New classes of quasi-helically symmetric stellarators

Quasisymmetric stellarators are appealing intellectually and as fusion reactor candidates since the guiding center particle trajectories and neoclassical transport are isomorphic to those in a tokamak, implying good confinement. Previously, quasisymmetric magnetic fields have been identified by applying black-box optimization algorithms to minimize symmetry-breaking Fourier modes of the field strength B. Here instead we directly construct magnetic fields in cylindrical coordinates that are quasisymmetric to leading order in distance from the magnetic axis, without using optimization. The method involves solution of a 1-dimensional nonlinear ordinary differential equation, originally derived by Garren and Boozer [Phys. Fluids B 3, 2805 (1991)]. We demonstrate the usefulness and accuracy of this optimization-free approach by providing the results of this construction as input to the codes VMEC and BOOZ_XFORM, confirming the purity and scaling of the magnetic spectrum. The space of magnetic fields that are quasisymmetric to this order is parameterized by the magnetic axis shape along with three other real numbers, one of which reflects the on-axis toroidal current density, and another one of which is zero for stellarator symmetry. The method here could be used to generate good initial conditions for conventional optimization, and its speed enables exhaustive searches of parameter space. †

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“…1995; Garabedian 1996; Zarnstorff et al. 2001; Ku & Boozer 2011; Drevlak et al. 2013, 2018; Henneberg et al.…”

Section: Introductionmentioning

confidence: 99%

Direct construction of optimized stellarator shapes. Part 2. Numerical quasisymmetric solutions

2019

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“…The coil filament shapes can be obtained from the contours of the current potential. Because it is guaranteed to find a global minimum, NESCOIL is often used in the preliminary stages of the design process [5][6][7]. It was used for the initial coil configuration studies for NCSX [8].…”

Section: Introductionmentioning

confidence: 99%

An adjoint method for gradient-based optimization of stellarator coil shapes

et al. 2018

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We present a method for stellarator coil design via gradient-based optimization of the coil-winding surface. The REGCOIL (Landreman 2017 Nucl. Fusion 57 046003) approach is used to obtain the coil shapes on the winding surface using a continuous current potential. We apply the adjoint method to calculate derivatives of the objective function, allowing for efficient computation of analytic gradients while eliminating the numerical noise of approximate derivatives. We are able to improve engineering properties of the coils by targeting the root-mean-squared current density in the objective function. We obtain winding surfaces for W7-X and HSX which simultaneously decrease the normal magnetic field on the plasma surface and increase the surface-averaged distance between the coils and the plasma in comparison with the actual winding surfaces. The coils computed on the optimized surfaces feature a smaller toroidal extent and curvature and increased inter-coil spacing. A technique for visualization of the sensitivity of figures of merit to normal surface displacement of the winding surface is presented, with potential applications for understanding engineering tolerances.

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“…9,10 As shown in Fig. 1, the superbanana diffusion coefficient increases strongly with energy E for small minor radius q, but not for large minor radius.…”

Section: Superbanana Diffusionmentioning

confidence: 84%

Effect of superbanana diffusion on fusion reactivity in stellarators

Hinton

2012

Physics of Plasmas

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Fusion reactivity is usually obtained using a Maxwellian distribution. However, energy-dependent radial diffusion can modify the energy distribution. Superbanana diffusion is energy-dependent and occurs in nonaxisymmetric magnetic confinement devices, such as stellarators, because of rippletrapped particles which can take large steps between collisions. In this paper, the D-T fusion reactivity is calculated using a non-Maxwellian energy distribution obtained by solving the Fokker-Planck equation numerically, including radial superbanana diffusion as well as energy scattering. The ions in the tail of the distribution, with energies larger than thermal, which are most needed for fusion, are depleted by superbanana diffusion. In this paper, it is shown that the D-T fusion reactivity is reduced by tail ion depletion due to superbanana diffusion, by roughly a factor of 0.5 for the parameters used in the calculation.

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New classes of quasi-helically symmetric stellarators

Cited by 35 publications

References 23 publications

Direct construction of optimized stellarator shapes. Part 2. Numerical quasisymmetric solutions

Direct construction of optimized stellarator shapes. Part 2. Numerical quasisymmetric solutions

An adjoint method for gradient-based optimization of stellarator coil shapes

Effect of superbanana diffusion on fusion reactivity in stellarators

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