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

Abstract

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 of calculation of the island width is that of Cary & Hanson (1991) (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 in Reiman & Greenside (1986). The method is also applied to the calculation of the shape gradient of the width of a magnetic island in an NCSX vacuum configuration with respect to positions on a coil. A gradient-based optimization is applied to a magnetic field configuration studied in Hanson & Cary (1984) 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 was 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. Moreoever, 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.

arXiv comment41 pages, 8 figures

References in corpus (5)

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• Experimental and numerical study of error fields in the CNT stellarator
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• Adjoint approach to calculating shape gradients for three-dimensional magnetic confinement equilibria. Part II: Applications

Cited by in corpus (5)

• Single-stage gradient-based stellarator coil design: stochastic optimization
• Numerical study of $\delta$-function current sheets arising from resonant magnetic perturbations
• Computing the shape gradient of stellarator coil complexity with respect to the plasma boundary
• Adjoint methods for quasisymmetry of vacuum fields on a surface
• Characterisation of X- and O-points in Wendelstein 7-X with respect to coil currents