Analytic Solutions of Del X B = alpha B in a Straight Cylinder with alpha = alpha (R)

摘要

Analytic solutions of del x B = alpha B are presented for reversed field pinch (RFP) configurations in a straight cylinder with alpha = alpha (r) where r is the radial coordinate. The function alpha (r) is a smooth function of r vanishing at the wall (r = a). Closed form parametric formulas for a family of F-THETA curves are obtained from the analytic, cylindrically symmetric, force-free fields. These formulas can be used to fit experimental F-THETA curves and hence facilitate comparison between the various existing RFP experiments. The advantage of these formulas lies in the fact that they are expressed in terms of easily obtainable Bessel functions of the first kind, eliminating the need of mumerical integration. Results of the least-square fits of two typical ZT-40M shots are presented. (ERA citation 10:053014)