An adjoint method for neoclassical stellarator optimization

Abstract

Stellarators are a promising route to steady-state fusion power. However, to achieve the required confinement, the magnetic geometry must be highly optimized. This optimization requires navigating high-dimensional spaces, often necessitating the use of gradient-based methods. The gradient of the neoclassical fluxes is expensive to compute with classical methods, requiring $O(N)$ flux computations, where $N$ is the number of parameters. To reduce the cost of the gradient computation, we present an adjoint method for computing the derivatives of moments of the neoclassical distribution function for stellarator optimization. The linear adjoint method allows derivatives of quantities which depend on solutions of a linear system, such as moments of the distribution function, to be computed with respect to many parameters from the solution of only two linear systems. This reduces the cost of computing the gradient to the point that the finite-collisionality neoclassical fluxes can be used within an optimization loop. With the neoclassical adjoint method, we compute solutions of the drift kinetic equation and an adjoint drift kinetic equation to obtain derivatives of neoclassical quantities with respect to geometric parameters. When the number of parameters in the derivative is large ($\mathcal{O}(10^2)$), this adjoint method provides up to a factor of 200 reduction in cost. We demonstrate adjoint-based optimization of the field strength to obtain minimal bootstrap current on a surface. With adjoint-based derivatives, we also compute the local sensitivity to magnetic perturbations on a flux surface and identify regions where tight tolerances on error fields are required for control of the bootstrap current or radial transport. Furthermore, the solve for the ambipolar electric field is accelerated using a Newton method with derivatives obtained from the adjoint method.

References in corpus (12)

• Multiscale Gyrokinetics for Rotating Tokamak Plasmas: Fluctuations, Transport and Energy Flows
• Comparison of particle trajectories and collision operators for collisional transport in nonaxisymmetric plasmas
• Direct multiscale coupling of a transport code to gyrokinetic turbulence codes
• Properties of a new quasi-axisymmetric configuration
• Direct construction of optimized stellarator shapes. I. Theory in cylindrical coordinates
• An adjoint method for gradient-based optimization of stellarator coil shapes
• Generalized universal instability: Transient linear amplification and subcritical turbulence
• Electrostatic potential variations on stellarator magnetic surfaces in low collisionality regimes
• Optimisation of confinement in a fusion reactor using a nonlinear turbulence model
• Rotation and Neoclassical Ripple Transport in ITER
• Stellarator bootstrap current and plasma flow velocity at low collisionality
• Adjoint approach to calculating shape gradients for 3D magnetic confinement equilibria

Cited by in corpus (4)

• Combined plasma-coil optimization algorithms
• Optimized finite-build stellarator coils using automatic differentiation
• An adjoint method for determining the sensitivity of island size to magnetic field variations
• Adjoint methods for quasisymmetry of vacuum fields on a surface