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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Observation of magnetic islands in tokamak plasmas during the suppression of edge-localized modes

In tokamaks, a leading platform for fusion energy, periodic filamentary plasma eruptions known as edge-localized modes occur in plasmas with high-energy confinement and steep pressure profiles at the plasma edge. These edge-localized modes could damage the tokamak wall but can be suppressed using small three-dimensional magnetic perturbations. Here we demonstrate that these magnetic perturbations can change the magnetic topology just inside the steep gradient region of the plasma edge. We identify signatures of a magnetic island, and their observation is linked to the suppression of edge-localized modes. We compare high-resolution measurements of perturbed magnetic surfaces with predictions from ideal magnetohydrodynamic theory where the magnetic topology is preserved. Although ideal magnetohydrodynamics adequately describes the measurements in plasmas exhibiting edge-localized modes, it proves insufficient for plasmas where these modes are suppressed. Nonlinear resistive magnetohydrodynamic modelling supports this observation. Our study experimentally confirms the predicted role of magnetic islands in inhibiting the occurrence of edge-localized modes. This will be beneficial for physics-based predictions in future fusion devices to control these modes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

An adjoint-based method for optimising MHD equilibria against the infinite- n , ideal ballooning mode

We demonstrate a fast adjoint-based method to optimise tokamak and stellarator equilibria against a pressure-driven instability known as the infinite-n ideal ballooning mode. We present three finite-β (the ratio of thermal to magnetic pressure) equilibria: one tokamak equilibrium and two stellarator equilibria that are unstable against the ballooning mode. Using the self-adjoint property of ideal magnetohydrodynamics, we construct a technique to rapidly calculate the change in the eigenvalue, a measure of ideal ballooning instability. Using the SIMSOPT optimisation framework, we then implement our fast adjoint gradient-based optimiser to minimise the eigenvalue and find stable equilibria for each of the three originally unstable equilibria.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Verification of global gyrokinetic simulation of low frequency mode excited by thermal plasma in spherical tokamak

A low frequency Alfven eigenmode in the ST40 spherical tokamak (ST) is found to be resonantly excited by thermal ions from global gyrokinetic GTC simulations. The analyses of phase-space resonances and wave-particle energy exchanges show that the Beta-induced Alfvén-Acoustic Eigenmode (BAAE) is primarily driven unstable by thermal ions, but is stabilized by energetic particles (EPs). When all kinetic effects are artificially suppressed, GTC simulations in the ideal magnetohydrodynamic (MHD) limit confirm the existence of the MHD eigenmode with a frequency in the BAAEs gap, as previously found by the ideal MHD code NOVA. The kinetic effects of thermal ions induce a frequency downshift compared to the stable BAAE in the MHD simulations. These results support the verification for global gyrokinetic simulations of the BAAE in the ST. However, the simulations do not explain the experimental observations of the BAAE in the ST40, possibly owing to the limitation of the collisionless gyrokinetic Monte Carlo model for the EPs.

Alfvén eigenmode↗
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

Magnetorotational instability in a swirling partially ionized gas

ABSTRACT The magnetorotational instability (MRI) has been proposed as the method of angular momentum transport that enables accretion in astrophysical discs. However, for weakly ionized discs, such as protoplanetary discs, it remains unclear whether the combined non-ideal magnetohydrodynamic (MHD) effects of Ohmic resistivity, ambipolar diffusion, and the Hall effect make these discs MRI stable. While much effort has been made to simulate non-ideal MHD MRI, these simulations make simplifying assumptions and are not always in agreement with each other. Furthermore, it is difficult to directly observe the MRI astrophysically because it occurs on small scales. Here, we propose the concept of a swirling gas experiment of weakly ionized argon gas between two concentric cylinders threaded with an axial magnetic field that can be used to study non-ideal MHD MRI. For our proposed experiment, we derive the hydrodynamic equilibrium flow and a dispersion relation for MRI that includes the three non-ideal effects. We solve this dispersion relation numerically for the parameters of our proposed experiment. We find it should be possible to produce a non-ideal MRI in such an experiment because of the Hall effect, which increases the MRI growth rate when the vertical magnetic field is anti-aligned with the rotation axis. As a proof of concept, we also present experimental results for a hydrodynamic flow in an unmagnetized prototype. We find that our prototype has a small, but non-negligible, α-parameter that could serve as a baseline for comparison to our proposed magnetized experiment, which could be subject to additional turbulence from the MRI.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
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 OSTI2024

Development of a neural network model for peeling–ballooning stability analysis in the KSTAR tokamak pedestals

The neural network model, MISHKA-NN is developed to mitigate the computational burden associated with the linear ideal magnetohydrodynamic (MHD) stability analysis of the pedestal based on the peeling–ballooning (P–B) model. By utilizing both 1D plasma profiles (current density, pressure gradient, and safety factor) and 0D parameters (plasma geometry, total current, and toroidal mode number), the model predicts linear growth rate of edge-localized ideal MHD instability in a given equilibrium state. By enabling the prediction of each instability within a second, the model reduces the time required for plotting a pedestal P–B stability diagram (j - α diagram) from approximately 100 CPU hours to a few CPU minutes. Notably, even with the utilization of parametric pressure and current profiles and plasma boundary shapes for the training dataset, the model shows a satisfactory level of performance in benchmarking the j - α diagram for the reconstructed equilibrium from a KSTAR tokamak experiment. We anticipate the model to serve as a versatile alternative to 2D linear MHD stability codes, alleviating numerical costs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

A study of resistive peeling–ballooning modes across spherical tokamaks

We investigate how non-ideal-magnetohydrodynamics (MHD) effects, in particular plasma resistivity, impact the peeling–ballooning stability thresholds in spherical tokamaks. This analysis follows the discovery of resistive kink-peeling modes in ELMing National Spherical Torus Experiment (NSTX) discharges. In the present study we extend this modeling to ELMing pulses in the Mega Ampere Spherical Tokamak (MAST) and MAST—Upgrade (MAST-U), where we find a clear resistive scaling for peeling–ballooning modes. While in NSTX ideal-MHD predicts stability for ELMing discharges, in MAST-U we find that the plasma is slightly unstable to peeling–ballooning modes, but is fully stabilized once diamagnetic effects are considered in terms of a growth rate normalization. A resistive power law scaling is calculated for these modes on MAST-U, which lies in between that of tearing modes and resistive interchange modes. A comparison between M3D-C1 and NIMROD shows reasonable agreement for this scaling. Resistivity destabilizes the modes and the peeling–ballooning unstable domain is considerably expanded in both, MAST and MAST-U. In addition to the MAST/-U pulses we also analyze resistive PB stability in a NSTX-similarity discharge on DIII-D. While having a different aspect ratio from NSTX, this discharge uses NSTX-like shaping parameters, toroidal field and plasma current. By considering these discharges alongside NSTX cases, we identify conditions influencing the onset of resistive peeling–ballooning modes. Furthermore, our findings indicate that magnetic shear in the pedestal region is closely linked to the emergence of resistive edge modes.

MAST-U↗
DOE OSTI2025

Ohm’s Law, the Reconnection Rate, and Energy Conversion in Collisionless Magnetic Reconnection

Magnetic reconnection is a ubiquitous plasma process that transforms magnetic energy into particle energy during eruptive events throughout the universe. Reconnection not only converts energy during solar flares and geomagnetic substorms that drive space weather near Earth, but it may also play critical roles in the high energy emissions from the magnetospheres of neutron stars and black holes. In this review article, we focus on collisionless plasmas that are most relevant to reconnection in many space and astrophysical plasmas. Guided by first-principles kinetic simulations and spaceborne in-situ observations, we highlight the most recent progress in understanding this fundamental plasma process. We start by discussing the non-ideal electric field in the generalized Ohm’s law that breaks the frozen-in flux condition in ideal magnetohydrodynamics and allows magnetic reconnection to occur. We point out that this same reconnection electric field also plays an important role in sustaining the current and pressure in the current sheet and then discuss the determination of its magnitude (i.e., the reconnection rate), based on force balance and energy conservation. This approach to determining the reconnection rate is applied to kinetic current sheets with a wide variety of magnetic geometries, parameters, and background conditions. We also briefly review the key diagnostics and modeling of energy conversion around the reconnection diffusion region, seeking insights from recently developed theories. Finally, future prospects and open questions are discussed.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Magnetic fields with general omnigenity

Omnigenity is a desirable property of toroidal magnetic fields that ensures confinement of trapped particles. Confining charged particles is a basic requirement for any fusion power plant design, but it can be difficult to satisfy with the non-axisymmetric magnetic fields used by the stellarator approach. Every ideal magnetohydrodynamic equilibrium previously found to approximate omnigenity has been either axisymmetric, quasi-symmetric or has poloidally closed contours of magnetic field strength $B$ . However, general omnigenous equilibria are a much larger design space than these subsets. A new model is presented and employed in the DESC stellarator optimization suite to represent and discover the full parameter space of omnigenous equilibria. Although exact omnigenity aside from quasi-symmetry is impossible, these results reveal that excellent particle confinement can be achieved in practice. Examples far from quasi-symmetry with poloidally, helically and toroidally closed $B$ contours are attained with DESC and shown to have low neoclassical collisional transport and fast particle losses.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Numerical minimization of neoclassical poloidal viscosity for supersonic equilibria in tokamak geometry

Extensive experimental evidence has shown that the presence of poloidal flow in tokamaks can dramatically improve transport properties. However, theory indicates that poloidal flows are damped by poloidal viscosity, thus necessitating external drivers, such as neutral beam injection or radio frequency heating. In this work, ideal magnetohydrodynamic equilibria are calculated via the FORTRAN code FLOW [Guazzotto et al., Phys. Plasmas 11, 604 (2004)] and a postprocessor is used to estimate the neoclassical poloidal viscosity. The equilibrium inputs, which correspond to intuitive physical quantities, are then numerically optimized to reduce a viscosity figure of merit. We present supersonic equilibria in tokamak geometry with minimized neoclassical poloidal viscosities for various velocity free function inputs, plasma aspect ratios, and collisionality regimes. Benchmarks are made against an analytic theory as well as a classical expression of poloidal viscosity. Numerical confirmation of the analytic theory is obtained in the high aspect ratio and high collisionality limit. Good agreement is also seen near the plasma core and edge, with discrepancies arising in the intermediate region. Outside of these limits, rotation input function profiles are found that provide ∼order of magnitude improvements over the analytic theory, with additional progress being made toward predictions for tokamak-relevant equilibria.

Physics↗
DOE OSTI2024

Sparsified time-dependent Fourier neural operators for fusion simulations

This paper presents a sparsified Fourier neural operator for coupled time-dependent partial differential equations (ST-FNO) as an efficient machine learning surrogate for fluid and particle-based fusion codes such as NIMROD (Non-Ideal Magnetohydrodynamics with Rotation - Open Discussion) and GTC (Gyrokinetic Toroidal Code). ST-FNO leverages the structures in the governing equations and utilizes neural operators to represent Green's function-like numerical operators in the corresponding numerical solvers. Once trained, ST-FNO can rapidly and accurately predict dynamics in fusion devices compared with first-principle numerical algorithms. In general, ST-FNO represents an efficient and accurate machine learning surrogate for numerical simulators for multi-variable nonlinear time-dependent partial differential equations, with the proposed architectures and loss functions. The efficacy of ST-FNO has been demonstrated using quiescent H-mode simulation data from NIMROD and kink-mode simulation data from GTC. The ST-FNO H-mode results show orders of magnitude reduction in memory and central processing unit usage in comparison with the numerical solvers in NIMROD when computing fields over a selected poloidal plane. The ST-FNO kink-mode results achieve a factor of 2 reduction in the number of parameters compared to baseline FNO models without accuracy loss.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Effects of zero and reversed magnetic shear on resistive wall modes in a straight limiter tokamak with zero beta

Advanced tokamak scenarios often feature equilibriums with zero and reversed magnetic shear. To isolate and investigate their impacts on the resistive wall mode (RWM) instability analytically, we construct a series of cylindrical limiter equilibriums with different magnetic shear in the core and toward plasma edge, as a prototype of the configurations in advanced tokamak scenarios. Equilibriums with zero β are considered so that the analysis focuses on the current-driven RWMs. Analytical solutions for the n=1 resistive wall mode, derived from the reduced ideal magnetohydrodynamics (MHD) equations, consistently demonstrate key insights for both the core and the edge: the growth rate of RWMs is inversely proportional to the averaged magnetic shear when the safety factor at the edge (qa) is held constant. Specifically, an increase in positive averaged magnetic shear results in a decreased growth rate, whereas an increase in negative averaged magnetic shear leads to an increased growth rate. Furthermore, the influence of nqa on the mode's stability significantly surpasses the effects of magnetic shear changes previously discussed. These analytical calculation results provide a verification of NIMROD simulations.

Wan, Sui (ORCID:0009000464121677)↗
DOE OSTI2024

Fast ion relaxation in ITER mediated by Alfvén instabilities

Abstract We address the critical issue for future burning plasmas of whether high-energy fusion products or auxiliary heating-beam ions will be confined for a sufficiently long time to compensate for thermal plasma energy losses. This issue can be mitigated by one of the most deleterious collective phenomena—the instability of low, sub-cyclotron frequency Alfvén eigenmodes (AEs), such as toroidicity-induced AEs and reversed-shear AEs in the ITER steady-state scenario. Using a revised quasi-linear (QL) theory applied to energetic particle (EP) relaxation in the presence of AEs, we find that the AE instabilities can affect both neutral beam ions and alpha particles, although the resulting fast ion transport is expected to be modest if classical particle slowing down is assumed. On the other hand, the QL theory predicts that the AE amplitudes will be enhanced by the background microturbulence, although this topic remains outside our scope due to the significant numerical effort required to evaluate these effects. We report our results for EP relaxation dynamics obtained utilizing several tools: (i) a comprehensive linear stability study of the sub-cyclotron Alfvénic spectrum as computed by ideal magnetohydrodynamic NOVA simulations for the AE eigenproblem, (ii) drift kinetic NOVA-C calculations for wave–particle interaction and AE growth/damping rates, and (iii) predictive QL modeling coupled with the global transport code TRANSP to assess the EP relaxation on the equilibrium timescale.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Determination of confinement regime boundaries via separatrix parameters on Alcator C-Mod based on a model for interchange-drift-Alfvén turbulence

The separatrix operational space (SepOS) model (Eich and Manz 2021 Nucl. Fusion 61 086017) is shown to predict the L–H transition, the L-mode density limit, and the ideal magnetohydrodynamic ballooning limit in terms of separatrix parameters for a wide range of Alcator C-Mod plasmas. The model is tested using Thomson scattering measurements across a wide range of operating conditions on C-Mod, spanning $\overline{n}_{\mathrm{e}}$ = 0.3–5.5 $\times 10^{20}\,$m −3 , $B_{\mathrm{t}} = 2.5$–8.0 T, and $B_{\mathrm{p}}$= 0.1–1.2 T. An empirical regression for the electron pressure gradient scale length, $\lambda_{{p}_{\mathrm{e}}}$, against a turbulence control parameter, $\alpha_{\mathrm{t}}$, and the poloidal fluid gyroradius, $\rho_{\mathrm{s,p}}$, is constructed for H-modes and found to require positive exponents for both regression parameters, indicating turbulence widening of near-scrape-off layer widths at high $\alpha_{\mathrm{t}}$ and an inverse scaling with $B_{\mathrm{p}}$, consistent with results on ASDEX Upgrade. The SepOS model is also tested in the unfavorable drift direction and found to apply well to all three boundaries, including the L–H transition as long as a correction to the Reynolds energy transfer term, $\alpha_\mathrm{RS} \lt 1$ is applied. I-modes typically exist in the unfavorable drift direction for values of $\alpha_{\mathrm{t}} \lesssim 0.3$. Finally, an experiment studying the transition between the Type-I ELMy and EDA H-mode is analyzed using the same framework. It is found that a recently identified boundary $\alpha_{\mathrm{t}} = 0.55$ at excludes most EDA H-modes but that the balance of wavenumbers responsible for the L-mode density limit, namely $k_\mathrm{EM} = k_\mathrm{RBM}$, may better describe the transition on C-Mod. The ensemble of boundaries validated and explored is then applied to project regime access and limit avoidance for the SPARC primary reference discharge parameters.

ELM suppression↗
DOE OSTI2026

Instantaneous difference frequency locking observed during toroidicity-induced Alfvén eigenmode coupling in the DIII-D tokamak

In magnetic confinement fusion, toroidicity-induced Alfvén eigenmodes (TAEs) are well-studied, weakly stable solutions of the linearized ideal magnetohydrodynamic equations. Driven unstable by suprathermal populations of energetic particles, TAE pose a key vulnerability to the confinement of high-energy alpha particles generated by fusion reactions. Hence, it is paramount to understand TAE dynamics if a working reactor is to be realized. In this work, we detect and characterize signatures of nonstationary nonlinear coupling between TAE using a novel, time-resolved bispectral analysis; results are supported by analytic signal of band-passed data. Crucially, a stationary phase relationship between two TAE and a nascent low frequency fluctuation is observed precisely when the triple product of magnetic fluctuation amplitudes is enhanced. Local mode number and frequency spectrum, gleaned from beam-emission spectroscopy, corroborates simultaneous satisfaction of nonlinear matching conditions, and provides a tool to identify theorized pathways of energy transfer, e.g. TAE parametric instability.

bispectral analysis↗
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 OSTI2024

Kink Instability of Flux Ropes in Partially Ionized Plasmas

In the solar atmosphere, flux ropes are subject to current-driven instabilities that are crucial in driving plasma eruptions, ejections, and heating. A typical ideal magnetohydrodynamics instability developing in flux ropes is the helical kink, which twists the flux rope axis. The growth of this instability can trigger magnetic reconnection, which can explain the formation of chromospheric jets and spicules, but its development has never been investigated in a partially ionized plasma (PIP). Here, we study the kink instability in PIP to understand how it develops in the solar chromosphere, where it is affected by charge-neutral interactions. Partial ionization speeds up the onset of the nonlinear phase of the instability, as the plasma β of the isolated plasma is smaller than the total plasma β of the bulk. The distribution of the released magnetic energy changes in fully ionized plasma and PIP, with a larger increase in internal energy associated with the PIP cases. The temperature in PIP increases faster also due to heating terms from the two-fluid dynamics. PIP effects trigger kink instability on shorter time scales, which is reflected in more explosive chromospheric flux rope dynamics. These results are crucial to understanding the dynamics of small-scale chromospheric structures—minifilament eruptions—that thus far have been largely neglected but could significantly contribute to chromospheric heating and jet formation.

79 ASTRONOMY AND ASTROPHYSICS↗