Nonaxisymmetric, multi-region relaxed magnetohydrodynamic equilibrium solutions

We describe a magnetohydrodynamic (MHD) constrained energy functional for equilibrium calculations that combines the topological constraints of ideal MHD with elements of Taylor relaxation. Extremizing states allow for partially chaotic magnetic fields and non-trivial pressure profiles supported by a discrete set of ideal interfaces with irrational rotational transforms. Numerical solutions are computed using the Stepped Pressure Equilibrium Code, SPEC, and benchmarks and convergence calculations are presented.Comment: Submitted to Plasma Physics and Controlled Fusion for publication with a cluster of papers associated with workshop: Stability and Nonlinear Dynamics of Plasmas, October 31, 2009 Atlanta, GA on occasion of 65th birthday of R.L. Dewar. V2 is revised for referee

Hamilton--Jacobi theory for continuation of magnetic field across a toroidal surface supporting a plasma pressure discontinuity

The vanishing of the divergence of the total stress tensor (magnetic plus kinetic) in a neighborhood of an equilibrium plasma containing a toroidal surface of discontinuity gives boundary and jump conditions that strongly constrain allowable continuations of the magnetic field across the surface. The boundary conditions allow the magnetic fields on either side of the discontinuity surface to be described by surface magnetic potentials, reducing the continuation problem to that of solving a Hamilton--Jacobi equation. The characteristics of this equation obey Hamiltonian equations of motion, and a necessary condition for the existence of a continued field across a general toroidal surface is that there exist invariant tori in the phase space of this Hamiltonian system. It is argued from the Birkhoff theorem that existence of such an invariant torus is also, in general, sufficient for continuation to be possible. An important corollary is that the rotational transform of the continued field on a surface of discontinuity must, generically, be irrational.Comment: Prepared for submission to Phys. Letts.

A SCF MO Treatment of Some Tropone Derivatives

Recent work in these laboratories has led to the development of a semiempirical SCF MO treatm ent which seems to give extremely good results for ground States of conjugated molecules of ali kinds composed of carbon, hydrogen, nitrogen and oxygen. We have now applied this treatm ent to a problem of current interest, namely the structures of tropolone and tropone deri­ vatives. The calculations lead to the conclusion that neither of these ring systems is in itself aromatic, while tropone is now re- cognized to be polyenoid, tropolone still seems to be generally regarded as aromatic. This belief, however, arose from the behavior of tropolone derivatives in strong acid solution, where they exist as hydroxy tropylium derivatives, or in alkali where they form mesomeric anions. Calculated heats of formation, resonance ener- gies, and bond lengths are reporte