Strong "quantum" chaos in the global ballooning mode spectrum of three-dimensional plasmas

The spectrum of ideal magnetohydrodynamic (MHD) pressure-driven (ballooning) modes in strongly nonaxisymmetric toroidal systems is difficult to analyze numerically owing to the singular nature of ideal MHD caused by lack of an inherent scale length. In this paper, ideal MHD is regularized by using a $k$-space cutoff, making the ray tracing for the WKB ballooning formalism a chaotic Hamiltonian billiard problem. The minimum width of the toroidal Fourier spectrum needed for resolving toroidally localized ballooning modes with a global eigenvalue code is estimated from the Weyl formula. This phase-space-volume estimation method is applied to two stellarator cases.Comment: 4 pages typeset, including 2 figures. Paper accepted for publication in Phys. Rev. Letter

Medical Malpractice: A New Treatment for an Old Illness

The rising cost of medical malpractice insurance has been one of the most difficult issues faced by the Florida Legislature for many years. In an effort to reach a comprehensive solution to this recurring problems, the 1986 Legislature created the Academic Task Force for the Review of the Insurance and Tort Systems, and directed it to conduct a thorough review of Florida\u27s tort system. In 1988, the Legislature implemented several of the recommendations of the Task Force. In this Article, the authors explore the factual findings and the recommendations of the Task Force and analyze the effects that the 1988 legislation will have on the continuing medical malpractice saga

Plasmoid solutions of the Hahm--Kulsrud--Taylor equilibrium model

The Hahm--Kulsrud (HK) [T. S. Hahm and R. M. Kulsrud, Phys. Fluids {\bf 28}, 2412 (1985)] solutions for a magnetically sheared plasma slab driven by a resonant periodic boundary perturbation illustrate fully shielded (current sheet) and fully reconnected (magnetic island) responses. On the global scale, reconnection involves solving a magnetohydrodynamic (MHD) equilibrium problem. In systems with a continuous symmetry such MHD equilibria are typically found by solving the Grad--Shafranov equation, and in slab geometry the elliptic operator in this equation is the 2-D Laplacian. Thus, assuming appropriate pressure and poloidal current profiles, a conformal mapping method can be used to transform one solution into another with different boundary conditions, giving a continuous sequence of solutions in the form of partially reconnected magnetic islands (plasmoids) separated by Syrovatsky current sheets. The two HK solutions appear as special cases.This research has been supported by the Australian Research Council and the U.S. National Science Foundation and Department of Energy. The plots were made using Mathematica 9

Turbulent edge structure formation in complex configurations

Formation of nonlinear structures in drift-Alfvén turbulence is investigated in the often complex edge geometries of stellarator and tokamak configurations, by analysis of drift waveturbulence simulations using a model in which three-dimensional magnetic geometries are approximated. The structures of parallel mode extension, radially sheared zonal flows and perpendicular mode spectra are highlighted in particular for three-dimensional stellaratormagnetic fields and shaped tokamaks. Specific characteristics of advanced stellarators in comparison to (lower aspect ratio) circular tokamaks are a less pronounced ballooning structure of the modes, a strong influence of local magnetic shear on amplitude structure and average, and stronger level of zonal flows due to lower geodesic curvature.This work was partly funded by grants within the ‘‘Australian-German Joint Research Co-operation scheme’’ ~PPP project no. D/0205403!

Nonequilibrium statistical mechanics of shear flow: invariant quantities and current relations

In modeling nonequilibrium systems one usually starts with a definition of the microscopic dynamics, e.g., in terms of transition rates, and then derives the resulting macroscopic behavior. We address the inverse question for a class of steady state systems, namely complex fluids under continuous shear flow: how does an externally imposed shear current affect the microscopic dynamics of the fluid? The answer can be formulated in the form of invariant quantities, exact relations for the transition rates in the nonequilibrium steady state, as discussed in a recent letter [A. Baule and R. M. L. Evans, Phys. Rev. Lett. 101, 240601 (2008)]. Here, we present a more pedagogical account of the invariant quantities and the theory underlying them, known as the nonequilibrium counterpart to detailed balance (NCDB). Furthermore, we investigate the relationship between the transition rates and the shear current in the steady state. We show that a fluctuation relation of the Gallavotti-Cohen type holds for systems satisfying NCDB.Comment: 24 pages, 11 figure

Electronic Correlations in Oligo-acene and -thiophene Organic Molecular Crystals

From first principles calculations we determine the Coulomb interaction between two holes on oligo-acene and -thiophene molecules in a crystal, as a function of the oligomer length. The relaxation of the molecular geometry in the presence of holes is found to be small. In contrast, the electronic polarization of the molecules that surround the charged oligomer, reduces the bare Coulomb repulsion between the holes by approximately a factor of two. In all cases the effective hole-hole repulsion is much larger than the calculated valence bandwidth, which implies that at high doping levels the properties of these organic semiconductors are determined by electron-electron correlations.Comment: 5 pages, 3 figure

Anderson localization of ballooning modes, quantum chaos and the stability of compact quasiaxially symmetric stellarators

The radially local magnetohydrodynamic(MHD) ballooning stability of a compact, quasiaxially symmetric stellarator (QAS), is examined just above the ballooning beta limit with a method that can lead to estimates of global stability. Here MHDstability is analyzed through the calculation and examination of the ballooning modeeigenvalue isosurfaces in the 3-space (s,α,θk); s is the edge normalized toroidal flux, α is the field linevariable, and θk is the perpendicular wave vector or ballooning parameter. Broken symmetry, i.e., deviations from axisymmetry, in the stellarator magnetic field geometry causes localization of the ballooning mode eigenfunction, and gives rise to new types of nonsymmetric eigenvalue isosurfaces in both the stable and unstable spectrum. For eigenvalues far above the marginal point, isosurfaces are topologically spherical, indicative of strong “quantum chaos.” The complexity of QAS marginal isosurfaces suggests that finite Larmor radius stabilization estimates will be difficult and that fully three-dimensional, high-nMHD computations are required to predict the beta limit.Research supported by U.S. DOE Contract No. DEAC02-76CH0373. John Canik held a U.S. DOE National Undergraduate Fellowship at Princeton Plasma Physics Laboratory, during the summer of 2000