Geometric concepts for stellarator permanent magnet arrays

Abstract

The development of stellarators that use permanent magnet arrays to shape their confining magnetic fields has been a topic of recent interest, but the requirements for how such magnets must be shaped, manufactured, and assembled remain to be determined. To address these open questions, we have performed a study of geometric concepts for magnet arrays with the aid of the newly developed Magpie code. A proposed experiment similar to the National Compact Stellarator Experiment (NCSX) is used as a test case. Two classes of magnet geometry are explored: curved bricks that conform to a regular grid in cylindrical coordinates, and hexahedra that conform to the toroidal plasma geometry. In addition, we test constraints on the magnet polarization. While magnet configurations constrained to be polarized normally to a toroidal surface around the plasma are unable to meet the required magnetic field parameters when subject to physical limitations on the strength of present-day magnets, configurations with unconstrained polarizations are shown to satisfy the physics requirements for a targeted plasma.

Calculation of permanent magnet arrangements for stellarators: A linear least-squares method

“…The calculation was also repeated taking the initial d to have a random variation in θ and ζ within [0, 0.1] m. As shown in figure 9, differences between these differently-initialized calculations converged steadily towards zero as the iterations proceeded. This behavior is in contrast to the formulations in [14,13] in which dependence on the initial condition was observed. The independence of REGCOIL PM results from the initial condition is advantageous, since a user need not worry about how best to select the initial condition.…”

“…We will consider two possible arrangements of dipoles, shown in figure 10: first, dipoles of uniform magnitude but arbitrary direction, as in a REGCOIL PM solution; and second, dipoles oriented normal to the outer surface but with arbitrary magnitude. This second case is considered because dipoles oriented normal to a surface have been considered in recent papers [12,13]. We will show the magnetization magnitude in the first approach is half of the maximum magnetization in the second.…”

“…We therefore now show how regions of the permanent magnets can be removed for ports. The feasibility of including ports in the 0.5 T NCSX configuration was examined previously in [14,12,13].…”

“…Numerical solution of nonlinear optimization problems can be fragile due to the existence of multiple local minima, with the possibility of the solver stopping in a local minimum that is not the global optimum, resulting in sensitivity to the initial condition. Indeed, dependence of the solution on the initial guess was noted in [14,13]. Here instead we do not formulate the design problem as a nonlinear optimization problem.…”

Design of an arrangement of cubic magnets for a quasi-axisymmetric stellarator experiment

“…Design of the magnet layout was facilitated by the MAGPIE code [23], which was upgraded to accommodate the present concept with cubic magnets. The code can position magnets around any smooth toroidal surface, so the layout scheme can be easily generalized to any stellarator with a plasma-conforming containment vessel.…”