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DOE OSTI2025

Low- n stability and plasma response to RMP in various STEP scenarios

The low-n (n is the toroidal mode number) magnetohydrodynamic (MHD) stability and plasma response are numerically investigated for various scenarios designed for STEP, that are relevant for the H-mode pedestal analysis. Control of the edge-localized modes (ELMs) with externally applied resonant magnetic perturbations (RMPs) is considered. Optimization of the ELM control coil current configuration, based on the computed plasma MHD response and well-established figures of merit validated on present-day experiments, finds reasonable robustness of a fixed coil phasing (for a given n-number) to control ELMs in all five STEP plasmas considered. Based on certain semi-empirical criteria, the required coil current to achieve ELM suppression is estimated to be about 10–20 kAt with the n = 1 or 2 RMP configuration and about 100–200 kAt for the n = 4 RMP. Systematic linear stability calculations are used to map out stability windows for the low-n kink-peeling modes, in terms of the ideal-wall location and variation of the edge safety factor q 95 with respect to the target design. The kink-peeling stability boundary is found to be generally sensitive to the q 95 variation, which has implications for achieving the quiescent H-mode regime in STEP. Full toroidal quasilinear initial-value simulations for these STEP plasmas find that generation of the edge-harmonic oscillations (EHOs) depends sensitively on the plasma scenario, the initial linear stability of the kink-peeling modes, the initial plasma toroidal flow and q 95 . In general, it is easier (more robust) to access the EHO-regime for two of the cases considered with smaller plasma volume and higher on-axis safety factor. Finally, quasilinear simulations find robust density pumpout due to applied RMPs in these STEP plasmas, but the effect on the plasma toroidal flow varies among different cases.

EHO↗

NASA NTRS2023

Magnetosonic ULF Waves With Anomalous Plasma–Magnetic Field Correlations: Standing Waves and Inhomogeneous Plasmas

Ultra-low frequency (ULF) wave observations across the heliosphere often rely on the sign of correlations between plasma (density/pressure) and magnetic field perturbations to distinguish between fast and slow magnetosonic modes. However, the assumptions behind this magnetohydrodynamic result are not always valid, particularly within the magnetosphere which is inhomogeneous and supports standing waves along the geomagnetic field. Through theory and a global simulation, we find both effects can result in anomalous plasma–magnetic field correlations. The interference pattern in standing waves can lead both body and surface magnetosonic waves to have different cross-phases than their constituent propagating waves. Furthermore, if the scale of gradients in the background are shorter than the wavelength or the waves are near-incompressible, then advection by the wave of inhomogeneities can overcome the wave's inherent sense of compression. These effects need to be allowed for and taken into account when applying the typical diagnostic to observations.

MHD Waves↗

DOE OSTI2023

Ab-initio General-relativistic Neutrino-radiation Hydrodynamics Simulations of Long-lived Neutron Star Merger Remnants to Neutrino Cooling Timescales

Abstract We perform the first 3D ab-initio general-relativistic neutrino-radiation hydrodynamics of a long-lived neutron star merger remnant spanning a fraction of its cooling timescale. We find that neutrino cooling becomes the dominant energy loss mechanism after the gravitational-wave dominated phase (∼20 ms postmerger). Electron flavor antineutrino luminosity dominates over electron flavor neutrino luminosity at early times, resulting in a secular increase of the electron fraction in the outer layers of the remnant. However, the two luminosities become comparable ∼20–40 ms postmerger. A dense gas of electron antineutrinos is formed in the outer core of the remnant at densities ∼10 14.5 g cm −3 , corresponding to temperature hot spots. The neutrinos account for ∼10% of the lepton number in this region. Despite the negative radial temperature gradient, the radial entropy gradient remains positive, and the remnant is stably stratified according to the Ledoux criterion for convection. A massive accretion disk is formed from the material squeezed out of the collisional interface between the stars. The disk carries a large fraction of the angular momentum of the system, allowing the remnant massive neutron star to settle to a quasi-steady equilibrium within the region of possible, stable, rigidly rotating configurations. The remnant is differentially rotating, but it is stable against the magnetorotational instability. Other MHD mechanisms operating on longer timescales are likely responsible for the removal of the differential rotation. Our results indicate the remnant massive neutron star is thus qualitatively different from a protoneutron stars formed in core-collapse supernovae.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2015

An MHD Code for the Study of Magnetic Structures in the Solar Wind

We have developed a 2.5D MHD code designed to study how the solar wind influences the evolution of transient events in the solar corona and inner heliosphere. The code includes thermal conduction, coronal heating and radiative cooling. Thermal conduction is assumed to be magnetic field-aligned in the inner corona and transitions to a collisionless formulation in the outer corona. We have developed a stable method to handle field-aligned conduction around magnetic null points. The inner boundary is placed in the upper transition region, and the mass flux across the boundary is determined from 1D field-aligned characteristics and a 'radiative energy balance' condition. The 2.5D nature of this code makes it ideal for parameter studies not yet possible with 3D codes. We have made this code publicly available as a tool for the community. To this end we have developed a graphical interface to aid in the selection of appropriate options and a graphical interface that can process and visualize the data produced by the simulation. As an example, we show a simulation of a dipole field stretched into a helmet streamer by the solar wind. Plasmoids periodically erupt from the streamer, and we perform a parameter study of how the frequency and location of these eruptions changed in response to different levels of coronal heating. As a further example, we show the solar wind stretching a compact multi-polar flux system. This flux system will be used to study breakout coronal mass ejections in the presence of the solar wind.

corona↗

NASA NTRS2025

On the Stability Analysis of Astrophysical Cooling Functions

To model the temperature evolution of optically thin astrophysical environments at MHD scales, radiative and collisional cooling rates are typically either pretabulated or fit into a functional form and then input into MHD codes as a radiative loss function. Thermal balance requires estimates of the analogous heating rates, which are harder to calculate, and due to uncertainties in the underlying dissipative heating processes these rates are often simply parameterized. The resulting net cooling function defines an equilibrium curve that varies with density and temperature. Such cooling functions can make the gas prone to thermal instability (TI), which will cause departures from equilibrium. There has been no systematic study of thermally unstable parameter space for nonequilibrium states. Motivated by our recent finding that there is a related linear instability, catastrophic cooling instability, that can dominate over TI, here we carry out such a study. We show that Balbus instability criteria for TI can be used to define a critical cooling rate, Λc, that permits a nonequilibrium analysis of cooling functions through the mapping of TI zones. We furthermore illustrate how thermal conduction modifies the shape of TI zones. Upon applying a Λc-based stability analysis to coronal loop simulations, we find that loops undergoing periodic episodes of coronal rain formation are linearly unstable to catastrophic cooling instability, while TI is stabilized by thermal conduction.

Amanda Stricklan↗

DOE OSTI2025

On the Stability Analysis of Astrophysical Cooling Functions

To model the temperature evolution of optically thin astrophysical environments at MHD scales, radiative and collisional cooling rates are typically either pretabulated or fit into a functional form and then input into MHD codes as a radiative loss function. Thermal balance requires estimates of the analogous heating rates, which are harder to calculate, and due to uncertainties in the underlying dissipative heating processes these rates are often simply parameterized. The resulting net cooling function defines an equilibrium curve that varies with density and temperature. Such cooling functions can make the gas prone to thermal instability (TI), which will cause departures from equilibrium. There has been no systematic study of thermally unstable parameter space for nonequilibrium states. Motivated by our recent finding that there is a related linear instability, catastrophic cooling instability, that can dominate over TI, here we carry out such a study. We show that Balbus instability criteria for TI can be used to define a critical cooling rate, Λ c , that permits a nonequilibrium analysis of cooling functions through the mapping of TI zones. We furthermore illustrate how thermal conduction modifies the shape of TI zones. Upon applying a Λ c -based stability analysis to coronal loop simulations, we find that loops undergoing periodic episodes of coronal rain formation are linearly unstable to catastrophic cooling instability, while TI is stabilized by thermal conduction.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

WEST L-mode record long pulses guided by predictions using Integrated Modeling

A new record was set on the WEST Tokamak, designed to operate long duration plasmas in a tungsten (W) environment, with an injected energy of 1.15 GJ and a plasma duration 364s. Scenario development was supported by integrated modeling using the High Fidelity Plasma Simulator (HFPS), the European IMAS-coupled version of JETTO/JINTRAC, which integrates physics-driven modules into a unified framework. In particular, a reduced model for Lower-Hybrid heating and Current-Drive (LHCD) and the quasi-linear turbulent transport model TGLF are crucial for long pulses predictions up to the Last Closed Flux Surface (LCFS). Using this workflow, a 100 s reference discharge was modeled and plasma kinetic profiles and loop voltage were quantitatively well matched. In preparation for the recent long duration experiments, non-inductive current-drive actuators (I P , n e , P LHCD ) were varied to determine the operational domain going towards fully non-inductive discharges. In particular, decreasing the plasma current is shown to ease the access to such conditions, with a careful monitoring of (n e , P LHCD ) to avoid machine limitations. In addition, post-prediction experiments conducted within the investigated parameter range validated the predicted dependencies and were shown to be in quantitative agreement. Exploratory work on the use of ECCD for MHD stability purpose is also introduced.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

ITER cold VDEs in the limit of perfectly conducting walls

Recently, it has been shown that a vertical displacement event (VDE) can occur in ITER even when the walls are perfect conductors, as a consequence of the current quench (CQ) [A. H. Boozer, Phys. Plasmas 26, 114501 (2019)]. We used the extended-MHD code M3D-C1 with an ITER-like equilibrium and induced a CQ to explore cold VDEs in the limit of perfectly conducting walls, using different wall geometries. In the case of a rectangular first wall with the side walls far away from the plasma, we obtained very good agreement with the analytical model developed by Boozer that considers a top/bottom flat-plates wall. We show that the solution in which the plasma remains at the initial equilibrium position is improved when bringing the side walls closer to the plasma. When approximating the ITER first wall as a perfect conductor, the plasma remains stable at the initial equilibrium position far beyond the value predicted by the flat-plates wall limit. When considering an opposite limit in which only the inner shell of the ITER vacuum vessel acts as a perfect conductor, the plasma is displaced during the CQ, but the edge safety factor remains above 2 longer in the current decay compared to the flat-plates wall limit. In all the simulated cases, the VDE is found to be strongly dependent on the plasma current, in agreement with a similar finding in the flat-plates wall limit, showing an important difference with hot VDEs in which the CQ is not a necessary condition.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Demonstration of RELAP5-3D for transient analysis of a dual coolant lead lithium fusion blanket concept

Our research aims to build a multiphysics framework for transient analysis of the Dual- Coolant Lead-Lithium (DCLL) blanket design of the proposed Fusion Nuclear Science Facility (FNSF) for all Onticipated Operational Occurrences (AOOs) using Reduced Order Models (ROMs). This paper presents an assessment of using RELAP5-3D for transient thermal-hydraulic blanket analysis of the DCLL design. Preliminary validation studies for the RELAP5-3D properties were conducted using a representative vertical flow loop model and a comparison study using experimental data from the thermal convection corrosion loops at ORNL. These studies inspected the thermal hydraulic response of Lead-Lithium Eutectic (PbLi) systems within the RELAP5-3D code; mainly pressure drop and heat transfer, as compared to analytical calculations and experimental data. The Magnetohydrodynamic (MHD) pressure drop effect for liquid metal under the effects of a uniform magnetic field was implemented into our models using an equivalent forms loss coefficient based on the phasic momentum equations. We verified our implementation of MHD pressure drop within RELAP5-3D using a systematic approach consisting of two studies. Models were developed to perform comparison studies based on experimental data from the Argonne Liquid metal EXperiment (ALEX) facility and the Magnetohydrodynamic PbLi Experiment (MaPLE) facility. Using the developed validation basis, we built a simplified DCLL channel model within RELAP5-3D, inspected MHD pressure drop and performed transient temperature analysis. The DCLL channel model used radial heating data from the International Thermonuclear Experimental Reactor (ITER) which was normalized to the FNSF design. Here, a representative startup transient was performed using a relative power curve from the initial ramp up of a long-term power pulse of the Tore Supra reactor. This study demonstrated that RELAP5-3D ROMs are capable of accurate transient analysis of the DCLL blanket. We have since utilized MCNP to develop heating profiles based on the FNSF design and are working toward implementing them into our DCLL model.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

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↗

DOE OSTI2023

Growth or Decay – I: universality of the turbulent dynamo saturation

The turbulent small-scale dynamo (SSD) is likely to be responsible for the magnetisation of the interstellar medium (ISM) that we observe in the Universe today. The SSD efficiently converts kinetic energy E kin into magnetic energy E mag , and is often used to explain how an initially weak magnetic field with E mag $\ll$ E kin is amplified, and then maintained at a level E mag ≲ E kin . Usually, this process is studied by initialising a weak seed magnetic field and letting the turbulence grow it to saturation. However, in this Part I of the Growth or Decay series, using three-dimensional, visco-resistive magnetohydrodynamical turbulence simulations up to magnetic Reynolds numbers of 2000, here we show that the same final state in the integral quantities, energy spectra, and characteristic scales of the magnetic field can also be achieved if initially E mag ~ E kin or even if initially E mag $\gg$ E kin . This suggests that the final saturated state of the turbulent dynamo is set by the turbulence and the material properties of the plasma, independent of the initial structure or amplitude of the magnetic field. We discuss the implications this has for the maintenance of magnetic fields in turbulent plasmas and future studies exploring the dynamo saturation.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Toward fusion plasma scenario planning for NSTX-U using machine-learning-accelerated models

One of the most promising devices for realizing power production through nuclear fusion is the tokamak. To maximize performance, it is preferable that tokamak reactors achieve advanced operating scenarios characterized by good plasma confinement, improved magnetohydrodynamic (MHD) stability, and a largely non-inductively driven plasma current. Such scenarios could enable steady-state reactor operation with high \emph{fusion gain} --- the ratio of produced fusion power to the external power provided through the plasma boundary. Precise and robust control of the evolution of the plasma boundary shape as well as the spatial distribution of the plasma current, density, temperature, and rotation will be essential to achieving and maintaining such scenarios. The complexity of the evolution of tokamak plasmas, arising due to nonlinearities and coupling between various parameters, motivates the use of model-based control algorithms that can account for the system dynamics. In this work, a learning-based accelerated model trained on data from the National Spherical Torus Experiment Upgrade (NSTX-U) is employed to develop planning and control strategies for regulating the density and temperature profile evolution around desired trajectories. The proposed model combines empirical scaling laws developed across multiple devices with neural networks trained on empirical data from NSTX-U and a database of first-principles-based computationally intensive simulations. The reduced execution time of the accelerated model will enable practical application of optimization algorithms and reinforcement learning approaches for scenario planning and control development. An initial demonstration of applying optimization approaches to the learning-based model is presented, including a strategy for mitigating the effect of leaving the finite validity range of the accelerated model. The approach shows promise for actuator planning between experiments and in real-time.

machine learning↗

DOE OSTI2024

Kinetic-ballooning-limited pedestals in spherical tokamak plasmas

Abstract A theoretical model is presented that for the first time matches experimental measurements of the pedestal width-height Diallo scaling in the low-aspect-ratio high- β tokamak NSTX. Combining linear gyrokinetics with self-consistent pedestal equilibrium variation, kinetic-ballooning, rather than ideal-ballooning plasma instability, is shown to limit achievable confinement in spherical tokamak pedestals. Simulations are used to find the novel Gyrokinetic Critical Pedestal constraint, which determines the steepest pressure profile a pedestal can sustain subject to gyrokinetic instability. Gyrokinetic width-height scaling expressions for NSTX pedestals with varying density and temperature profiles are obtained. These scalings for STs depart significantly from that of conventional aspect ratio tokamaks.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1994

Dynamics of flux tubes in accretion disks

The study of magnetized plasmas in astrophysics is complicated by a number of factors, not the least of which is that in considering magnetic fields in stars or accretion disks, we are considering plasmas with densities well above those we can study in the laboratory. In particular, whereas laboratory plasmas are dominated by the confining magnetic field pressure, stars, and probably accretion disks, have magnetic fields whose beta (ratio of gas pressure to magnetic field pressure) is much greater than 1. Observations of the Sun suggest that under such circumstances the magnetic field breaks apart into discrete flux tubes with a small filling factor. On the other hand, theoretical treatments of MHD turbulence in high-beta plasmas tend to assume that the field is more or less homogeneously distributed throughout the plasma. Here we consider a simple model for the distribution of magnetic flux tubes in a turbulent medium. We discuss the mechanism by which small inhomogeneities evolve into discrete flux tubes and the size and distribution of such flux tubes. We then apply the model to accretion disks. We find that the fibrilation of the magnetic field does not enhance magnetic buoyancy. We also note that the evolution of an initially diffuse field in a turbulent medium, e.g., any uniform field in a shearing flow, will initially show exponential growth as the flux tubes form. This growth saturates when the flux tube formation is complete and cannot be used as the basis for a self-sustaining dynamo effect. Since the typical state of the magnetic field is a collection of intense flux tubes, this effect is of limited interest. However, it may be important early in the evolution of the galactic magnetic field, and it will play a large role in numerical simulations. Finally, we note that the formation of flux tubes is an essential ingredient in any successful dynamo model for stars or accretion disks.

Vishniac, E. T.↗

DOE OSTI2026

Narrow operator models of stellarator equilibria in Fourier Zernike basis

Numerical computation of the ideal magnetohydrodynamic (MHD) equilibrium magnetic field is at the base of stellarator optimisation and provides the starting point for solving more sophisticated partial differential equations like transport or turbulence models. Conventional approaches solve for a single stationary point of the ideal MHD equations, which is fully defined by three invariants and the numerical scheme employed by the solver. We present the first numerical approach that can solve for a continuous distribution of equilibria with fixed boundary and rotational transform, varying only the pressure invariant. This approach minimises the force residual by optimising parameters of multilayer perceptrons that map from a scalar pressure multiplier to the Fourier Zernike basis as implemented in the modern stellarator equilibrium solver DESC.

fusion plasma↗

DOE OSTI2025

Nonlinear Alfvén instability simulation and EP transport for ITER reversed shear (steady-state) and monotonic q-profile regimes *

The nonlinear evolution and dynamics of energetic particle (EP) driven instabilities in both steady-state (reversed shear q-profile) and monotonic q-profile regimes of ITER are examined using the global gyro-Landau closure model FAR3d. Both neutral beam and alpha components are included, leading to synergistic effects between the two populations. In order to maintain computational feasibility, the present nonlinear simulation includes all toroidal mode numbers ranging from n = 0 to 15. It cannot be excluded that n’s above this range could introduce larger linear growth rates; however, as indicated from the results, the n = 0 to 15 range is sufficient to provide a strong linear drive and significant nonlinear transport effects. While the toroidal mode numbers n = 6,13 dominate the linear instability growth phase, nonlinear energy transfers in the saturated phase reverse this trend, leading to the dominance of lower n’s in the saturated phase of the simulation. Zonal flow structure generation and EP density flattening are further consequences of the nonlinear phase. The density profile flattening is caused by collectively driven EP radial transport fluxes, which have non-local characteristics. Instantaneous alpha particle transport fluxes are significant (Γ α ~ 2 x 10 20 m –2 s –1 ) for the reversed shear regime and lower (Γ α ~ 1.1 x 10 20 m –2 s –1 ) for the monotonic q-profile case.

AE↗

DOE OSTI2024

Overview of physics results from MAST upgrade towards core-pedestal-exhaust integration

Recent results from MAST Upgrade are presented, emphasising understanding the capabilities of this new device and deepening understanding of key physics issues for the operation of ITER and the design of future fusion power plants. The impact of MHD instabilities on fast ion confinement have been studied, including the first observation of fast ion losses correlated with Compressional and Global Alfvén Eigenmodes. High-performance plasma scenarios have been developed by tailoring the early plasma current ramp phase to avoid internal reconnection events, resulting in a more monotonic q profile with low central shear. The impact of m/n = 3/2, 2/1 and 1/1 modes on thermal plasma confinement and rotation profiles has been quantified, and scenarios optimised to avoid them have transiently reached values of normalised beta approaching 4.2. In pedestal and ELM physics, a maximum pedestal top temperature of ~350 eV has been achieved, exceeding the value achieved on MAST at similar heating power. Mitigation of type-I ELMs with n = 1 RMPs has been observed. Studies of plasma exhaust have concentrated on comparing conventional and Super-X divertor configurations, while X-point target, X-divertor and snowflake configurations have been developed and studied in parallel. In L-mode discharges, the separatrix density required to detach the outer divertors is approximately a factor 2 lower in the Super-X than the conventional configuration, in agreement with simulations. Detailed analysis of spectroscopy data from studies of the Super-X configuration reveal the importance of including plasma-molecule interactions and D 2 Fulcher band emission to properly quantify the rates of ionisation, plasma-molecule interactions and volumetric recombination processes governing divertor detachment. In H-mode with conventional and Super-X configurations, the outer divertors are attached in the former and detached in the latter with no impact on core or pedestal confinement.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Radiation GRMHD simulations of M87: funnel properties and prospects for gap acceleration

Here, we use the public code EBHLIGHT to carry out 3D radiative general relativistic magnetohydrodynamics (GRMHD) simulations of accretion on to the supermassive black hole in M87. The simulations self-consistently evolve a frequency-dependent Monte Carlo description of the radiation field produced by the accretion flow. We explore two limits of accumulated magnetic flux at the black hole (SANE and MAD), each coupled to several subgrid prescriptions for electron heating that are motivated by models of turbulence and magnetic reconnection. We present convergence studies for the radiation field and study its properties. We find that the near-horizon photon energy density is an order of magnitude higher than is predicted by simple isotropic estimates from the observed luminosity. The radially dependent photon momentum distribution is anisotropic and can be modeled by a set of point-sources near the equatorial plane. We draw properties of the radiation and magnetic field from the simulation and feed them into an analytic model of gap acceleration to estimate the very high energy (VHE) γ-ray luminosity from the magnetized jet funnel, assuming that a gap is able to form. We find luminosities of $\rm \sim 10^{41} \, erg \, s^{-1}$ for MAD models and $\rm \sim 2\times 10^{40} \, erg \, s^{-1}$ for SANE models, which are comparable to measurements of M87’s VHE flares. The time-dependence seen in our calculations is insufficient to explain the flaring behaviour. Our results provide a step towards bridging theoretical models of near-horizon properties seen in black hole images with the VHE activity of M87.

79 ASTRONOMY AND ASTROPHYSICS↗