Exact and appoximate geometric calculations for toroidal D-shaped plasmas: Application to Ignitor-Ult

摘要

For a tiroidal D-shaped plasma, this paper presents exact formulas to calculate geometrical quantities of interest to plasma physicists and engineers. Each quantity (plasma cross section, volume, circumference and surface, including outboard and inboard fractions) can be expressed in the form Q=Q(sub circ)F(sub Q), where Q is the quantity pertaining to the D-shaped plasma (characterized by major radius R(sub 0), minor radii a, b and triangularity (tau)); Q(sub circ) is the corresponding quantity for the circular plasma of parameteres R(sub 0), a; and F(sub Q) is an adimensional factor (only containing simple integrals) which depends on (tau), on the elongation (kappa)=b/a and on the aspect ratio A=R(sub 0)/a. Besides giving exact formulas, it is proposed two approximating procedures, one graphical and one numerical. Within their validity limits (0<=(tau)<=1, 1.4<=(kappa)<=2.6 and any A) the approximating formulas - only derived for plasma cross section, volume, circumference and surface - allow a quick determination of the quantities Q with an accuracy better than 1%. As an example, it is presented the results of calculations performed by exact formulas and by approximating procedures for the triangular plasma of the Ignitor-Ult tokamak.