Optimization.html

Stellarator Optimization Theory

The design of modern stellarators involves a numerical optimization process that varies the 3-dimensional plasma shape in order to improve a variety of physics and engineering properties of the plasma. These include:
- plasma transport and confinement (collisional transport, energetic particle transport)

- plasma stability (Mercier, ballooning, kink, neoclassical tearing, vertical displacements)

- keep the plasma current and its profile close to the in-situ current (bootstrap current) that the plasma generates naturally

- acheive a compact (low aspect ratio) design

- consider only plasma shapes that can be generated by feasible coil geometries

- avoid narrow thickness regions in the plasma where neutrals can penetrate and transport energy out through charge exchange reactions

- avoid other pathological plasma shapes (cusp regions, strong elongations, etc.)

Table of typical plasma optimization Targets

Once the optimization targets have been developed, a numerical optimization loop is followed which uses the Levenberg-Marquardt algorithm to converge to the optimized plasma shape that provides the best compromise between the various target functions.

Diagram of the physics optimization process

After an optimized plasma shape has been determined, a set of magnetic coils that produce this shape must be synthesized. This is currently done as a separate optimization loop; however, eventually the coil shape will be varied directly in conjunction with the physics optimization. The coil optimization is based on minimizing the normal component of magnetic field at the plasma surface. This makes the outer surface of the plasma coincide with a magnetic flux surface. In order to obtain coil geometries that are desirable from an engineering standpoint, the following targets are used in the coil optimization:
- Keep the minimum separation between adjacent coils above a certain level

- Keep the minimum separation between coils and plasma above a certain level (necessary for extrapolation to a compact reactor)

- Avoid small radii of curvature in the coil geometry

- Minimize the total length of individual coils

- Minimize extension of the coils into the open space in the center of the torus (i.e., to allow access for Ohmic heating, planar toroidal, and vertical field coils)

Diagram of the coil optimization process