Control-matrix approach to stellarator design and control

The full space Z={Z(j=1,...,Nz)} of independent variables defining a stella rator configuration is large. To, find attractive design points in this spa ce, or to understand operational flexibility about a given design point, on e needs insight into the topography in Z-space of the physics figures of me rit P-i which characterize the machine performance, and means of determinin g those directions in Z-space which give one independent control over the P -i, as well as those which affect none of them, and so are available for de sign flexibility. The control matrix (CM) approach described here provides a mathematical means of obtaining these. In this work, the CM approach is d escribed and used in studying some candidate Quasi-Axisymmetric (QA) stella rator configurations the National Compact Stellarator Experiment design gro up has been considering. In the process of the analysis, a first exploratio n of the topography of the configuration space in the vicinity of these can didate systems has been performed, whose character is discussed. (C) 2000 A merican Institute of Physics. [S1070-664X(00)00912-5].