Eigenvalues associated with relaxed states of toroidal plasmas

Abstract

Characteristics of the toroidal relaxed state of reversed field pinches and comparison with experimental results Phys.

Constrained Resonance in Magnetic Self-Organization

“…In contrast to the conventional belief [19] that only the smallest of k c 1 and the eigenvalues of flux-free CK modes is of practical importance, we find that the new resonance at k c 1 , which is substantially up-shifted from k 1 , is the cause for meaningful flux amplification in a ST. It also governs the k dependence of flux amplification factor.…”

“…(3) and (4) when t is set to zero. Contrary to an earlier claim [19], these are not additional flux-free CK modes that are defined by r r A i k i r A i with A i j @ 0, but a set of Yoshida-Giga modes that are formed by linear combinations of flux-carrying CK modes whose net toroidal flux are canceled by the vacuum field from the wall current of the flux conserver [18]. This subtlety is demonstrated in Fig.…”

“…B. Taylor for bringing to our attention Refs. [10,19] and the U.S. Department of Energy for support under Contract No. W-7405-ENG-36.…”

Numerical computation of the helical Chandrasekhar–Kendall modes

“…Certainly the standard separation of variable analysis in such a torus does not yield an eigenmode. This was what motivated numerical computation that takes into account the collective roles of many force-free expansion bases [21,26,22].…”

“…(3) everywhere except for the boundary condition are available as analytic functions. The w is then expanded in these functional bases and the eigenvalues are found by imposing the boundary condition [21,22], which involves only the boundary nodes since the equation is automatically satisfied in the interior by the choice of the expansion bases. Having a simple boundary, for example, rectangular cross section, appears to be the key for the utility of this approach, as indicated by the semianalytic calculations to date (e.g.…”