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 fully integrated paperfluidic molecular diagnostic chip for the extraction, amplification, and detection of nucleic acids from clinical samples

Paper diagnostics have successfully been employed to detect the presence of antigens or small molecules in clinical samples through immunoassays; however, the detection of many disease targets relies on the much higher sensitivity and specificity achieved via nucleic acid amplification tests (NAAT). The steps involved in NAAT have recently begun to be explored in paper matrices, and our group, among others, has reported on paper-based extraction, amplification, and detection of DNA and RNA targets. Here, we integrate these paper-based NAAT steps into a single paperfluidic chip in a modular, foldable system that allows for fully integrated fluidic handling from sample to result. We showcase the functionality of the chip by combining nucleic acid isolation, isothermal amplification, and lateral flow detection of human papillomavirus (HPV) 16 DNA directly from crude cervical specimens in less than 1 hour for rapid, early detection of cervical cancer. The chip is made entirely of paper and adhesive sheets, making it low-cost, portable, and disposable, and offering the potential for a point-of-care molecular diagnostic platform even in remote and resource-limited settings.U54 EB015403 - NIBIB NIH HHS; U54 EB015408 - NIBIB NIH HHS; U54-EB015403-S1 - NIBIB NIH HH

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