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Results for “Equilibrium, MHD - Toroidal”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Investigation of island formation due to RMPs in DIII-D plasmas with the SIESTA resistive MHD equilibrium code

The SIESTA magnetohydrodynamic (MHD) equilibrium code has been used to compute a sequence of ideally stable equilibria resulting from numerical variation of the helical resonant magnetic perturbation (RMP) applied to an axisymmetric DIII-D plasma equilibrium. Increasing the perturbation strength at the dominant m=2, n=-1 , resonant surface leads to lower MHD energies and increases in the equilibrium island widths at the m=2 (and sidebands) surfaces, in agreement with theoretical expectations. Island overlap at large perturbation strengths leads to stochastic magnetic fields which correlate well with the experimentally inferred field structure. The magnitude and spatial phase (around the dominant rational surfaces) of the resonant (shielding) component of the parallel current are shown to change qualitatively with the magnetic island topology.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2017

Extension of the SIESTA MHD equilibrium code to free-plasma-boundary problems

Here, SIESTA is a recently developed MHD equilibrium code designed to perform fast and accurate calculations of ideal MHD equilibria for three-dimensional magnetic configurations. Since SIESTA does not assume closed magnetic surfaces, the solution can exhibit magnetic islands and stochastic regions. In its original implementation SIESTA addressed only fixed-boundary problems. That is, the shape of the plasma edge, assumed to be a magnetic surface, was kept fixed as the solution iteratively converges to equilibrium. This condition somewhat restricts the possible applications of SIESTA. In this paper we discuss an extension that will enable SIESTA to address free-plasma-boundary problems, opening up the possibility of investigating problems in which the plasma boundary is perturbed either externally or internally. As an illustration, SIESTA is applied to a configuration of the W7-X stellarator.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

Using motional Stark splitting of D$_α$ emission to constrain MHD equilibrium analysis in DIII-D plasmas

Herein we report tests of an alternate technique for constraining MHD equilibrium analysis in tokamak plasmas using internal magnetic field measurements based on |$B$| measurements from the motional Stark splitting of D$_α$ spectral lines emitted by a neutral heating beam (MSE-LS). We compare results using MSE-LS with those of the standard equilibrium analysis technique based on line polarization of the D$_α$ emission (MSE-LP). An alternative to MSE-LP is needed in future devices such as ITER where MSE-LP will be difficult due to a plasma-induced coating of the first optical element. The tests utilized data from 10 DIII-D shots with 7 MSE-LS and 14 MSE-LP views covering a range of radii along the outer midplane of the plasma. Seven MSE-LS measurements can contribute significantly to the equilibrium reconstruction of pressure and q profiles using both synthetic and experimental DIII-D MSE-LS data. For example, 7 MSE-LS plus seven MSE-LP measurements give a fit quality that is as good as the same cases with 14 MSE-LP measurements. Analyzing synthetic data for 14 MSE-LS measurements shows significant improvement in fitting quality over the case with 7 MSE-LS locations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Quasi-static magnetic compression of field-reversed configuration plasma: amended scalings and limits from two-dimensional MHD equilibrium

In this work, several key scaling laws of the quasi-static magnetic compression of field reversed configuration (FRC) plasma (Spencer et al 1983 Phys. Fluids 26 1564) are amended from a series of two-dimensional FRC MHD equilibriums numerically obtained using the Grad–Shafranov equation solver NIMEQ. Based on the new scaling for the elongation and the magnetic fields at the separatrix and the wall, the empirically stable limits for the compression ratio, the fusion gain, and the neutron yield are evaluated, which may serve as a more accurate estimate for the upper ceiling of performance from the magnetic compression of FRC plasma as a potential fusion energy as well as neutron source devices.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Public Data Set: Effects of Injected Current Streams on MHD Equilibrium Reconstruction of Local Helicity Injection Plasmas in a Spherical Tokamak

This public data set contains openly-documented, machine readable digital research data corresponding to figures published in J.D. Weberski et al., 'Effects of Injected Current Streams on MHD Equilibrium Reconstruction of Local Helicity Injection Plasmas in a Spherical Tokamak,' Journal of Fusion Energy 43, 72 (2024).

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Edge ICRF simulations in 3D geometry: From MHD equilibrium to coupling determination

We present in this work a consistent numerical scheme that allows the computation of 3D magnetic fields a nd 3D density profiles and their usage in ion cyclotron range of frequencies (ICRF) coupling simulations. We first utilize the PARVMEC code to compute the 3D free-boundary plasma equilibrium in the ideal magnetohydrodynamic (MHD) approximation. Since the PARVMEC solution is only defined within the last closed flux surface (LCFS), the magnetic field domain is extended to the scrape-off layer (SOL) via the BMW code, which computes a divergence-free magnetic field solution arising from the external conductors’ vacuum field a nd t he PARVMEC flux surface currents. This magnetic reconstruction is then used in the EMC3-EIRENE transport code in order to compute 3D density profiles. In the last step, the RAPLICASOL code is utilized to compute the ICRF antenna S-matrices resulting from the 3D density profiles. We exemplify this scheme for the ASDEX Upgrade tokamak. A new implementation of a curved model for the ASDEX Upgrade ICRF 2-strap antenna in RAPLICASOL allows simulations in realistic geometry, without any coordinate transformations.

Lopez, Graham↗
DOE OSTI2026

Improving ideal MHD equilibrium accuracy with physics-informed neural networks

We present a novel approach to compute three-dimensional magnetohydrodynamic equilibria with isotropic pressure profiles and nested surfaces by parametrizing Fourier modes with artificial neural networks (NNs). The full nonlinear global force residual of single equilibria across the volume in real space is then minimized with first order optimizers and compared to equilibria computed by conventional solvers. Already, we observe competitive computational cost to arrive at the same minimum residuals computable with existing codes. With increased computational cost, lower minima of the residual are computable with the NNs than with any other tested solver, establishing a new lower bound for the force residual. We use minimally complex NNs, and we expect significant improvements for solving not only single equilibria with NNs, but also for creating NN models valid over continuous distributions of equilibria.

ideal magnetohydrodynamics↗
DOE OSTI2024

Grad–Shafranov equilibria via data-free physics informed neural networks

A large number of magnetohydrodynamic (MHD) equilibrium calculations are often required for uncertainty quantification, optimization, and real-time diagnostic information, making MHD equilibrium codes vital to the field of plasma physics. In this paper, we explore a method for solving the Grad–Shafranov equation by using physics-informed neural networks (PINNs). For PINNs, we optimize neural networks by directly minimizing the residual of the partial differential equation as a loss function. We show that PINNs can accurately and effectively solve the Grad–Shafranov equation with several different boundary conditions, making it more flexible than traditional solvers. This method is flexible as it does not require any mesh and basis choice, thereby streamlining the computational process. We also explore the parameter space by varying the size of the model, the learning rate, and boundary conditions to map various tradeoffs such as between reconstruction error and computational speed. Additionally, we introduce a parameterized PINN framework, expanding the input space to include variables such as pressure, aspect ratio, elongation, and triangularity in order to handle a broader range of plasma scenarios within a single network. Parameterized PINNs could be used in future work to solve inverse problems such as shape optimization.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Necessary and sufficient conditions for quasisymmetry

A necessary and sufficient set of conditions for a quasisymmetric magnetic field in the form of constraint equations is derived from first principles. Without any assumption regarding the magnetohydrodynamic (MHD) equilibrium of the plasma, conditions for quasisymmetry are constructed starting from the single-particle Lagrangian to the leading order. The conditions presented in the paper are less restrictive than the set recently obtained by Burby et al. [“Some mathematics for quasi-symmetry,” arXiv:1912.06468 (2019)], and could facilitate ongoing efforts toward investigating the existence of global quasisymmetric MHD equilibria. Finally, it is also shown that quasisymmetry implies the existence of flux surfaces, regardless of whether the field corresponds to an MHD equilibrium.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Tokamak plasma equilibrium problems with anisotropic pressure and rotation and their numerical solution

In the MHD tokamak plasma theory, the plasma pressure is usually assumed to be isotropic. However, plasma heating by neutral beam injection and RF heating can lead to a strong anisotropy of plasma parameters and rotation of the plasma. The development of MHD equilibrium theory taking into account the plasma inertia and anisotropic pressure began a long time ago, but until now it has not been consistently applied in computational codes for engineering calculations of the plasma equilibrium and evolution in tokamak. This paper contains a detailed derivation of the axisymmetric plasma equilibrium equation in the most general form (with arbitrary rotation and anisotropic pressure) and description of the specialized version of the SPIDER code. The original method of calculation of the equilibrium with an anisotropic pressure and a prescribed rotational transform profile is proposed. Examples of calculations and discussion of the results are also presented.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Helical core formation and evolution during current ramp-up in the high-field tokamak Alcator C-Mod

We report that large, spontaneous m/n = 1/1 helical cores are predicted in tokamaks with extended regions of low- or reversed-magnetic shear profiles in a region within the q = 1 surface and an onset condition determined by constant (dp/dρ)/B$2\atop{t}$ along the threshold. These 3D modes occurred frequently in Alcator C-Mod during ramp-up when slow current penetration results in a reversed shear q-profile. The onset and early development of a helical core in C-Mod were simulated using a new 3D time-dependent equilibrium reconstruction, based on the ideal MHD equilibrium code VMEC. The reconstruction used the experimental density, temperature, and soft-X-ray fluctuations. The pressure profile can become hollow due to an inverted, hollow electron temperature profile caused by molybdenum radiation in the plasma core during the current ramp-up phase before the onset of sawteeth, which may also occur in ITER with tungsten. Lastly, based on modeling, it is found that a reverse shear q-profile combined with a hollow pressure profile reduces the onset condition threshold, enabling helical core formation from an otherwise axisymmetric equilibrium.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Minimizing the Electromechanical Stresses in Poloidal Field Coils by Optimizing their Numbers and Locations using FREDA Framework

Poloidal field (PF) and central solenoid (CS) coils play a crucial role in sustaining the equilibrium and preserving the shape of highly confined tokamak plasmas. Ensuring that PF coil current and mechanical stress stay within superconducting and structural limitations is an important check in the design assessment. Minimizing the PF coil currents and mechanical stresses influences reliability, cost, and performance. A free-boundary MHD equilibrium code—FreeGS is employed within the fusion reactor design and assessment (FREDA) whole facility modeling (WFM) framework to construct the plasma equilibrium based on the configuration and currents in the PF coils. Here, we present the capability of the FreeGS code to minimize the currents, forces, and electromagnetic stresses on the PF coils by optimizing their number, sizes, structures, and locations while maintaining an MHD stable plasma configuration with a large confinement factor. The workflow is initialized with a configuration of plasma parameters and coils’ locations from the 0-D tokamak build systems code in the FREDA framework. Then, FreeGS is called to calculate the initial equilibrium at the minimum total current in PF coils. Thereafter, FreeGS’s internal optimizer minimizes the currents and hoop and central forces on the PF coils while maintaining the reference equilibrium. Finally, the input configuration is updated with the optimized parameters for equilibria over the ramp-up phase of a burning-plasma operation. FREDA’s whole facility optimization capability, which includes all magnetic field coil systems, blanket, vacuum vessel (VV), first wall, divertor, etc., is under development and out of the scope for this study.

Hassan, Ehab [ORNL] (ORCID:0000000181060301)↗
DOE OSTI2015

The effect of three-dimensional fields on bounce averaged particle drifts in a tokamak

The impact of applied 3D magnetic fields on the bounce-averaged precessional drifts in a tokamak plasma are calculated. Local 3D MHD equilibrium theory is used to construct solutions to the equilibrium equations in the vicinity of a magnetic surface for a large aspect ratio circular tokamak perturbed by applied 3D fields. Due to modulations of the local shear caused by near-resonant Pfirsch-Schlüter currents, relatively weak applied 3D fields can have a large effect on trapped particle precessional drifts.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Shear Alfvén wave continuum spectrum with bifurcated helical core equilibria

Here, the radial structure of the continuum spectrum of shear Alfvén and Alfvén-acoustic waves in the beta-induced Alfvén eigenmode (BAE) frequency range is modeled for tokamak plasmas in the presence of 3D effects obtained from the bifurcated MHD equilibrium reconstruction. Plasma compressibility and geodesic curvature effects responsible for the low-frequency continuum spectrum calculations are invoked. In the equilibrium calculations we find that the helically distorted MHD equilibria may exist even for the axisymmetric devices if q = 1 rational surfaces are present. The continuum calculations with the bifurcated equilibria lead to a frequency splitting between the highest frequency branch and the lowest frequency branch continua at the frequency accumulation point. Radially localised shifting of modes happens via coupling of the adjacent n – 1 continuum around an accumulation point. Our modelling (including 3D effects) correctly reproduces the phenomenon of continuum frequency splitting and provides a possible solution for the differences of few kHz in frequency splitting, which remained unexplained with the 2D kinetic calculations. The pressure scaling confirms the increase of helical excursion of the magnetic axis in equilibrium reconstruction and hence the range of continuum frequency splitting. In our calculations, the existence of low-frequency continua is in agreement with the experimentally observed low-frequency modes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Asymptotic quasisymmetric high-beta three-dimensional magnetohydrodynamic equilibria near axisymmetry

Quasisymmetry (QS), a hidden symmetry of the magnetic field strength, is known to support nested flux surfaces and provide superior particle confinement in stellarators. In this work, we study the ideal magnetohydrodynamic (MHD) equilibrium and stability of high-beta plasma in a large-aspect-ratio stellarator. In particular, we show that the lowest-order description of a near-axisymmetric equilibrium vastly simplifies the problem of three-dimensional quasisymmetric MHD equilibria, which can be reduced to a standard elliptic Grad–Shafranov equation for the flux function. We show that any large-aspect-ratio tokamak, deformed periodically in the vertical direction, is a stellarator with approximate volumetric QS. We discuss exact analytical solutions and numerical benchmarks. Finally, we discuss the ideal ballooning and interchange stability of some of our equilibrium configurations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Structure of pressure-gradient-driven current singularity in ideal magnetohydrodynamic equilibrium

Abstract Singular currents typically appear on rational surfaces in non-axisymmetric ideal magnetohydrodynamic (MHD) equilibria with a continuum of nested flux surfaces and a continuous rotational transition. These currents have two components: a surface current (Dirac δ -function in flux surface labeling) that prevents the formation of magnetic islands, and an algebraically divergent Pfirsch–Schlüter current density when a pressure gradient is present across the rational surface. On flux surfaces adjacent to the rational surface, the traditional treatment gives the Pfirsch–Schlüter current density scaling as J ∼ 1 / Δ ι , where Δ ι is the difference of the rotational transform relative to the rational surface. If the distance s between flux surfaces is proportional to Δ ι , the scaling relation J ∼ 1 / Δ ι ∼ 1 / s will lead to a paradox that the Pfirsch–Schlüter current is not integrable. In this work, we investigate this issue by considering the pressure-gradient-driven singular current in the Hahm–Kulsrud–Taylor problem, which is a prototype for singular currents arising from resonant magnetic perturbations. We show that not only the Pfirsch–Schlüter current density but also the diamagnetic current density are divergent as ∼ 1 / Δ ι . However, due to the formation of a Dirac δ -function current sheet at the rational surface, the neighboring flux surfaces are strongly packed with s ∼ ( Δ ι ) 2 . Consequently, the singular current density J ∼ 1 / s , making the total current finite, thus resolving the paradox. Furthermore, the strong packing of flux surfaces causes a steepening of the pressure gradient near the rational surface, with ∇ p ∼ d p / d s ∼ 1 / s . In general non-axisymmetric MHD equilibrium, contrary to Grad’s conjecture that the pressure profile is flat around densely distributed rational surfaces, our result suggests a pressure profile that densely steepens around them.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Accuracy of kinetic equilibrium reconstruction of NSTX and NSTX-U plasmas and its impact on the transport and stability analysis

An accurate magnetohydrodynamic (MHD) equilibrium reconstruction is an essential starting point for stability and transport plasma analysis. Herein this work describes an approach for obtaining kinetic equilibrium reconstructions using the OMFIT framework, which has been applied for the first time to spherical tokamak data from NSTX and NSTX-U. The EFIT equilibrium solver is integrated with experimental data analysis procedures and subsequent TRANSP transport simulations to enhance the accuracy of the reconstruction, in particular, at the edge region, by adding constraints on the total pressure and current density profiles, based on the transport code solution. The accuracy of the equilibrium reconstruction depends on the uncertainty and number of constraints, as well as the choice of basis functions to represent the pressure and current density profiles. Improved fidelity of the equilibrium reconstruction is demonstrated by reducing the variability of the magnetic axis and boundary locations from several centimeters, for reconstructions based on magnetic and experimental pressure constraints, to only several millimeters, for kinetic reconstructions based on transport code constraints, when different representations of basis functions were tested. The variability of the safety factor on axis was reduced ten times in the same sensitivity study. The accuracy of the equilibrium reconstruction and subsequent mapping of the experimental kinetic profile data have a significant impact on the trapped gyro Landau fluid and linear CGYRO turbulence simulations, which predict different spectra of unstable modes and turbulent fluxes for cases with different numbers of constraints in the equilibrium reconstruction. Conversely, the stability analysis performed using the GATO code shows plasmas that are stable to n = 1 MHD modes in both equilibria using magnetic and experimental pressure constraints as well as the transport code constrained equilibrium. However, a scan of parameters away from these conditions shows considerable deviation in the threshold of unstable modes between these reconstructions. Therefore, for reliable plasma analysis and use in turbulence and stability calculations, a high-fidelity equilibrium reconstruction with accurate kinetic constraints based on transport code solutions is necessary.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗