Stellarator coil design and plasma sensitivity

Abstract

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, (3) choose the ratios of the magnitudes of the 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) that are either smoother or can be located much farther from the plasma boundary than those of the present design.

Stellarator design

“…2007, 2008), figure 2. Boozer and Ku studied the sensitivity of stellarator neoclassical transport (Ku & Boozer 2010 b ; Boozer & Ku 2011), figure 3. In both studies, the plasma sensitivity was found to drop essentially exponentially.…”

“…Park studied the sensitivity of tokamaks to perturbations that drive magnetic islands (Park et al 2007(Park et al , 2008, figure 2. Boozer and Ku studied the sensitivity of stellarator neoclassical transport (Ku & Boozer 2010b;Boozer & Ku 2011), figure 3. In both studies, the plasma sensitivity was found to drop essentially exponentially.…”

Hessian matrix approach for determining error field sensitivity to coil deviations

“…Generally, lower f B implies lower residual normal field on the surface, and a coil set which more accurately reproduces the desired plasma shape. Although it's proven that the plasma doesn't have the same sensitivity to all external magnetic perturbations [18], we can easily modify the evaluation function by replacing f B with a suitably weighted summation as m,n w m,n B n m,n in the future. The first and second derivatives of f B with respect to all the coil parameters in X, namely the gradient g and the Hessian H, can be calculated analytically in FOCUS.…”

Comparison of Options for a Pilot Plant Fusion Nuclear Mission

“…In addition to concept investigations, plasma studies were carried out looking at aspect-ratio scans for improvements on magnet complexity and computational searches to identify attractive quasi-symmetric configurations [25][26].…”