National Compact Stellarator Experiment Research Articles

FP3D: A code for calculating 3D magnetic field and particle motion

An efficient numerical code FP3D has been developed to calculate particle orbits and evaluate particle confinement in 3D magnetic fields including stellarators and tokamaks with 3D fields. The magnetic field is either calculated from coils directly or obtained from equilibrium codes. FP3D has been verified with the 3D equilibrium code Variational Moments Equilibrium Code [Hirshman and Whitson, Phys. Fluids 26, 3553–3568 (1983)] for magnetic field calculation and with the drift-kinetic code Stellarator Fokker–Planck Iterative Neoclassical Conservative Solver [Landreman et al., Phys. Plasmas 21(4), 042503 (2014)] for neoclassical transport. The code has been applied successfully to the National Compact Stellarator Experiment stellarator [Nelson et al., Fusion Eng. Des. 66, 169–174 (2003)] for the calculation of neoclassical transport coefficient with the 3D magnetic field obtained directly from coils. FP3D is also used to calculate ripple losses in the tokamak Experimental Advanced Superconducting Tokamak [Y. Wan, Plasma Sci. Technol. 8(3) (2006)].

Global stochastic optimization of stellarator coil configurations

In the construction of a stellarator, the manufacturing and assembling of the coil system is a dominant cost. These coils need to satisfy strict engineering tolerances, and if those are not met the project could be cancelled as in the case of the National Compact Stellarator Experiment (NCSX) project (R.L. Orbach, 2008, https://ncsx.pppl.gov/DOE_NCSX_052208.pdf). Therefore, our goal is to find coil configurations that increase construction tolerances without compromising the performance of the magnetic field. In this paper, we develop a gradient-based stochastic optimization model which seeks robust stellarator coil configurations in high dimensions. In particular, we design a two-step method: first, we perform an approximate global search by a sample efficient trust-region Bayesian optimization; second, we refine the minima found in step one with a stochastic local optimizer. To this end, we introduce two stochastic local optimizers: BFGS applied to the sample average approximation; and Adam, equipped with a control variate for variance reduction. Numerical simulations performed on a W7-X-like coil configuration demonstrate that our global optimization approach finds a variety of promising local solutions at less than $0.1\,\%$ of the cost of previous work, which considered solely local stochastic optimization.

An adjoint method for determining the sensitivity of island size to magnetic field variations

An adjoint method to calculate the gradient of island width in stellarators is presented and applied to a set of magnetic field configurations. The underlying method for calculation of the island width is that of Cary & Hanson (Phys. Fluids B, vol. 3, issue 4, 1991, pp. 1006–1014) (with a minor modification), and requires that the residue of the island centre be small. Therefore, the gradient of the residue is calculated in addition. Both the island width and the gradient calculations are verified using an analytical magnetic field configuration introduced by Reiman & Greenside (Comput. Phys. Commun., vol. 43, issue 1, 1986, pp. 157–167). The method is also applied to the calculation of the shape gradient of the width of a magnetic island in a National Compact Stellarator Experiment (NCSX) vacuum configuration with respect to positions on a coil. A gradient-based optimization is applied to a magnetic field configuration studied by Hanson & Cary (Phys. Fluids, vol. 27, issue 4, 1984, pp. 767–769) to minimize stochasticity by adding perturbations to a pair of helical coils. Although only vacuum magnetic fields and an analytical magnetic field model are considered in this work, the adjoint calculation of the island width gradient could also be applied to a magnetohydrodynamic (MHD) equilibrium if the derivative of the magnetic field, with respect to the equilibrium parameters, is known. Using the island width gradient calculation presented here, more general gradient-based optimization methods can be applied to design stellarators with small magnetic islands. Moreover, the sensitivity of the island size may itself be optimized to ensure that coil tolerances, with respect to island size, are kept as high as possible.

Comparison of local and global gyrokinetic calculations of collisionless zonal flow damping in quasi-symmetric stellarators

The linear collisionless damping of zonal flows is calculated for quasi-symmetric stellarator equilibria in flux-tube, flux-surface, and full-volume geometry. Equilibria are studied from the quasi-helical symmetry configuration of the Helically Symmetric eXperiment (HSX), a broken symmetry configuration of HSX, and the quasi-axial symmetry geometry of the National Compact Stellarator eXperiment (NCSX). Zonal flow oscillations and long-time damping affect the zonal flow evolution, and the zonal flow residual goes to zero for small radial wavenumber. The oscillation frequency and damping rate depend on the bounce-averaged radial particle drift in accordance with theory. While each flux tube on a flux surface is unique, several different flux tubes in HSX or NCSX can reproduce the zonal flow damping from a flux-surface calculation given an adequate parallel extent. The flux-surface or flux-tube calculations can accurately reproduce the full-volume long-time residual for moderate kx, but the oscillation and damping time scales are longer in local representations, particularly for small kx approaching the system size.

ВИВЧЕННЯ ФІЗИКО-МЕХАНІЧНИХ ХАРАКТЕРИСТИК ВИСОКОНАПОВНЕНИХ ШЛАКОВМІЩУЮЧИХ ЦЕМЕНТІВ, МОДИФІКОВАНИХ ОРГАНО-МІНЕРАЛЬНИМИ ДОБАВКАМИ ВИРОБНИЦТВА ТОВ «МЦ БАУХЕМІ»

Abstract. The physical and mechanical characteristics of highly filled slag cements modified by the organic-mineral complex of LLC “MC Bauhemi” have been investigated. As a result of optimization, the area of permissible concentrations of organic-mineral additives was established according to the maximum criteria for the timing of the beginning and end of setting and strength in compression at the age of 7 and 28 days. It is shown that the expansion of the beginning of setting and its end is positively influenced by the presence of the plasticizer MC-PowerFlow 2695 from 0.43 to 0.8% and the organic-mineral complex Centrilit NC and Centrilit Fume SX in an amount from 3 / 5.25 to 5.2 / 7%, that with a simultaneous increase in the slag content from 50 to 70% in the composition of Portland cement, the start-end time of setting increases from 225/250 to 320/330 minutes, which is 1.3 / 1.5 times higher than similar indicators of no additive Portland cement. It was noted that at the age of 7 and 28 days, the introduction of an organic-mineral complex of the composition MC-PowerFlow 2695 from 0.28 to 0.64%, Centrilit NC from 4.23 to 7% and Centrilit Fume SX from 3 to 7% and at the content of GDSH in the amount of 50 and 70% contributes to the production of an artificial stone of the M500 brand with compressive strength in the range of 47 / 52.8 and 46/48 MPa. Using the method of superposition of response functions, the optimal area of permissible concentrations of the components of the Bauhemi organic-mineral complex, affecting the stated criteria, was determined when the slag content in Portland cement was 50 and 70%, namely: 0.6% MC-PowerFlow 2695, 5% Centrilit NC and 5 % Centrilit Fume SX. Further research will be aimed at studying the effect of this complex on the physical and mechanical properties with a slag content of 50 and 70% in the composition of Portland cement.

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.

Identification of important error fields in stellarators using the Hessian matrix method

Error fields are predominantly attributed to inevitable coil imperfections. Controlling error fields during coil fabrication and assembly is crucial for stellarators. Excessively tight coil tolerance increases time and cost, and, in part, led to the cancellation of the National Compact Stellarator Experiment and delay of W7-X. In this paper, we improve the recently proposed Hessian matrix method to rapidly identify important coil deviations. Two of the most common figures of merit, magnetic island size and quasi-symmetry, are analytically differentiated over coil parameters. By extracting the eigenvectors of the Hessian matrix, we can directly identify sensitive coil deviations in the order of the eigenvalues. The new method is applied to the upcoming Chinese First Quasi-axisymmetric Stellarator configuration. Important perturbations that enlarge n/m = 4/11 islands and deteriorate quasi-axisymmetry of the magnetic field are successfully determined. The results suggest each modular coil should have separate tolerance and some certain perturbation combinations will produce significant error fields. By relaxing unnecessary coil tolerance, this method will hopefully lead to a substantial reduction in time and cost.

Ion temperature gradient turbulence modification in quasi-axisymmetry

The large flexibility of the proposed QUASAR facility [Gates et al., Nucl. Fusion 57, 126064 (2017)] is leveraged in order to explore the effect of magnetic shear on adiabatic Ion Temperature Gradient (ITG) turbulence. The QUASAR facility is a reimagining of the National Compact Stellarator Experiment utilizing and expanding upon the already constructed coil set. Recent work using fixed boundary optimization of the LI383 equilibrium (upon which QUASAR is based) has suggested possible improvements to ITG turbulence [Mynick et al., Plasma Phys. Controlled Fusion 56, 094001 (2014)]. In this work, a different approach is taken, wherein a series of self-consistent free boundary VMEC equilibria are developed for QUASAR. These equilibria assume temperature and density profiles consistent with 2% beta and ohmic current drive. In each configuration, the toroidal field coils are energized to different values and the STELLOPT code is used to vary the modular coil current and net toroidal current. The edge value of rotational transform is targeted in the optimization, producing a magnetic shear scan. All these configurations share similar neoclassical transport levels, while nonlinear GENE flux tube simulations show up to a factor of four change in adiabatic ITG turbulence at various radii. Comparisons of proxy functions and linear flux tube runs are also made. This work highlights the capability of the QUASAR experiment as a tool to explore transport in 3D magnetic fields and the possibility of the further improvements to stellarators through optimization.

Collisionless microinstabilities in stellarators. II. Numerical simulations

Microinstabilities exhibit a rich variety of behavior in stellarators due to the many degrees of freedom in the magnetic geometry. It has recently been found that certain stellarators (quasi-isodynamic ones with maximum-J geometry) are partly resilient to trapped-particle instabilities, because fast-bouncing particles tend to extract energy from these modes near marginal stability. In reality, stellarators are never perfectly quasi-isodynamic, and the question thus arises whether they still benefit from enhanced stability. Here, the stability properties of Wendelstein 7-X and a more quasi-isodynamic configuration, QIPC, are investigated numerically and compared with the National Compact Stellarator Experiment and the DIII-D tokamak. In gyrokinetic simulations, performed with the gyrokinetic code GENE in the electrostatic and collisionless approximation, ion-temperature-gradient modes, trapped-electron modes, and mixed-type instabilities are studied. Wendelstein 7-X and QIPC exhibit significantly reduced growth rates for all simulations that include kinetic electrons, and the latter are indeed found to be stabilizing in the energy budget. These results suggest that imperfectly optimized stellarators can retain most of the stabilizing properties predicted for perfect maximum-J configurations.

Comparing linear ion-temperature-gradient-driven mode stability of the National Compact Stellarator Experiment and a shaped tokamak

One metric for comparing confinement properties of different magnetic fusion energy configurations is the linear critical gradient of drift wave modes. The critical gradient scale length determines the ratio of the core to pedestal temperature when a plasma is limited to marginal stability in the plasma core. The gyrokinetic turbulence code GS2 was used to calculate critical temperature gradients for the linear, collisionless ion temperature gradient (ITG) mode in the National Compact Stellarator Experiment (NCSX) and a prototypical shaped tokamak, based on the profiles of a JET H-mode shot and the stronger shaping of ARIES-AT. While a concern was that the narrow cross section of NCSX at some toroidal locations would result in steep gradients that drive instabilities more easily, it is found that other stabilizing effects of the stellarator configuration offset this so that the normalized critical gradients for NCSX are competitive with or even better than for the tokamak. For the adiabatic ITG mode, NCSX and the tokamak had similar adiabatic ITG mode critical gradients, although beyond marginal stability, NCSX had larger growth rates. However, for the kinetic ITG mode, NCSX had a higher critical gradient and lower growth rates until a/LT≈1.5 a/LT,crit, when it surpassed the tokamak's. A discussion of the results presented with respect to a/LT vs. R/LT is included.

Gyrokinetic studies of the effect of β on drift-wave stability in the National Compact Stellarator Experiment

The gyrokinetic turbulence code GS2 was used to investigate the effects of plasma β on linear, collisionless ion temperature gradient (ITG) modes and trapped electron modes (TEM) in National Compact Stellarator Experiment (NCSX) geometry. Plasma β affects stability in two ways: through the equilibrium and through magnetic fluctuations. The first was studied here by comparing ITG and TEM stability in two NCSX equilibria of differing β values, revealing that the high β equilibrium was marginally more stable than the low β equilibrium in the adiabatic-electron ITG mode case. However, the high β case had a lower kinetic-electron ITG mode critical gradient. Electrostatic and electromagnetic ITG and TEM mode growth rate dependencies on temperature gradient and density gradient were qualitatively similar. The second β effect is demonstrated via electromagnetic ITG growth rates' dependency on GS2's β input parameter. A linear benchmark with gyrokinetic codes GENE and GKV-X is also presented.

Simulating gyrokinetic microinstabilities in stellarator geometry with GS2

The nonlinear gyrokinetic code GS2 has been extended to treat non-axisymmetric stellarator geometry. Electromagnetic perturbations and multiple trapped particle regions are allowed. Here, linear, collisionless, electrostatic simulations of the quasi-axisymmetric, three-field period national compact stellarator experiment (NCSX) design QAS3-C82 have been successfully benchmarked against the eigenvalue code FULL. Quantitatively, the linear stability calculations of GS2 and FULL agree to within ∼10%.

Stellarator coil design and plasma sensitivity

The rich information contained in the plasma response to external magnetic perturbations can be used to help design stellarator coils more effectively. We demonstrate the feasibility by first developing a simple direct method to study perturbations in stellarators that do not break stellarator symmetry and periodicity. The method applies a small perturbation to the plasma boundary and evaluates the resulting perturbed free-boundary equilibrium to build up a sensitivity matrix for the important physics attributes of the underlying configuration. Using this sensitivity information, design methods for better stellarator coils are then developed. The procedure and a proof-of-principle application are given that (1) determine the spatial distributions of external normal magnetic field at the location of the unperturbed plasma boundary to which the plasma properties are most sensitive, (2) determine the distributions of external normal magnetic field that can be produced most efficiently by distant coils, and (3) choose the ratios of the magnitudes of the efficiently produced magnetic distributions so the sensitive plasma properties can be controlled. Using these methods, sets of modular coils are found for the National Compact Stellarator Experiment (NCSX) which are either smoother or can be located much farther from the plasma boundary than those of the present design.

Optimizing Stellarators for Turbulent Transport

Up to now, the term "transport-optimized" stellarators has meant optimized to minimize neoclassical transport, while the task of also mitigating turbulent transport, usually the dominant transport channel in such designs, has not been addressed, due to the complexity of plasma turbulence in stellarators. Here, we demonstrate that stellarators can also be designed to mitigate their turbulent transport, by making use of two powerful numerical tools not available until recently, namely, gyrokinetic codes valid for 3D nonlinear simulations and stellarator optimization codes. Two initial proof-of-principle configurations are obtained, reducing the level of ion temperature gradient turbulent transport from the National Compact Stellarator Experiment baseline design by a factor of 2-2.5.

Lessons Learned in Risk Management on NCSX

The National Compact Stellarator Experiment (NCSX) was designed to test physics principles of an innovative stellarator design developed by Princeton Plasma Physics Laboratory and Oak Ridge National Laboratory. Construction of some of the major components and subassemblies was completed, but the estimated cost and schedule for completing the project grew as the technical requirements and risks became better understood, leading to its cancellation in 2008. The project's risks stemmed from its technical challenges, primarily the complex component geometries and tight tolerances that were required. The initial baseline, which was established in 2004, was supported by a risk management plan and risk-based contingencies, both of which proved to be inadequate. Technical successes were achieved in the construction of challenging components and subassemblies, but cost and schedule growth was experienced. As part of an effort to improve project performance, a new risk management program was devised and implemented in 2007-2008. It led to a better understanding of project risks, a sounder basis for contingency estimates, and improved management tools. Although the risks were ultimately unacceptable to the sponsor, valuable lessons in risk management were learned through the experiences with the NCSX project.

Engineering Accomplishments in the Construction of NCSX

The National Compact Stellarator Experiment (NCSX) was designed to test a compact, quasi-axisymmetric stellarator configuration. Flexibility and accurate realization of its complex 3D geometry were key requirements affecting the design and construction. While the project was terminated before completing construction, there were significant engineering accomplishments in design, fabrication, and assembly. The design of the stellarator core device was completed. All of the modular coils, toroidal field coils, and vacuum vessel sectors were fabricated. Critical assembly steps were demonstrated. Engineering advances were made in the application of CAD modeling, structural analysis, and accurate fabrication of complex-shaped components and sub-assemblies. The engineering accomplishments of the project are summarized.

Status of the NCSX construction

The National Compact Stellarator Experiment (NCSX) has been under construction at the Princeton Plasma Physics Laboratory (PPPL) in partnership with the Oak Ridge National Laboratory (ORNL). The stellarator core is designed to produce a compact 3D plasma that combines stellarator and tokamak physics advantages. The complex geometry and tight fabrication tolerances of NCSX create some unique engineering and assembly challenges. The NCSX project was cancelled in May 2008; construction activities are presently being phased out in an orderly fashion. This paper will describe the progress of the fabrication and assembly activities of NCSX. Completion of the coil fabrication is on track for the summer of 2008. All three of the vacuum vessel 120° sections have been delivered. Assembly of vacuum vessel services began in May 2006 and is now complete. Assembly of the modular coils into 3-packs for safe storage is presently underway.

Stellarator pro and con

The cancellation of the National Compact Stellarator Experiment ( Physics Today July 2008, page 25 ) leaves a hole in the US and world fusion programs that are focused on ITER. Two physics points define the importance of the hole that NCSX filled. First, the shape of the plasma is the primary design freedom of magnetically confined fusion plasmas. The other determinants of plasma equilibria, which are the pressure and current profiles, are largely self-determined. Second, the excellent confinement of tokamaks, such as ITER, does not require axisymmetry. Only quasi-axisymmetry is required, which greatly increases the freedom of plasma shaping.In quasi-symmetry the magnetic field lines lie on nested toroidal surfaces, and the magnetic field strength on those surfaces has a symmetry—even when the shape of the surfaces does not. Particle trajectories are determined by the magnetic field strength, independent of the shape of the magnetic surfaces, and quasi-symmetry ensures the preservation of the constant of the motion that gives good confinement in axisymmetry. The deviation from axisymmetry can have any magnitude as long as it is constrained by quasi-axisymmetry. Axisymmetric shaping—aspect ratio, ellipticity, triangularity, and squareness—is considered essential to achieving the ITER mission, but most of the shaping freedom of toroidal plasmas requires the breaking of axisymmetry.The NCSX stellarator was the only experiment in the world designed to study quasi-axisymmetric shaping other than in the axisymmetric limit. Although the project is canceled, its costs do establish a required financial scale. The highest cost estimates for NCSX construction and research were about 15% of the annual US non-ITER construction budget for fusion, or about 1% of the envisioned world ITER budget. Expertise on quasi-axisymmetric shaping would give the US unique capabilities in exploiting the information from ITER to make fusion a reality, if that expertise were developed by the time the ITER information becomes available.As the primary design freedom, quasi-axisymmetric shaping is clearly important. It is the only type of non-axisymmetric shaping that can be applied to ITER-like plasmas when the fusion program moves to the design of a demonstration power plant. Non-axisymmetric shaping provides the only known solutions to a number of issues that must be addressed before magnetic fusion energy can be a reality. 1 1. For a discussion of issues facing magnetic fusion, see Priorities, Gaps, and Opportunities: Towards a Long-Range Strategic Plan for Magnetic Fusion Energy, Fusion Energy Sciences Advisory Committee, US Department of Energy, Washington, DC (2007); available at http://www.ofes.fusion.doe.gov/FESAC/Oct-2007/FESAC_Planning_Report.pdf. Management problems led to the cancellation of NCSX. Such problems cannot be allowed to undermine the fundamental strategic objectives of US fusion research: to develop the knowledge base for fusion energy, to have a world-leading fusion program, and to ensure the success of the ITER mission.REFERENCESection:ChooseTop of pageREFERENCE <<1. For a discussion of issues facing magnetic fusion, see Priorities, Gaps, and Opportunities: Towards a Long-Range Strategic Plan for Magnetic Fusion Energy, Fusion Energy Sciences Advisory Committee, US Department of Energy, Washington, DC (2007); available at http://www.ofes.fusion.doe.gov/FESAC/Oct-2007/FESAC_Planning_Report.pdf. Google Scholar© 2008 American Institute of Physics.

Stellarator pro and con

The recent cancellation of the National Compact Stellarator Experiment (NCSX; Physics Today, July 2008, page 25 ) calls to mind the fact that exactly 40 years ago the amazing Russian T-3 tokamak results burst upon the world and blindsided the US stellarator program. The ensuing shutdown of stellarator work at the Princeton Plasma Physics Laboratory and the rapid adoption of tokamaks at PPPL and other US laboratories were arguably the most important episodes in the US magnetic fusion program.Successively more powerful tokamaks with ever more impressive performance came on line. Nevertheless, new stellarator projects were eventually funded by the US Department of Energy (DOE) at fusion labs in Tennessee, Wisconsin, and elsewhere, with at best lackluster results and usually far worse. As suggested by your article, stellarators are more complicated magnetic confinement devices than tokamaks, and thereby have always appealed to theoreticians who possess complicated minds and access to supercomputers, but nature is indifferent to both.Having learned nothing from decades of tokamak progress and continued stellarator debacles, in the mid-1990s the directorate at PPPL and its counterpart at DOE reversed the 1968–69 revolution: They decided to shut down the flagship US tokamak fusion test reactor and replace it with a stellarator of unimaginable complexity, the recently aborted NCSX. Those foolish decisions have served only to expedite the ongoing demise of the US magnetic fusion program. Now, with the well-deserved termination of the NCSX project, perhaps limited resources can be refocused on the tokamak family as the only proven approach to magnetic fusion energy.© 2008 American Institute of Physics.

Neoclassical Viscosities in NCSX and QPS with Few Toroidal Periods and Low Aspect Ratios

Previously reported benchmarking examples of the analytical formulae of neoclassical viscosities were presented implicitly assuming applications in a future integrated simulation system of the Large Helical Device (LHD). Therefore, the assumed toroidal period numbers were mainly N = 10. However, in this type of calculation, an implicit (or sometimes explicit) assumption of ι/N « 1 is sometimes included. This assumption is included not only in simplified bounce-averaged drift kinetic equations for ripple diffusions, but also in the equation before the averaging for non-bounce-averaged effects determining neoclassical parallel viscosity and banana-plateau diffusions. For clarifying the applicability of the analytical methods for configurations with extremely low toroidal period numbers (required for low aspect ratios), we show recent benchmarking examples in the National Compact Stellarator Experiment (NCSX) with N = 3 and the Quasi-Poloidal Stellarator (QPS) with N = 2.