Finite element analysis of helically symmetric equilibria

It is well known that Taylor's force-free states, which satisfy the relation VxB=μB, can exist only for discrete values of μ when the mode number m is grater than zero and when the solution to the above equation has the lowest energy, the constant μ also takes the smallest value 3.11 for m=1, h=1.25 (where h is the helical pitch) under the condition that a plasma is enclosed by a straight perfectly conducting shell with a circular cross-section. However, dependence of the minimum-μ states on the shape of a shell still remains unclear. In this report, a finite element analysis of m=1 helically symmetric Taylor's force-free states is presented. In particular, we study the dependence of those states on the shape of perfectly conducting shells enclosing plasmas using the present scheme. (author) 4 refs., 5 figs