Abstract. Finding an easy-to-build coils set has been a critical issue for stellarator design for decades. Conventional approaches assume a toroidal "winding" surface.We'll investigate if the existence of winding surface unnecessarily constrains the optimization, and a new method to design coils for stellarators is presented. Each discrete coil is represented as an arbitrary, closed, one-dimensional curve embedded in three-dimensional space. A target function to be minimized that covers both physical requirements and engineering constraints is constructed. The derivatives of the target function are calculated analytically. A numerical code, named FOCUS, has been developed. Applications to a simple configuration, the W7-X, and LHD plasmas are presented.

A stellarator is a magnetic field configuration used to confine plasma, and it is a candidate configuration for fusion energy, as well as a general charged particle trap. A stellarator's magnetic field is typically produced using electromagnetic coils, and the shaping of the field and coils must be optimized to achieve good confinement. SIMSOPT is a collection of software components for carrying out these optimizations. These components include

The stepped-pressure equilibrium code (SPEC) [Hudson et al., Phys. Plasmas 19, 112502 (2012)] is extended to enable free-boundary, multi-region relaxed magnetohydrodynamic (MRxMHD) equilibrium calculations. The vacuum field surrounding the plasma inside an arbitrary 'computational boundary', D, is computed, and the virtual-casing principle is used iteratively to compute the normal field on D so that the equilibrium is consistent with an externally produced magnetic field. Recent modifications to SPEC are described, such as the use of Chebyshev polynomials to describe the radial dependence of the magnetic vector potential, and a variety of free-boundary verification calculations are presented.

We have developed a fast method to design perpendicular permanent magnets for simplifying stellarator coils based on existing codes. Coil complexity is one of the main challenges for stellarators. To date, only electromagnetic coils have been used to generate 3D fields for stellarators. Permanent magnets provide an alternative way to produce the desired magnetic field for optimized stellarators. In this paper, we revisit the concept of representing surface current using magnetic dipoles and carry out numerical validations. A surface magnetization is proven to be equivalent to the surface current that can be linearly solved by existing coil design codes. An incremental multi-layer method has been developed to obtain a practical solution that is attainable with present permanent magnets. With this method, we can reproduce a half-Tesla NCSX configuration using specially designed neodymium magnets together with simple planar coils. It shows that stellarator coils could be substantially simplified by adopting permanent magnets.