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

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

Eigenvalue problems for Beltrami fields arising in a three-dimensional toroidal magnetohydrodynamic equilibrium problem

A generalized energy principle for finite-pressure, toroidalmagnetohydrodynamic(MHD) equilibria in general three-dimensional configurations is proposed. The full set of ideal-MHD constraints is applied only on a discrete set of toroidal magnetic surfaces (invariant tori), which act as barriers against leakage of magnetic flux, helicity, and pressure through chaotic field-line transport. It is argued that a necessary condition for such invariant tori to exist is that they have fixed, irrational rotational transforms. In the toroidal domains bounded by these surfaces, full Taylor relaxation is assumed, thus leading to Beltrami fields ∇×B=λB, where λ is constant within each domain. Two distinct eigenvalue problems for λ arise in this formulation, depending on whether fluxes and helicity are fixed, or boundary rotational transforms. These are studied in cylindrical geometry and in a three-dimensional toroidal region of annular cross section. In the latter case, an application of a residue criterion is used to determine the threshold for connected chaos.This work was supported in part by the U.S. Department of Energy Contract No. DE-AC02-76CH03073 and Grant No. DE-FG02-99ER54546 and the Australian Research Council