arXiv subjects

K. C. Hammond

Publications and source records attributed to K. C. Hammond.

13 recordsLinked to original sources

arXiv2026

Neural network predictions of plasma confinement loss in Wendelstein 7-X pellet-fueled discharges

The energy confinement time is a key parameter of a magnetized fusion plasma, helping to determine whether ignition can occur. Experiments in tokamaks and stellarators have shown that the confinement time can be improved via pellet injection. The state of enhanced confinement brought about by a given pellet typically deteriorates over time unless and until a subsequent pellet is injected. In this work, we develop a data-driven model that predicts, at any moment, the remaining time before a plasma in Wendelstein 7-X (W7-X) will lose its enhanced confinement state. This "remaining time" metric effectively sets a deadline for when the next pellet must be injected in order to steadily maintain a high confinement time. We describe the development and training of the model and compare its predictions to observations from previous experiments. At least 90% of the model predictions are accurate to within 51 ms, which is below the typical W7-X energy confinement time as well as the minimum time separation between subsequent pellet injections. The model can be evaluated rapidly and could be suitable for use in a control system that optimizes the pellet injection rate in real time.

physics.plasm-ph↗

arXiv2025

A framework for discrete optimization of stellarator coils

Designing magnets for three-dimensional plasma confinement is a key task for advancing the stellarator as a fusion reactor concept. Stellarator magnets must produce an accurate field while leaving adequate room for other components and being reasonably simple to construct and assemble. In this paper, a framework for coil design and optimization is introduced that enables the attainment of sparse magnet solutions with arbitrary restrictions on where coils may be located. The solution space is formulated as a "wireframe" consisting of a mesh of interconnected wire segments enclosing the plasma. Two methods are developed for optimizing the current distribution on a wireframe: Regularized Constrained Least Squares (RCLS), which uses a linear least-squares approach to optimize the currents in each segment, and Greedy Stellarator Coil Optimization (GSCO), a fully discrete procedure in which loops of current are added to the mesh one by one to achieve the desired magnetic field on the plasma boundary. Examples are presented of solutions obtainable with each method, some of which achieve high field accuracy while obeying spatial constraints that permit easy assembly.

physics.plasm-ph↗

arXiv2024

Flexible Stellarator Physics Facility

We propose to build a Flexible Stellarator Physics Facility to explore promising regions of the vast parameter space of disruption-free stellarator solutions for Fusion Pilot Plants (FPPs).

physics.plasm-ph↗

arXiv2024

Improved stellarator permanent magnet designs through combined discrete and continuous optimizations

A common optimization problem in the areas of magnetized plasmas and fusion energy is the design of magnets to produce a given three-dimensional magnetic field distribution to high precision. When designing arrays of permanent magnets for stellarator plasma confinement, such problems have tens of thousands of degrees of freedom whose solutions, for practical reasons, should be constrained to discrete spaces. We perform a direct comparison between two algorithms that have been developed previously for this purpose, and demonstrate that composite procedures that apply both algorithms in sequence can produce substantially improved results. One approach uses a continuous, quasi-Newton procedure to optimize the dipole moments of a set of magnets and then projects the solution onto a discrete space. The second uses an inherently discrete greedy optimization procedure that has been enhanced and generalized for this work. The approaches are both applied to design arrays cubic rare-Earth permanent magnets to confine a quasi-axisymmetric plasma with a magnetic field on axis of 0.5 T. The first approach tends to find solutions with higher field accuracy, whereas the second can find solutions with substantially (up to 30%) fewer magnets. When the approaches are combined, they can obtain solutions with magnet quantities comparable to the second approach while matching the field accuracy of the first.

physics.plasm-ph↗

arXiv2022

Design of an arrangement of cubic magnets for a quasi-axisymmetric stellarator experiment

The usage of permanent magnets to shape the confining magnetic field of a stellarator has the potential to reduce or eliminate the need for non-planar coils. As a proof-of-concept for this idea, we have developed a procedure for designing an array of cubic permanent magnets that works in tandem with a set of toroidal-field coils to confine a stellarator plasma. All of the magnets in the design are constrained to have identical geometry and one of three polarization types in order to simplify fabrication while still producing sufficient field accuracy. We present some of the key steps leading to the design, including the geometric arrangement of the magnets around the device, the procedure for optimizing the polarizations according to the three allowable magnet types, and the choice of magnet types to be used. We apply these methods to design an array of rare-Earth permanent magnets that can be paired with a set of planar toroidal-field coils to confine a quasi-axisymmetric plasma with a toroidal magnetic field strength of about 0.5 T on axis.

physics.plasm-ph↗

arXiv2021

Initial operation and data processing on a system for real-time evaluation of Thomson scattering signals on the Large Helical Device

A scalable system for real-time analysis of electron temperature and density based on signals from the Thomson scattering diagnostic, initially developed for and installed on the NSTX-U experiment, was recently adapted for the Large Helical Device (LHD) and operated for the first time during plasma discharges. During its initial operation run, it routinely recorded and processed signals for four spatial points at the laser repetition rate of 30 Hz, well within the system's rated capability for 60 Hz. We present examples of data collected from this initial run and describe subsequent adaptations to the analysis code to improve the fidelity of the temperature calculations.

physics.plasm-ph↗

arXiv2020

Geometric concepts for stellarator permanent magnet arrays

The development of stellarators that use permanent magnet arrays to shape their confining magnetic fields has been a topic of recent interest, but the requirements for how such magnets must be shaped, manufactured, and assembled remain to be determined. To address these open questions, we have performed a study of geometric concepts for magnet arrays with the aid of the newly developed MAGPIE code. A proposed experiment similar to the National Compact Stellarator Experiment (NCSX) is used as a test case. Two classes of magnet geometry are explored: curved bricks that conform to a regular grid in cylindrical coordinates, and hexahedra that conform to the toroidal plasma geometry. In addition, we test constraints on the magnet polarization. While magnet configurations constrained to be polarized normally to a toroidal surface around the plasma are unable to meet the required magnetic field parameters when subject to physical limitations on the strength of present-day magnets, configurations with unconstrained polarizations are shown to satisfy the physics requirements for a targeted plasma.

physics.plasm-ph↗

arXiv2017

Overdense microwave plasma heating in the CNT stellarator

Overdense plasmas have been attained with 2.45 GHz microwave heating in the low-field, low-aspect-ratio CNT stellarator. Densities higher than four times the ordinary (O) mode cutoff density were measured with 8 kW of power injected in the O-mode and, alternatively, with 6.5 kW in the extraordinary (X) mode. The temperature profiles peak at the plasma edge. This was ascribed to collisional damping of the X-mode at the upper hybrid resonant layer. The X-mode reaches that location by tunneling, mode-conversions or after polarization-scrambling reflections off the wall and in-vessel coils, regardless of the initial launch being in O- or X-mode. This interpretation was confirmed by full-wave numerical simulations. Also, as the CNT plasma is not completely ionized at these low microwave power levels, electron density was shown to increase with power. A dependence on magnetic field strength was also observed (for O-mode launch) and discussed.

physics.plasm-ph↗

arXiv2017

High-$β$ equilibrium and ballooning stability of the low aspect ratio CNT stellarator

The existence and ballooning-stability of low aspect ratio stellarator equilibria is predicted for CNT with the aid of 3D numerical tools. In addition to having a low aspect ratio, CNT is characterized by a low magnetic field and small plasma volume. Also, highly overdense plasmas were recently heated in CNT by means of microwaves. These characteristics suggest that CNT might attain relatively high values of plasma $β$ and thus be of use in the experimental study of stellarator stability to high-$β$ instabilities such as ballooning modes. As a first step in that direction, here the ballooning stability limit is found numerically. Depending on the particular magnetic configuration we expect volume-averaged $β$ limits in the range 0.9-3.0%, and possibly higher, and observe indications of a second region of ballooning stability. As the aspect ratio is reduced, stability is found to increase in some configurations and decrease in others. Energy-balance estimates using stellarator scaling laws indicate that the lower $β$ limit may be attainable with overdense heating at powers of of 40 to 100 kW. The present study serves the additional purpose of testing VMEC and other stellarator codes at high values of $β$ and at low aspect ratios. For this reason, the study was carried out both for free boundary, for maximum fidelity to experiment, as well as with a fixed boundary, as a numerical test.

physics.plasm-ph↗

arXiv2016

Onion-peeling inversion of stellarator images

An onion-peeling technique is developed for inferring the emissivity profile of a stellarator plasma from a two-dimensional image acquired through a CCD or CMOS camera. Each pixel in the image is treated as an integral of emission along a particular line-of-sight. Additionally, the flux surfaces in the plasma are partitioned into discrete layers, each of which is assumed to have uniform emissivity. If the topology of the flux surfaces is known, this construction permits the development of a system of linear equations that can be solved for the emissivity of each layer. We present initial results of this method applied to wide-angle visible images of the CNT stellarator plasma.

physics.plasm-ph↗

arXiv2016

Experimental and numerical study of error fields in the CNT stellarator

Sources of error fields were indirectly inferred in a stellarator by reconciling computed and numerical flux surfaces. Sources considered so far include the displacements and tilts (but not the deformations, yet) of the four circular coils featured in the simple CNT stellarator. The flux surfaces were measured by means of an electron beam and phosphor rod, and were computed by means of a Biot-Savart field-line tracing code. If the ideal coil locations and orientations are used in the computation, agreement with measurements is poor. Discrepancies are ascribed to errors in the positioning and orientation of the in-vessel interlocked coils. To that end, an iterative numerical method was developed. A Newton-Raphson algorithm searches for the coils' displacements and tilts that minimize the discrepancy between the measured and computed flux surfaces. This method was verified by misplacing and tilting the coils in a numerical model of CNT, calculating the flux surfaces that they generated, and testing the algorithm's ability to deduce the coils' displacements and tilts. Subsequently, the numerical method was applied to the experimental data, arriving at a set of coil displacements whose resulting field errors exhibited significantly improved quantitative and qualitative agreement with experimental results.

physics.plasm-ph↗

arXiv2014

Metamaterial lens of specifiable frequency-dependent focus and adjustable aperture for electron cyclotron emission in the DIII-D tokamak

Electron Cyclotron Emission (ECE) of different frequencies originates at different locations in non-uniformly magnetized plasmas. For simultaneous observation of multiple ECE frequencies from the outside edge of a toroidal plasma confinement device (e.g. a tokamak), the focal length of the collecting optics should increase with the frequency to maximize the resolution on a line of sight along the magnetic field gradient. Here we present the design and numerical study of a zoned metamaterial lens with such characteristics, for possible deployment with the 83-130 GHz ECE radiometer in the DIII-D tokamak. The lens consists of a concentric array of miniaturized element phase-shifters. These were reverse-engineered starting from the desired Gaussian beam waist locations and further optimized to account for diffraction and finite-aperture effects that tend to displace the waist. At the same time we imposed high and uniform transmittance, averaged over all phase-shifters. The focal length is shown to increase from 1.37 m to 1.97 m over the frequency range of interest, as desired for low-field DIII-D discharges (B = -1.57 T). Retracting the lens to receded positions rigidly moves the waists accordingly, resulting in a good match -within a fraction of the Rayleigh length- of the EC-emitting layer positions at higher fields (up to B = -2.00 T). Further, it is shown how varying the lens aperture might move the waists "non-rigidly" to better match the non-rigid movement of the EC-emitting layers with the magnetic field. The numerical method presented is very general and can be used to engineer any dependence of the focal length on the frequency, including zero or minimal chromatic aberration.

physics.optics↗

arXiv2014

Proto-CIRCUS Tilted-Coil Tokamak-Torsatron Hybrid: Design and Construction

We present the field-line modeling, design and construction of a prototype circular-coil tokamak-torsatron hybrid called Proto-CIRCUS. The device has a major radius R = 16 cm and minor radius a < 5 cm. The six "toroidal field" coils are planar as in a tokamak, but they are tilted. This, combined with induced or driven plasma current, is expected to generate rotational transform, as seen in field-line tracing and equilibrium calculations. The device is expected to operate at lower plasma current than a tokamak of comparable size and magnetic field, which might have interesting implications for disruptions and steady-state operation. Additionally, the toroidal magnetic ripple is less pronounced than in an equivalent tokamak in which the coils are not tilted. The tilted coils are interlocked, resulting in a relatively low aspect ratio, and can be moved, both radially and in tilt angle, between discharges. This capability will be exploited for detailed comparisons between calculations and field-line mapping measurements. Such comparisons will reveal whether this relatively simple concept can generate the expected rotational transform.

physics.plasm-ph↗