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At least 235 records · Page 13

Integrability, normal forms, and magnetic axis coordinates

Integrable or near-integrable magnetic fields are prominent in the design of plasma confinement devices. Such a field is characterized by the existence of a singular foliation entirely consisting of invariant submanifolds. A compact regular leaf (a flux surface) of this foliation must be diffeomorphic to the two-torus. In a neighborhood of a flux surface, it is known that the magnetic field admits several exact smooth normal forms in which the field lines are straight. However, these normal forms break down near singular leaves, including elliptic and hyperbolic magnetic axes. In this work, the existence of exact smooth normal forms for integrable magnetic fields near elliptic and hyperbolic magnetic axes is established. In the elliptic case, smooth near-axis Hamada and Boozer coordinates are defined and constructed. Ultimately, these results establish previously conjectured smoothness properties for smooth solutions of the magnetohydrodynamic equilibrium equations. The key arguments are a consequence of a geometric reframing of integrability and magnetic fields: they are presymplectic systems.

97 MATHEMATICS AND COMPUTING↗

Conceptual Design and Performance Considerations for Superconducting Magnets in the Material Plasma Exposure eXperiment

An important step toward the advent of nuclear fusion as a future power source is the development of plasmafacing materials that can function as designed for a long period of time. While ITER and other devices including Wendelstein 7-X and the Joint European Torus will provide insight into divertor and first wall performance, a dedicated device to advance the understanding of material performance in the representative plasma environments is needed. The Material Plasma Exposure eXperiment has been proposed as a linear plasma device to generate and to direct fusion reactor-like plasma energy and particle flux at the target materials with electron temperatures of 1-15 eV and electron densities of 10 20 -10 21 m -3 . Given that the requirements for radio frequency (RF) heating on-axis field are no greater than 2.5 T and the warm bore diameters must be between 60 cm and 1.5 m, the conceptual design was developed for the experiments on a set of superconducting magnets carried out using commercially available NbTi superconductors. This conceptual design evaluated the cryogenic heat loads, mechanical loads, and quench protection to ensure that the current design is compatible with current technologies. In addition, an alternative evaluation of this design relative to ReBCO high-temperature superconducting magnets determined the conditions under which these technologies could be advantageous.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Constrained stellarator coil curvature optimization with FOCUS

Finding less complicated coils that have adequately low field errors is a crucial step in stellarator development. One coil metric that is of high importance is the maximum curvature of the coil centreline, or coil single filament. Conductors cannot be bent below some threshold minimum radius of curvature. High coil curvatures can cause strains to exceed acceptable levels, especially in superconducting coils. We investigate three ways to optimize coil curvature and find that applying penalty functions to the coil curvature solves for coils that have a constrained maximum curvature and low field error. Penalty functions are implemented in FOCUS and coil solutions optimized for an HSX-like ‘plasma boundary’ are presented.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Adjoint methods for quasi-symmetry of vacuum fields on a surface

Adjoint methods can speed up stellarator optimisation by providing gradient information more efficiently compared with finite-difference evaluations. Adjoint methods are herein applied to vacuum magnetic fields, with objective functions targeting quasi-symmetry and a rotational transform value on a surface. Here to measure quasi-symmetry, a novel way of evaluating approximate flux coordinates on a single flux surface without the assumption of a neighbourhood of flux surfaces is proposed. The shape gradients obtained from the adjoint formalism are evaluated numerically and verified against finite-difference evaluations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Measures of quasisymmetry for stellarators

Quasisymmetric stellarators are an attractive class of optimised magnetic confinement configurations. The property of quasisymmetry (QS) is in practice limited to be approximate, and thus the construction requires measures that quantify the deviation from the exact property. In this paper we study three measure candidates used in the literature, placing the focus on their origin and a comparison of their forms. The analysis shows clearly the lack of universality in these measures. As these metrics do not directly correspond to any physical property (except when exactly quasisymmetric), optimisation should employ additional physical metrics for guidance. It is suggested that close to QS minima, one should treat QS metrics through inequality constraints so that additional physics metrics dominate optimisation. The impact of different quasisymmetric measures on optimisation is presented through an example, for which the standard metric that weights the asymmetric Fourier modes of the field magnitude appears to perform best.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A fast, accurate and easy to implement Kapur–Rokhlin quadrature scheme for singular integrals in axisymmetric geometries

Many applications in magnetic confinement fusion require the efficient calculation of surface integrals with singular integrands. The singularity subtraction approaches typically used to handle such singularities are complicated to implement and low-order accurate. In contrast, we demonstrate that the Kapur–Rokhlin quadrature scheme is well-suited for the logarithmically singular integrals encountered for a toroidally axisymmetric confinement system, is easy to implement and is high-order accurate. As an illustration, we show how to apply this quadrature scheme for the efficient and accurate calculation of the normal component of the magnetic field due to the plasma current on the plasma boundary, via the virtual-casing principle.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

The DESC stellarator code suite Part 3: Quasi-symmetry optimization

The DESC stellarator optimization code takes advantage of advanced numerical methods to search the full parameter space much faster than conventional tools. Only a single equilibrium solution is needed at each optimization step thanks to automatic differentiation, which efficiently provides exact derivative information. A Gauss–Newton trust-region optimization method uses second-order derivative information to take large steps in parameter space and converges rapidly. With just-in-time compilation and GPU portability, high-dimensional stellarator optimization runs take orders of magnitude less computation time with DESC compared to other approaches. This paper presents the theory of the DESC fixed-boundary local optimization algorithm along with demonstrations of how to easily implement it in the code. Example quasi-symmetry optimizations are shown and compared to results from conventional tools. Three different forms of quasi-symmetry objectives are available in DESC, and their relative advantages are discussed in detail. In the examples presented, the triple product formulation yields the best optimization results in terms of minimized computation time and particle transport. This paper concludes with an explanation of how the modular code suite can be extended to accommodate other types of optimization problems.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Physics basis for the Wisconsin HTS Axisymmetric Mirror (WHAM)

The Wisconsin high-temperature superconductor axisymmetric mirror experiment (WHAM) will be a high-field platform for prototyping technologies, validating interchange stabilization techniques and benchmarking numerical code performance, enabling the next step up to reactor parameters. A detailed overview of the experimental apparatus and its various subsystems is presented. WHAM will use electron cyclotron heating to ionize and build a dense target plasma for neutral beam injection of fast ions, stabilized by edge-biased sheared flow. At 25 keV injection energies, charge exchange dominates over impact ionization and limits the effectiveness of neutral beam injection fuelling. This paper outlines an iterative technique for self-consistently predicting the neutral beam driven anisotropic ion distribution and its role in the finite beta equilibrium. Beginning with recent work by Egedal et al. ( Nucl. Fusion , vol. 62, no. 12, 2022, p. 126053) on the WHAM geometry, we detail how the FIDASIM code is used to model the charge exchange sources and sinks in the distribution function, and both are combined with an anisotropic magnetohydrodynamic equilibrium solver method to self-consistently reach an equilibrium. We compare this with recent results using the CQL3D code adapted for the mirror geometry, which includes the high-harmonic fast wave heating of fast ions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Design and construction of the MUSE permanent magnet stellarator

This paper documents the design and construction of MUSE, the world's first permanent magnet (PM) stellarator and the first quasi-axisymmetric experiment. The purpose of MUSE is to develop and assess a new way of building optimised stellarators that uses simple planar coils PMs. Our PM optimisation algorithm consists of initialising a geometry to pack dipoles densely, running the FAMUS code to minimise surface field error subject to PM constraints and applying discrete jumps to reach a physically realisable solution. FAMUS treats the PM system as a set of ideal point dipoles. From there we construct finite-volume magnet towers to be housed in 3D-printed PM holders. We describe the design of the PM holders, which were validated by laser metrology. We analyse the effects of finite permeability, sensitivity to perturbations and magnetostatic forces. An exact analytic formula for the magnetic field from a finite-volume PM tower is presented to compute PM–PM forces and stress on the PM holder. Stellarator construction is complete and experiments are underway.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Direct, simple and efficient computation of all components of the virtual-casing magnetic field in axisymmetric geometries with Kapur–Rokhlin quadrature

In a recent publication (Toler et al., J. Plasma Phys., vol. 89, issue 2, 2023, p. 905890210), we demonstrated that for axisymmetric geometries, the Kapur–Rokhlin quadrature rule provided an efficient and high-order accurate method for computing the normal component, on the plasma surface, of the magnetic field due to the toroidal current flowing in the plasma, via the virtual-casing principle. The calculation was indirect, as it required the prior computation of the magnetic vector potential from the virtual-casing principle, followed by the computation of its tangential derivative by Fourier differentiation, to obtain the normal component of the magnetic field. Our approach did not provide the other components of the virtual-casing magnetic field. In this letter, we show that a more direct and more general approach is available for the computation of the virtual-casing magnetic field. The Kapur–Rokhlin quadrature rule accurately calculates the principal value integrals in the expression for all the components of the magnetic field on the plasma boundary, and the numerical error converges at a rate nearly as high as the indirect method we presented previously.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Exploration of the parameter space of quasisymmetric stellarator vacuum fields through adjoint optimisation

Optimising stellarators for quasisymmetry leads to strongly reduced collisional transport and energetic particle losses compared with unoptimised configurations. Although stellarators with precise quasisymmetry have been obtained in the past, it remains unclear how broad the parameter space is where good quasisymmetry may be achieved. We study the range of aspect ratios and rotational transform values for which stellarators with excellent quasisymmetry on the boundary can be obtained. A large number of Fourier harmonics is included in the boundary representation, which is made computationally tractable by the use of adjoint methods to enable fast gradient-based optimisation and by the direct optimisation of vacuum magnetic fields, which converge more robustly compared with solutions from magnetohydrostatics. Several novel configurations are presented, including stellarators with record levels of quasisymmetry on a surface, three field period quasiaxisymmetric stellarators with substantial magnetic shear, and compact quasisymmetric stellarators at low aspect ratios similar to tokamaks.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Overview of the physics basis for the ARC fusion power plant

Commonwealth Fusion Systems plans to build ARC as the first fusion power plant at a site in Chesterfield County, Virginia, USA by the early 2030s. We present an overview of analysis comprising the physics basis of the ARC V3A design, a high-magnetic-field tokamak with 𝐵 0 =11.4 T, 𝐼 𝑝 =12.0 MA, 𝑅 0 =4.62 m, 𝑎 =1.18 m. ARC V3A is designed to produce 𝑃 𝑓⁡𝑢⁢𝑠 ≈1.13 GW DT fusion power and deliver ⩾400 MW net electric power to the grid. This overview includes quantitative analysis of fundamental issues for design of and operational plasma scenarios for a tokamak power plant, and lays out the design targets and strategic choices for ARC, including empirical fusion performance projections, assessment of H-mode access, ion cyclotron resonance heating simulations, alpha particle physics and time-dependent full-pulse simulations. This is complemented by topical papers on fusion performance and transport, disruption physics, boundary physics and magnetohydrodynamic stability. Critically, these studies identify key model uncertainties and physics risks to be retired through SPARC operation. Due to the modular nature of ARC, early results from SPARC can be incorporated into the design of the first ARC as well as subsequent replacements of the ARC vacuum vessel.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

1D kinetic study of pinch formation in a dense plasma focus: Transition from collisional to collisionless regimes

Here, the pinch-formation stage of a deuterium dense plasma focus, and associated “shock-flash” neutron yield, is studied using 1D kinetic simulations considering a plasma column with initial pressure P, initial radius R, and the compression to be driven by a constant current I. The relative behavior of the compression is shown to be similar for fixed ratios of the characteristic ion mean free path to the radius of the plasma column at stagnation, $λ_{st}/R_{st}$. This dimensionless parameter is shown to scale like $I^4/(P^3R^5)$. The compression ratio, $R/R_{st}$, is found to be a minimum when $λ_{st}/R_{st} ≈$ 1 and is the largest in the collisionless limit where $λ_{st} \gg R_{st}$. This behavior is in contrast to the analogous planar pinch where R/Rst decreases from one constant for λst/Rst$\ll$1 to a smaller constant for $λ_{st}/R_{st} \gg$ 1. The yield in the collisionless regime is shown to fall between the two well-known $I^4$ scaling laws. Furthermore, this regime exhibits qualities that potentially make it appealing for radiography applications, such as increased localization in time and space of the neutron formation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Fusion yield of plasma with velocity-space anisotropy at constant energy

Velocity-space anisotropy can significantly modify fusion reactivity. The nature and magnitude of this modification depends on the plasma temperature, as well as the details of how the anisotropy is introduced. For plasmas that are sufficiently cold compared to the peak of the fusion cross section, anisotropic distributions tend to have higher yields than isotropic distributions with the same thermal energy. At higher temperatures, it is instead isotropic distributions that have the highest yields. However, the details of this behavior depend on exactly how the distribution differs from an isotropic Maxwellian. Therefore, this paper describes the effects of anisotropy on fusion yield for the class of anisotropic distribution functions with the same energy distribution as a 3D isotropic Maxwellian and compares those results with the yields from bi-Maxwellian distributions. In many cases, especially for plasmas somewhat below reactor-regime temperatures, the effects of anisotropy can be substantial.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Spatiotemporal measurements of striations in a glow discharge’s positive column using laser-collisional induced fluorescence

Here we have observed the behavior of striations caused by ionization waves propagating in low-pressure helium DC discharges using the non-invasive laser-collision induced fluorescence (LCIF) diagnostic. To achieve this, we developed an analytic fit of collisional radiative model (CRM) predictions to interpret the LCIF data and recover quantitative two-dimensional spatial maps of the electron density, n e , and the ratios of LCIF emission states that can be correlated with T e with the use of accurate distribution functions at localized positions within striated helium discharges at 500 mTorr, 750 mTorr, and 1 Torr. To our knowledge, these are the first spatiotemporal, laser-based, experimental measurements of n e in DC striations. The n e and 447:588 ratio distributions align closely with striation theory. Constriction of the positive column appears to occur with decreased gas pressure, as shown by the radial n e distribution. We identify a transition from a slow ionization wave to a fast ionization wave between 750 mTorr and 1 Torr. These experiments validate our analytic fit of n e , allowing the implementation of an LCIF diagnostic in helium without the need to develop a CRM.

42 ENGINEERING↗

2nd and 3rd order spectral energy corrections with penumbral de-blurring methodology for opacity platform used on the National Ignition Facility

The Opacity Spectrometer (OpSpec) used in the National Ignition Facility’s opacity experiments measures x-ray spectra from 0.9 to 2.1 keV from the different experimental regions: the backlight source, emission source, and the absorption region with the transmission calculated from these regions. The OpSpec designs have gone through several iterations to help improve the signal-to-noise ratio, remove alternate crystal plane reflections, and improve spectral resolution, which helps to increase the validity of the opacity measurements. However, the source spans well outside the current working spectral range, and higher-order reflections are intrinsic to the crystal, which increases the overall signal seen in the data regions. The recorded data are the convolution of 1st order transmission, higher-order reflections, and the penumbra blurring. In conclusion, this work represents the details for deconvolving the 2nd and 3rd order spectral energy corrections with a penumbral de-blurring to correct the relative measurement of x-ray intensity of different spectral energies and further analysis of datasets relevant to the opacity experiments.

47 OTHER INSTRUMENTATION↗

Managing photon flux in a miniaturized photoionization detector

Miniaturized photoionization detectors (PIDs) are used in conjunction with gas chromatography systems to detect volatile compounds in gases by collecting the current from the photoionized gas analytes. PIDs should be inexpensive and compatible with a wide range of analyte species. One such PID is based on the formation of a He plasma in a dielectric barrier discharge (DBD), which generates vacuum UV (VUV) photons from excited states of He to photoionize gas analytes. There are several design parameters that can be leveraged to increase the ionizing photon flux to gas analytes to increase the sensitivity of the PID. To that end, the methods to maximize the photon flux from a pulsed He plasma in a DBD-PID were investigated using a two-dimensional plasma hydrodynamics model. The ionizing photon flux originated from the resonance states of helium, He(3P) and He(2 1 P), and from the dimer excimer He 2 *. While the photon flux from the resonant states was modulated over the voltage pulse, the photon flux from He 2 * persisted long after the voltage pulse passed. Several geometrical optimizations were investigated, such as using an array of pointed electrodes. However, increasing the capacitance of the dielectric enclosing the plasma chamber had the largest effect on increasing the VUV photon fluence to gas analytes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗