Effect of elongation in divertor tokamaks

Method of maps developed by Punjabi and Boozer [A. Punjabi, A. Verma, and A. Boozer, Phys.Rev. Lett. \textbf{69}, 3322 (1992)] is used to calculate the effects of elongation on stochastic layer and magnetic footprint in divertor tokamaks. The parameters in the map are chosen such that the poloidal magnetic flux $\chi _{SEP}$ inside the ideal separatrix, the amplitude $\delta $ of magnetic perturbation, and the height $H$ of the ideal separatrix surface are held fixed. The safety factor $q$ for the flux surfaces that are nonchaotic as a function of normalized distance $d$ from the O-point to the X-point is also held approximately constant. Under these conditions, the width $W$ of the ideal separatrix surface in the midplane through the O-point is varied. The relative width $w$ of stochastic layer near the X-point and the area $A$ of magnetic footprint are then calculated. We find that the normalized width $w$ of stochastic layer scales as $W^{-7}$, and the area $A$ of magnetic footprint on collector plate scales as $W^{-10}$.