Effects of shear on the magnetic footprint and stochastic layer in double-null divertor tokamak

We have developed a new area-preserving map, called the Adjustable Shear Map, to calculate effects of shear on the magnetic footprint and stochastic layer in double-null divertor tokamak. The map is given by equations$x_{n+1} =x_n -ky_n [(1-y_n^2 )(1+sy_n )+sx_{n+1}^2 ),y_{n+1} =y_n +kx_{n+1} [1+s(x_{n+1}^2 +y_n^2 )]$. k is the map parameter and s is the shear parameter. O-point of the map is (0, 0), and the X-points are (0, 1), and (0, -1). For s=0, k=0.6, the last good surface is y=0.9918 with q $\sim $3. Here we will report on the effects of shear on the stochastic layer and magnetic footprint as the shear parameter is varied from 0 to -1. Here we will report the preliminary results on the effect of shear on the magnetic foot print and the stochastic layer where the shear parameter $s$ has values between -1 and 0. using method of maps [1-4]. This work is done under the DOE grant number DE-FG02-01ER54624. 1. A. Punjabi, A. Boozer, and A. Verma, \textit{Phys}. \textit{Rev. lett.}, \textbf{69}, 3322 (1992). 2. H. Ali, A. Punjabi, and A. Boozer, \textit{Phys. Plasmas }\textbf{11}, 4527 (2004). 3. A. Punjabi, H. Ali, and A. Boozer, \textit{Phys. Plasmas} \textbf{10}, 3992 (2003). 4. A. Punjabi, H. Ali, and A. Boozer, \textit{Phys. Plasmas} \textbf{4}, 337 (1997).