M.↗

NASA NTRS1994

Nonlinear decay of magnetic helicity in magnetohydrodynamic turbulence with a mean magnetic field

We show that the magnetic helicity associated with fluctuations in homogeneous incompressible magnetohydrodynamic (MHD) turbulence with a mean magnetic field decays in time because of nonlinear processes. Evidence is obtained numerically, by use of both dissipative and nondissipative spectral method simulations. The described effect stands in contrast to expectations based on studies of MHD turbulence without an applied mean field, in which magnetic helicity is transferred nonlinearly to long wavelengths and is preserved in time because of selective decay when dissipation is present. The process of nonlinear decay is described in terms of a generalized ideal helicity invariant and is characterized by the transient production of a mean induced electric field aligned with the applied magnetic field, an effect reminiscent of the alpha effect in dynamo theory. A simple phenomenological model for the decay process is proposed.

Stribling, Troy↗

DOE OSTI2022

An intergalactic medium temperature from a giant radio galaxy

ABSTRACT The warm–hot intergalactic medium (warm–hot IGM, or WHIM) pervades the filaments of the Cosmic Web and harbours half of the Universe’s baryons. The WHIM’s thermodynamic properties are notoriously hard to measure. Here we estimate a galaxy group–WHIM boundary temperature using a new method. In particular, we use a radio image of the giant radio galaxy (giant RG, or GRG) created by NGC 6185, a massive nearby spiral. We analyse this extraordinary object with a Bayesian 3D lobe model and deduce an equipartition pressure Peq = 6 × 10−16 Pa – among the lowest found in RGs yet. Using an X-ray-based statistical conversion for Fanaroff–Riley II RGs, we find a true lobe pressure $P = 1.5\substack{+1.7\\ -0.4}\times 10^{-15}\ \mathrm{Pa}$. Cosmic Web reconstructions, group catalogues, and MHD simulations furthermore imply an Mpc–scale IGM density $1 + \delta _\mathrm{IGM} = 40\substack{+30\\ -10}$. The buoyantly rising lobes are crushed by the IGM at their inner side, where an approximate balance between IGM and lobe pressure occurs: PIGM ≈ P. The ideal gas law then suggests an IGM temperature $T_\mathrm{IGM} = 11\substack{+12\\-5} \times 10^6\ \mathrm{K}$, or $k_\mathrm{B}T_\mathrm{IGM} = 0.9\substack{+1.0\\-0.4}\ \mathrm{keV}$, at the virial radius – consistent with X-ray-derived temperatures of similarly massive groups. Interestingly, the method is not performing at its limit: in principle, estimates TIGM ∼ 4 × 106 K are already possible – rivalling the lowest X-ray measurements available. The technique’s future scope extends from galaxy group outskirts to the WHIM. In conclusion, we demonstrate that observations of GRGs in Cosmic Web filaments are finally sensitive enough to probe the thermodynamics of galaxy groups and beyond.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1981

On the mechanism of ray closure in comet tails

The folding phenomenon of comet tail rays is explained by means of an electric drift due to convectional electric fields. This mechanism results in an angular rate of closure which reduces to that obtained by Ness and Donn (1966) if the velocity profile across the tail is linear and the plasma conductivity is ideal. Observations of both the ray closure and the disconnection events point to the phenomenon of anomalous resistivity. Magnetic fields of about 30-40 gammas in the coma and of 10 gammas in the distant tail (at 1 AU) are estimated from the MHD momentum equation.

Ershkovich, A. I.↗

NASA NTRS1998

Global Magnetohydrodynamic Modeling of the Solar Corona

The coronal magnetic field defines the structure of the solar corona, the position of the heliospheric current sheet, the regions of fast and slow solar wind, and the most likely sites of coronal mass ejections. There are few measurements of the magnetic fields in the corona, but the line-of-sight component of the global magnetic fields in the photosphere have been routinely measured for many years (for example, at Stanford's Wilcox Solar Observatory, and at the National Solar Observatory at Kitt Peak). The SOI/MDI instrument is now providing high-resolution full-disk magnetograms several times a day. Understanding the large-scale structure of the solar corona and inner heliosphere requires accurately mapping the measured photospheric magnetic field into the corona and outward. Ideally, a model should not only extrapolate the magnetic field, but should self-consistently reconstruct both the plasma and magnetic fields in the corona and solar wind. Support from our NASA SR&T contract has allowed us to develop three-dimensional magnetohydrodynamic (MHD) computations of the solar corona that incorporate observed photospheric magnetic fields into the boundary conditions. These calculations not only describe the magnetic field in the corona and interplanetary spice, but also predict the plasma properties as well. Our computations thus far have been successful in reproducing many aspects of both coronal and interplanetary data, including the structure of the streamer belt, the location of coronal hole boundaries, and the position and shape of the heliospheric current sheet. The most widely used technique for extrapolating the photospheric magnetic field into the corona and heliosphere are potential field models, such as the potential field source-surface model (PFSS),and the potential field current-sheet (PFCS) model

Linker, Jon A.↗

DOE OSTI2024

Design and Analysis of Liquid Lithium Plasma Facing Components

In this study, liquid metal (LM) on plasma-facing components (PFCs) creates a renewable protective cover enhancing power exhaust and protecting the solid substrate. Additionally, energy confinement improvement through particle pumping can be achieved in the case of liquid lithium (LL). A new variant of PFCs was recently introduced at Princeton Plasma Physics Laboratory (PPPL) where a porous wall is used to stabilize the LM surface, while using magnetohydrodynamic (MHD) drive to push the LM flow inside the component. This arrangement allows efficient heat exhaust, and enhanced control of the LM surface temperature, leading to spatial control of evaporation and condensation of LL on the plasma interface. This feature is particularly attractive when vapor shielding is introduced to allow heat flux redistribution. This system has the advantage that as the heat flux increases, the evaporation rate will increase, while decreasing heat flux will decrease the evaporation rate of lithium, ideally creating a feedback effect which could self-regulate the amount of lithium evaporated. Analytical and numerical models for LL PFCs were developed in PPPL. To calculate the target temperature distribution for the case of evaporation from the divertor, we apply an iterative process allowing two-way coupling between the fluid-kinetic analysis of plasma using SOLPS-ITER code and the flow and heat transfer analysis of the PFC using an analytical model. In the last stage, the results are validated using computational fluid dynamics (CFD) analysis with customized version of the CFX code from ANSYS. CFX was modified at PPPL to allow MHD analysis at the high magnetic field typical for fusion applications. Results of the analysis for NSTX-U tokamak conditions will be presented.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1988

Evolution of recurrent solar wind structures between 14 AU and the termination shock

The solar wind conditions observed from Voyager 2 at approximately 14 AU are extrapolated to the region of the outer heliosphere bounded by the termination shock, using an MHD simulation model. Results from two simulation studies are presented for two sets of nearly recurrent solar wind interaction regions, with initial conditions generated from plasma and magnetic field data observed on March 1984 at 13.8 AU, and on November 1984 at 15.4, respectively. Each simulation describes an idealized recurrent solar wind structure in the supersonic region of the outer heliosphere out to the termination shock far beyond the present reaches of the Pioneer and Voyager spacecraft. It is shown that a collision between the forward shock and the reverse shock occurs approximately every 40 AU. When a forward shock interacts with the termination shock, the latter is weakened and moves outward; the termination shock is strengthened and moves inward when a reverse shock interacts with it.

Whang, Y. C.↗

DOE OSTI2021

On the non-existence of stepped-pressure equilibria far from symmetry

The Stepped Pressure Equilibrium Code (SPEC) (Hudson et al 2012 Phys. Plasmas 19 112502) has been successful in the construction of equilibria in 3D configurations that contain a mixture of flux surfaces, islands and chaotic magnetic field lines. In this model, the plasma is sliced into sub-volumes separated by ideal interfaces, and in each volume the magnetic field is a Beltrami field. In the cases where the system is far from possessing a continuous symmetry, such as in stellarators, the existence of solutions to a stepped-pressure equilibrium with given constraints, such as a multi-region relaxed MHD minimum energy state, is not guaranteed but is often taken for granted. Using SPEC, we have studied two different scenarios in which a solution fails to exist in a slab with analytic boundary perturbations. Here we found that with a large boundary perturbation, a certain interface becomes fractal, corresponding to the break up of a Kolmogorov–Arnold–Moser (KAM) surface. Moreover, an interface can only support a maximum pressure jump while a solution of the magnetic field consistent with the force balance condition can be found. An interface closer to break-up can support a smaller pressure jump. We discovered that the pressure jump can push the interface closer to being non-smooth through force balance, thus significantly decreasing the maximum pressure it can support. Our work shows that a convergence study must be performed on a SPEC equilibrium with interfaces close to break-up. These results may also provide insights into the choice of interfaces and have applications in finding out the maximum pressure a machine can support.

3D equilibrium↗

DOE OSTI2022

Runaway electron deconfinement in SPARC and DIII-D by a passive 3D coil

The operation of a 3D coil—passively driven by the current quench (CQ) loop voltage—for the deconfinement of runaway electrons (REs) is modeled for disruption scenarios in the SPARC and DIII-D tokamaks. Nonlinear magnetohydrodynamic (MHD) modeling is carried out with the NIMROD code including time-dependent magnetic field boundary conditions to simulate the effect of the coil. Further modeling in some cases uses the ASCOT5 code to calculate advection and diffusion coefficients for REs based on the NIMROD-calculated fields, and the DREAM code to compute the runaway evolution in the presence of these transport coefficients. Compared with similar modeling in Tinguely et al (2021 Nucl. Fusion 61 124003), considerably more conservative assumptions are made with the ASCOT5 results, zeroing low levels of transport, particularly in regions in which closed flux surfaces have reformed. Of three coil geometries considered in SPARC, only the n = 1 coil is found to have sufficient resonant components to suppress the runaway current growth. Without the new conservative transport assumptions, full suppression of the RE current is maintained when the thermal quench MHD is included in the simulation or when the RE current is limited to 250kA, but when transport in closed flux regions is fully suppressed, these scenarios allow RE beams on the order of 1–2 MA to appear. Additional modeling is performed to consider the effects of the close ideal wall. In DIII-D, the CQ is modeled for both limited and diverted equilibrium shapes. In the limited shape, the onset of stochasticity is found to be insensitive to the coil current amplitude and governed largely by the evolution of the safety-factor profile. In both devices, prediction of the q-profile evolution is seen to be critical to predicting the later time effects of the coil.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Secular outflows from 3D MHD hypermassive neutron star accretion disc systems

Magnetized hypermassive neutron stars (HMNSs) have been proposed as a way for neutron star mergers to produce high electron fraction, high-velocity ejecta, as required by kilonova models to explain the observed light curve of GW170817. The HMNS drives outflows through neutrino energy deposition and mechanical oscillations, and raises the electron fraction of outflows through neutrino interactions before collapsing to a black hole (BH). Here, in this study, we perform 3D numerical simulations of HMNS–torus systems in ideal magnetohydrodynamics, using a leakage/absorption scheme for neutrino transport, the nuclear APR equation of state, and Newtonian self-gravity, with a pseudo-Newtonian potential added after BH formation. Due to the uncertainty in the HMNS collapse time, we choose two different parametrized times to induce collapse. We also explore two initial magnetic field geometries in the torus, and evolve the systems until the outflows diminish significantly ($\sim\!\! 1\!\! - \!\!2\ \mathrm{s}$). We find bluer, faster outflows as compared to equivalent BH–torus systems, producing M ∼ 10 −3 M ⊙ of ejecta with Y e ≥ 0.25 and v ≥ 0.25c by the simulation end. Approximately half the outflows are launched in disc winds at times $t\lesssim 500 \ \mathrm{ms}$, with a broad distribution of electron fractions and velocities, depending on the initial condition. The remaining outflows are thermally driven, characterized by lower velocities and electron fractions. Nucleosynthesis with tracer particles shows patterns resembling solar abundances in all models. Although outflows from our simulations do not match those inferred from two-component modelling of the GW170817 kilonova, self-consistent multidimensional detailed kilonova models are required to determine whether our outflows can power the blue kilonova.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Effects of equilibrium pressure on plasma response to RMPs in a spherical tokamak

This study presents a comprehensive analysis of the equilibrium pressure on the plasma response to resonant magnetic perturbations (RMPs) in the spherical tokamak (ST) MAST-U, employing both single-fluid and MHD-kinetic hybrid models (implemented via the MARS-F/K codes). As a key finding, the study identifies two different pressure-driven eigenmodes, exhibiting Sturmian property, that affect the Troyon no-wall limits for the onset of the n = 1 and n = 2 ( n is the toroidal mode number) ideal external kink instabilities as well as the corresponding plasma response to the applied RMP. With increasing equilibrium pressure, the plasma response to RMPs is significantly enhanced in the ST plasma, particularly in the high-pressure regime where kinetic effects strongly stabilize the external kink instability. The Troyon no-wall limit divides the plasma response into two regions: well below the limit, the response amplitudes and trends (versus pressure) are similar between the fluid and kinetic models; as the equilibrium pressure approaches the Troyon limit, the kinetic model predicts significant amplification of the RMP field, up to 30 times for cases considered. A relatively weak dependence of the optimal coil phasing on the equilibrium pressure is computed in this ST plasma, similar to the trend obtained for the conventional aspect ratio devices. These findings underscore the importance of incorporating kinetic effects in accurate prediction of the plasma response to RMPs in high-pressure ST tokamak plasmas and provide a theoretical basis for optimizing RMP-based control of the edge-localized modes in future ST devices.

RMP↗

DOE OSTI2020

Modeling of resistive plasma response in toroidal geometry using an asymptotic matching approach

The method of solving linear resistive plasma response, based on the asymptotic matching approach, is developed for full toroidal tokamaks by upgrading the Resistive DCON code [A.H. Glasser, Z.R. Wang and J.-K. Park, Physics of Plasmas, \textbf{23}, 112506 (2016)]. The derived matching matrix, asymptotically matching the outer and inner regions, indicates that the applied three dimension (3-D) magnetic perturbations contribute additional small solutions at each resonant surface due to the toroidal coupling of poloidal modes. In contrast, the resonant harmonic only affects the corresponding resonant surface in the cylindrical plasma. Since the solution of ideal outer region is critical to the asymptotic matching and is challenging to be solved in the toroidal geometry due to the singular power series solution at the resonant surfaces, systematic verification of the outer region $\Delta^\prime$ matrix is made by reproducing the well known analytical $\Delta^{\prime}$ result in [H.P. Furth, P.H. Rutherford and H. Selberg, The Physics of Fluids, \textbf{16}, 1054-1063 (1073)] as well as by making a quantitative benchmark with the PEST3 code [A. Pletzer and R.L. Dewar, J. Plasma Physics, \textbf{45}, 427-451 (1991)]. Finally, the reconstructed numerical solution of resistive plasma response from the toroidal matching matrix is presented. Comparing with the ideal plasma response, the global structure of the response can be affected by the small finite island at the resonant surfaces.

MHD simulation↗

NASA NTRS2010

Dynamics of Ring Current and Electric Fields in the Inner Magnetosphere During Disturbed Periods: CRCM-BATS-R-US Coupled Model

We present simulation results from a one-way coupled global MHD model (Block-Adaptive-Tree Solar-Wind Roe-Type Upwind Scheme, BATS-R-US) and kinetic ring current models (Comprehensive Ring Current Model, CRCM, and Fok Ring Current, FokRC). The BATS-R-US provides the CRCM/FokRC with magnetic field information and plasma density/temperature at the polar CRCM/FokRC boundary. The CRCM uses an electric potential from the BATS-R-US ionospheric solver at the polar CRCM boundary in order to calculate the electric field pattern consistent with the CRCM pressure distribution. The FokRC electric field potential is taken from BATS-R-US ionospheric solver everywhere in the modeled region, and the effect of Region II currents is neglected. We show that for an idealized case with southward-northward-southward Bz IMF turning, CRCM-BATS-R-US reproduces well known features of inner magnetosphere electrodynamics: strong/weak convection under the southward/northward Bz; electric field shielding/overshielding/penetration effects; an injection during the substorm development; Subauroral Ion Drift or Polarization Jet (SAID/PJ) signature in the dusk sector. Furthermore, we find for the idealized case that SAID/PJ forms during the substorm growth phase, and that substorm injection has its own structure of field-aligned currents which resembles a substorm current wedge. For an actual event (12 August 2000 storm), we calculate ENA emissions and compare with Imager for Magnetopause-to-Aurora Global Exploration/High Energy Neutral Atom data. The CRCM-BATS-R-US reproduces both the global morphology of ring current and the fine structure of ring current injection. The FokRC-BATS-R-US shows the effect of a realistic description of Region II currents in ring current-MHD coupled models.

Buzulukova, N.↗

DOE OSTI2024

MARS-F/K modeling of plasma response and fast ion losses due to RMP in KSTAR

Abstract The toroidal single-fluid magnetohydrodynamic (MHD) code MARS-F (Liu et al 2000 Phys. Plasmas 7 3681) and the MHD-kinetic hybrid code MARS-K (Liu et al 2008 Phys. Plasmas 15 112503) are utilized to study the plasma response to the n = 1 ( n is the toroidal mode number) resonant magnetic perturbation (RMP), applied to suppress the type-I edge localized mode (ELM) in a KSTAR discharge. Both the resistive-rotating and ideal-static plasma models identify strong screening of the resonant radial field harmonics of the applied RMP due to the plasma response, and predict a strong edge-peeling response of the plasma which is consistent with the optimal ELM control coil current configuration adopted in experiment. The RMP-induced radial displacement of the plasma, computed by the resistive-rotating plasma model, agrees reasonably well with that reconstructed from the measured data in the plasma core. Taking into account the drift kinetic response of fast ions, MARS-K hybrid modeling also finds quantitative agreement of the plasma core fluid pressure perturbation with experiment. Based on the MARS-F computed plasma response, a guiding-center orbit-tracing simulation finds about 0.3% of fast ion losses due the n = 1 RMP in the KSTAR ELM control experiment considered. Most losses are associated with counter-current fast ions located near the plasma edge.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1999

Moreton Waves

"Moreton waves," named for the observer who popularized them, are a solar phenomenon also known in scientific literature as "Moreton-Ramsey wave," "flare waves," "flare-associated waves," "MHD blast waves," "chromospheric shock fronts" and various other combinations of terms which connote violently propagating impulsive disturbances. It is unclear whether all of the observations to which these terms have been applied pertain to a single physical phenomenon: there has perhaps been some overlap between the observations and the assumed physical properties of the observed occurrence. Moreton waves are ideally observed in the wings of H alpha, and appear as semi-circular fronts propagating at speeds ranging from several hundred to over a thousand km/sec. They form an arc, or "brow shape" which can span up to 180 degrees. Extrapolating the speed and locations of the arc indicates that the phenomenon's origin intersects well with the impulsive phase of the associated H alpha flare (if the flare exhibits an impulsive phase). However, the arc may not form or may not be observable until it is tens of megameters from the flaring region, and subsequently can propagate to distances exceeding 100 megameters. The high speeds and distances of propagation, plus the associated radio and energetic particle observations, provided strong evidence of a coronal, rather than a chromospheric origin. The H alpha manifestation of the wave is assumed to be the "ground track" or "skirt" of a three-dimensional disturbance.

Thompson, B. J.↗

DOE OSTI2026

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↗