Stellarator equilibria and the problem of position control

J. P. Freidberg, P. A. Politzer, Philip Rosenau
1984 The Physics of Fluids  
A class of low-# stellarator MHD equilibria with -(a/Ro) 2 is introduced and the corresponding toroidal shift is calculated. It is shown that an apparent paradox exists with regard to the problem of position control in that a vertical field is capable of shifting vacuum flux surfaces, but produces no net body force on a current free stellarator. This paradox is resolved by an analysis of the transient response of the plasma and demonstrates how the vertical field can be used as a means of
more » ... on control. *This work was supported by the U.S. Department of Energy, Contract f DE AC02-78PT-51013. I 2. The problem of position control is quite different in a stellarator than in a tokamak. In the latter case the vertical field is adjusted to center the last flux surface within the vacuum chamber (or limiter). An incorrect value of vertical field causes the plasma to drift into the wall. In contrast, the outer surfaces of a stellarator are essentially held fixed by the external helical coils. These coils are carefully designed so that the last surface is approximately centered in the vacuum chamber. The problem of position control in a stellarator thus corresponds to that of moving the center of the plasma, a(0), keeping the last surface c(a) fixed. Equations (42) and (43) indicate that for t = 2 a combination of an upper helical sideband and either a vertical field or lower sideband can accomplish this task, although admittedly in an actual experiment this may be difficult to implement. For t > 3 a vertical field is quite effective for position control since the axis shift is much larger than the surface shift. 3. Unlike a tokamak, a centered stellarator, o(a) = 0, does not lead to a unique relationship between the vertical field and the major radius. The reason is associated with the fact that the externally applied helical
doi:10.1063/1.864833 fatcat:fyv2e6kayzesdchmx33ifseuoe