Geometrical Properties of a "Snow-Flake" Divertor

Using a simple set of poloidal field coils, one can reach the situation where the null of the poloidal magnetic field in the divertor region is of a second order, not of the first order as in the usual X-point divertor. Then, the separatrix in the vicinity of the null-point splits the poloidal plane not into four sectors, but into six sectors, making the whole structure looking like a snow-flake (whence a name, [1]). This arrangement allows one to spread the heat load over much broader area than in the case of a standard divertor. A disadvantage of this configuration is in that it is topologically unstable, and, with the current in the plasma varying with time, it would switch either to the standard X-point mode, or to the mode with two X-points close to each other. To avoid this problem, it is suggested to have a current in the divertor coils by roughly 5% higher than in an 'optimum' regime (the one where a snow-flake separatrix is formed). In this mode, the configuration becomes stable and can be controlled by varying the current in the divertor coils in concert with the plasma current; on the other hand, a strong flaring of the scrape-off layer still remains in force. Geometrical properties of this configurations are analyzed for a simple model. Potential advantages and disadvantages of this scheme are discussed