Title: New method to design stellarator coils without the winding surface,
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.