A gyrokinetic model for the plasma periphery of tokamak devices

A gyrokinetic model is presented that can properly describe strong flows, large and small amplitude electromagnetic fluctuations occurring on scale lengths ranging from the electron Larmor radius to the equilibrium perpendicular pressure gradient scale length, and large deviations from thermal equilibrium. The formulation of the gyrokinetic model is based on a second order description of the single charged particle dynamics, derived from Lie perturbation theory, where the fast particle gyromotion is decoupled from the slow drifts, assuming that the ratio of the ion sound Larmor radius to the perpendicular equilibrium pressure scale length is small. The collective behavior of the plasma is obtained by a gyrokinetic Boltzmann equation that describes the evolution of the gyroaveraged distribution function and includes a non-linear gyrokinetic Dougherty collision operator. The gyrokinetic model is then developed into a set of coupled fluid equations referred to as the gyrokinetic moment hierarchy. To obtain this hierarchy, the gyroaveraged distribution function is expanded onto a velocity-space Hermite-Laguerre polynomial basis and the gyrokinetic equation is projected onto the same basis, obtaining the spatial and temporal evolution of the Hermite-Laguerre expansion coefficients. The Hermite-Laguerre projection is performed accurately at arbitrary perpendicular wavenumber values. Finally, the self-consistent evolution of the electromagnetic fields is described by a set of gyrokinetic Maxwell's equations derived from a variational principle, with the velocity integrals of the gyroaveraged distribution function explicitly evaluated

Shear-thickening and entropy-driven reentrance

We discuss a generic mechanism for shear-thickening analogous to entropy-driven phase reentrance. We implement it in the context of non-relaxational mean-field glassy systems: although very simple, the microscopic models we study present a dynamical phase diagram with second and first order stirring-induced jamming transitions leading to intermittency, metastability and phase coexistence as seen in some experiments. The jammed state is fragile with respect to change in the stirring direction. Our approach provides a direct derivation of a Mode-Coupling theory of shear-thickening.Comment: 4 pages, 4 figures, minor changes, references adde

Current-induced vortex dynamics in Josephson-junction arrays: Imaging experiments and model simulations

We study the dynamics of current-biased Josephson-junction arrays with a magnetic penetration depth smaller than the lattice spacing. We compare the dynamics imaged by low-temperature scanning electron microscopy to the vortex dynamics obtained from model calculations based on the resistively-shunted junction model, in combination with Maxwell's equations. We find three bias current regions with fundamentally different array dynamics. The first region is the subcritical region, i.e. below the array critical current I_c. The second, for currents I above I_c, is a "vortex region", in which the response is determined by the vortex degrees of freedom. In this region, the dynamics is characterized by spatial domains where vortices and antivortices move across the array in opposite directions in adjacent rows and by transverse voltage fluctuations. In the third, for still higher currents, the dynamics is dominated by coherent-phase motion, and the current-voltage characteristics are linear.Comment: 10 pages, with eps figures. To appear in Phys. Rev.

Energetic Particle Tracing in Optimized Quasisymmetric Stellarator Equilibria

Recent developments in the design of magnetic confinement fusion devices have allowed the construction of exceptionally optimized stellarator configurations. The near-axis expansion in particular has proven to enable the construction of magnetic configurations with good confinement properties while taking only a fraction of the usual computation time to generate optimized magnetic equilibria. However, not much is known about the overall features of fast-particle orbits computed in such analytical, yet simplified, equilibria when compared to those originating from accurate equilibrium solutions. This work aims to assess and demonstrate the potential of the near-axis expansion to provide accurate information on particle orbits and to compute loss fractions in moderate to high aspect ratios. The configurations used here are all scaled to fusion-relevant parameters and approximate quasisymmetry in various degrees. This allows us to understand how deviations from quasisymmetry affect particle orbits and what are their effects on the estimation of the loss fraction. Guiding-center trajectories of fusion-born alpha particles are traced using gyronimo and SIMPLE codes under the NEAT framework, showing good numerical agreement. Discrepancies between near-axis and MHD fields have minor effects on passing particles but significant effects on trapped particles, especially in quasihelically symmetric magnetic fields. Effective expressions were found for estimating orbit widths and passing-trapped separatrix in quasisymmetric near-axis fields. Loss fractions agree in the prompt losses regime but diverge afterward.Comment: 24 pages, 15 figure

Lattice knot theory and quantum gravity in the loop representation

We present an implementation of the loop representation of quantum gravity on a square lattice. Instead of starting from a classical lattice theory, quantizing and introducing loops, we proceed backwards, setting up constraints in the lattice loop representation and showing that they have appropriate (singular) continuum limits and algebras. The diffeomorphism constraint reproduces the classical algebra in the continuum and has as solutions lattice analogues of usual knot invariants. We discuss some of the invariants stemming from Chern--Simons theory in the lattice context, including the issue of framing. We also present a regularization of the Hamiltonian constraint. We show that two knot invariants from Chern--Simons theory are annihilated by the Hamiltonian constraint through the use of their skein relations, including intersections. We also discuss the issue of intersections with kinks. This paper is the first step towards setting up the loop representation in a rigorous, computable setting.Comment: 23 pages, RevTeX, 14 figures included with psfi

Fluctuation theorem for stochastic dynamics

The fluctuation theorem of Gallavotti and Cohen holds for finite systems undergoing Langevin dynamics. In such a context all non-trivial ergodic theory issues are by-passed, and the theorem takes a particularly simple form. As a particular case, we obtain a nonlinear fluctuation-dissipation theorem valid for equilibrium systems perturbed by arbitrarily strong fields.Comment: 15 pages, a section rewritte

Comment on "Two Phase Transitions in the Fully frustrated XY Model"

The conclusions of a recent paper by Olsson (Phys. Rev. Lett. 75, 2758 (1995), cond-mat/9506082) about the fully frustrated XY model in two dimensions are questioned. In particular, the evidence presented for having two separate chiral and U(1) phase transitions are critically considered.Comment: One page one table, to Appear in Physical Review Letter

Anisotropic plasma-chemical etching by an electron-beam-generated plasma

Includes bibliographical references (page 2466).Anisotropic etching of SiO2 has been achieved with a plasma generated by a broad-area low-energy (150-300 eV) electron beam in a He + CF4 atmosphere. Etch rates of up to 330 Å/min for SiO2 and 220 Å/min for Si were obtained. Etching occurred with good uniformity over the entire area exposed to the electron-beam-generated plasma. The fluxes of energetic charged particles to the sample surface are discussed in relation to their possible contribution to the etching process

The effect of aluminium granulometry on the behaviour of filled epoxy resins for rapid tooling

Aluminium filled epoxies moulds have beenused in indirect rapid tooling. These moulds, whichhave a low cost processing, are very competitive,when applied in the manufacturing of low volumeseries.The geometry and the size distribution of thealuminium particles affect significantly the powderpacking density, the resin ratio, the thermalconductivity, the curing time, the homogeneity andthe mechanical characteristics of the tool.Using three high temperature epoxy resins itwas possible to understand the resin behaviour inthe presence of the aluminium filler and formulatefilled resins with the best compromise ofmechanical, thermal and processing performance