Persistent Currents and Edge States in a Quasi-One-Dimensional Mesoscopic Ring with a Screened Interaction

The effect ofthe edge state on the persistent current in quasi-1D mesoscopic rings with a screened interactionwhich exists only between nearest-neighboring particles is studied with the Hartree-Fock approximation. The theoreticalvalue of the current magnitude is greatly enhanced by both the edge state and the Coulomb interaction, and pinningthe electrons into a lattice is good for the enhancement if screening happens. In high dimensional systems the screeningeffect can make the interacting range show anisotropy, and create a tendency of gathering for particles with a repulsivepotential.     

Correlation between radon exhalation and radium content in granite samples used as construction material in Saudi Arabia

Measurements of radon exhalation for a total of 205 selected samples of construction materials used in Saudi Arabia were carried out using an active radon gas analyzer with an emanation container. It was found that granite samples were the main source of radon exhalation. The radon exhalation rates per unit area from these granite samples varied from below the minimum detection limit up to with an average of 1.5 . The radium contents of 27 granite samples were measured using an HPGe-based γ spectroscopy setup. The ²²⁶Ra content of the granites varied from below the minimum detection limit up to , with an average of . The linear correlation coefficient between exhaled radon and radium content was found to be 0.90.     

Modelling of DC Electric Fields Induced by RF Sheath in Front of ICRF Antenna

Reducing the ICRH (ion cyclotron range frequency) antenna-plasma interaction is one of the key points for reaching very long tokamak discharges. One problem which limits such discharges, is the appearance of hot spots on the surface of the antenna: Radio Frequency (RF) sheaths modify the properties of the edge plasma by rectifying the RF potential along open magnetic field lines and can induce hot spots. This paper investigates the corrections to sheath potentials introduced by the interactions between adjacent flux tubes. Our theoretical study started from an oscillating double Langmuir probe model, in which a transverse influx of current was included. This model was confronted with 1D PIC simulations along a magnetic field line, and demonstrated that current exchanges can decrease mean potentials. A 2D electrostatic fluid code was then developed, which couples adjacent flux tubes in a poloidal cross section with collisional conductivity or polarization currents. It showed that transverse currents are able to smooth structures smaller than a characteristic size in the sheath potential maps (results for Tore Supra). These computed rectified potentials can be used to obtain the DC electric fields in front of the antenna. And then, it gives an estimate of the particle drift and the energy flux on the antenna structure, which can explain hot spots.     

The Topoligical Sphere Theorem for Complete Submanifolds

A topological sphere theorem is obtained from the point of view of submanifold geometry. An important scalar is defined by the mean curvature and the squared norm of the second fundamental form of an oriented complete submanifold Mn in a space form of nonnegative sectional curvature. If the infimum of this scalar is negative, we then prove that the Ricci curvature of Mn has a positive lower bound. Making use of the Lawson–Simons formula for the nonexistence of stable k-currents, we eliminate Hk (Mn, Z) for all 1 ` k ` n – 1.We then observe that the fundamental group of Mn is trivial. It should be emphasized that our result is optimal.     

Residues in toric varieties

We study residues on a complete toric variety X, which are defined in terms of the homogeneous coordinate ring of X.We first prove a global transformation law for toric residues. When the fan of the toric variety has a simplicial cone of maximal dimension, we can produce an element with toric residue equal to 1. We also show that in certain situations, the toric residue is an isomorphism on an appropriate graded piece of the quotient ring. When X is simplicial, we prove that the toric residue is a sum of local residues. In the case of equal degrees, we also show how to represent X as a quotient (Y\{0})/C* such that the toric residue becomes the local residue at 0 in Y.     

A novel high-resolution interference spectrometer

A novel precision wavemeter is presented with a resolution of better than 0·01 nm. A Sagnac interferometer with two diffraction gratings forms the basis of the instrument. Using spatial heterodyning techniques and a CCD camera/frame grabber data acquisition system allows fast computer control and power spectrum analysis. The mode structure and mode hopping characteristics of a typical laser diode were examined as a function of diode injection current.     

Non-Contact Eddy Current Excitation Method for Vibration Testing

When a conductive material is subjected to a time changing magnetic field, eddy currents are induced in that structure. The eddy currents circulate inside the conductor resulting in a magnetic field that interacts with the applied field. The eddy current field is such that it opposes the change in flux resulting in a force between the source and conductor. The time changing magnetic field necessary to induce an electrometric force in the materials can be generated through a variety of different ways. In the present study, a permanent magnet will be mounted to the tip of an electromagnetic shaker such that the motion of the magnet relative to the structure will cause a time changing field and the formation of eddy currents. The actuator will be demonstrated to be beneficial due to its ability to apply actuation forces without contacting the structure. This study will show that the non-contact nature of the system eliminates mass loading and added stiffness which are downfalls of traditional excitation techniques. Additionally, it will be shown that the use of a non-contact device preserves the mode shapes of the structure, whereas a stinger results in distortions due to the added constraint. Using this concept, a model of the actuation system will be developed, allowing the beams response to be simulated. The actuation system will then be used to excite a cantilever beam to obtain the modal parameters without contacting the structure. The novel non-contact actuation system developed in this paper provides a new method performing vibration testing of on lightweight or flexible structures while preserving their dynamics.     

Spectral line shapes modeling in turbulent plasmas

In this work we investigate the influence of low frequency turbulence on Doppler spectral line shapes in magnetized plasmas. Low frequency refers here to fluctuations whose typical time scale is much larger than those characterizing the atomic processes, such as radiative decay, collisions and charge exchange. This ordering is in particular relevant for drift wave turbulence, ubiquitous in edge plasmas of fusion devices. Turbulent fluctuations are found to affect line shapes through both the spatial and time averages introduced by the measurement process. The profile is expressed in terms of the fluid fields describing the plasma. Assuming the spectrometer acquisition time to be much larger than the turbulent time scale, an ordering generally fulfilled in experiments, allows to develop a statistical formalism. We proceed by successively investigating the effects of density, fluid velocity and temperature fluctuations on the Doppler profile of a spectral line emitted by a charge exchange population of neutrals. Line shapes, and especially line wings are found to be affected by ion temperature or fluid velocity fluctuations, and can in some cases exhibit a power-law behavior. These effects are shown to be measurable with existing techniques, and their interpretation in each particular case would rely on already existing tools. From a fundamental point of view, this study gives some insights in the appearance of non-Boltzmann statistics, such as Lévy statistics, when dealing with averaged experimental data.     

Gyrotron travelling wave amplifier: I. Analysis of oscillations

The operation of the gyrotron travelling wave amplifier is based on the convective cyclotron maser instability. It is found that this convective instability may become absolute (nonconvective) at a sufficiently high current level, resulting in oscillation instead of amplification. This threshold current for the transition depends sensitively on the applied magnetic field. The axial wavelength and the characteristic frequency of oscillation at the onset of absolute instability are given. It is found that momentum spread has virtually no effect on the threshold current. A small amount of resistive wall loss, however, raises the threshold current significantly. Oscillations due to partial reflection at the ends of the system are also examined. Preliminary experimental results on both types of oscillations are reported and are found to be in good agreement with the theory.     

Generalized exterior boundary-value problems and optimization for the Helmholtz equation

A class of radiation problems is considered for the Helmholtz equation in exterior domains bounded by a smooth surface on which Dirichlet, Neumann, or Robin boundary conditions are imposed. The problem of finding the boundary data which maximizes far field power in a restricted subset of far field directions is formulated as a constrained maximization problem. Existence of an optimal solution in a variety of control domains is established. The particular case when the boundary is circular and the control domain is the unit ball inL ² is treated in detail. An algorithm for constructing the optimal solution is derived and used to obtain explicit numerical results.This work was supported by the US Air Force under Grant No. AFOSR 81-0156. The work was completed while the first author was on leave to the Institut für Numerische und Angewandte Mathematik, Universität Göttingen, Göttingen, BRD.