The DESC Stellarator Code Suite Part II: Perturbation and continuation methods

Conlin, Rory; Dudt, Daniel W.; Panici, Dario; Kolemen, Egemen

doi:10.48550/arxiv.2203.15927

Cited by 4 publications

(4 citation statements)

References 24 publications

(31 reference statements)

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“…To confirm the correctness of the near-axis method, each example below is checked using a fixed-boundary MHD equilibrium calculation that does not make a near-axis expansion, as follows. Given the constructed boundary, the field inside is computed and converted to Boozer coordinates with the DESC code (Dudt & Kolemen 2020;Conlin et al 2022;Dudt et al 2022;Panici et al 2022). Similar checks of near-axis solutions were done using the VMEC code (Hirshman & Whitson 1983) previously in , Plunk et al (2019), and .…”

Section: Example Configurationsmentioning

confidence: 99%

Mapping the space of quasisymmetric stellarators using optimized near-axis expansion

Landreman

2022

J. Plasma Phys.

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A method is demonstrated to rapidly calculate the shapes and properties of quasi-axisymmetric and quasi-helically symmetric stellarators. In this approach, optimization is applied to the equations of magnetohydrodynamic equilibrium and quasisymmetry, expanded in the small distance from the magnetic axis, as formulated by Garren & Boozer [Phys. Fluids B, vol. 3, 1991, p. 2805]. Due to the reduction of the equations by the expansion, the computational cost is significantly reduced, to times of the order of 1 cpu second, enabling wide and high-resolution scans over parameter space. In contrast to traditional stellarator optimization, here, the cost function serves to maximize the volume in which the expansion is accurate. A key term in the cost function is $\| \boldsymbol {\nabla }\boldsymbol B \|$ , the norm of the magnetic field gradient, to maximize scale lengths in the field. Using this method, a database of $5\times 10^5$ optimized configurations is calculated and presented. Quasisymmetric configurations are observed to exist in continuous bands, varying in the ratio of the magnetic axis length to average major radius. Several qualitatively new types of configuration are found, including quasi-helically symmetric fields in which the number of field periods is two or more than six.

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Section: Example Configurationsmentioning

confidence: 99%

Mapping the space of quasisymmetric stellarators using optimized near-axis expansion

Landreman

2022

J. Plasma Phys.

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“…Part 2 (Conlin et al 2023) of the three-part series presents a novel perturbation and continuation method used by the DESC code for solving and optimizing stellarator equilibria. The efficiency and utility of the method are shown in the computation of complicated equilibria, highlighting the benefits of automatic differentiation.…”

Section: Introductionmentioning

confidence: 99%

The DESC stellarator code suite. Part 1. Quick and accurate equilibria computations

Panici,

Conlin,

Dudt

et al. 2023

J. Plasma Phys.

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Three-dimensional equilibrium codes are vital for stellarator design and operation, and high-accuracy equilibria are also necessary for stability studies. This paper details comparisons of two three-dimensional equilibrium codes: VMEC, which uses a steepest-descent algorithm to reach a minimum-energy plasma state, and DESC, which minimizes the magnetohydrodynamic (MHD) force error in real space directly. Accuracy as measured by satisfaction of MHD force balance is presented for each code, along with the computation time. It is shown that DESC is able to achieve more accurate solutions, especially near axis. The importance of higher-accuracy equilibria is shown in DESC's better agreement of stability metrics with asymptotic formulae. DESC's global Fourier–Zernike basis also yields solutions with analytic derivatives explicitly everywhere in the plasma volume, provides improved accuracy in the radial direction versus conventional finite differences and allows for exponential convergence. Further, DESC can compute a solution with the same accuracy as VMEC in order-of-magnitude less time.

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“…Part 1 (Panici et al 2022) highlights the advantages of the DESC equilibrium solver through a comparison to VMEC. Part 2 (Conlin et al 2022) presents the novel perturbation and continuation methods available in DESC. This paper, Part 3, explains the theory and practice of how these tools can be combined to solve stellarator optimization problems with DESC.…”

Section: Introductionmentioning

confidence: 99%

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

2023

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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.

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The DESC Stellarator Code Suite Part II: Perturbation and continuation methods

Cited by 4 publications

References 24 publications

Mapping the space of quasisymmetric stellarators using optimized near-axis expansion

Mapping the space of quasisymmetric stellarators using optimized near-axis expansion

The DESC stellarator code suite. Part 1. Quick and accurate equilibria computations

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

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