Calibration of the high-frequency magnetic fluctuation diagnostic in plasma devices

The increasing reservoirs of energetic particles which drive high-frequency modes, together with advances in the understanding of magnetohydrodynamics, have led to a need for higher-frequency (50 kHz to >20MHz) measurements of magnetic field fluctuations in magnetic fusion devices such as tokamaks. This article uses transmission line equations to derive the voltage response of a Mirnov coil at the digitizer end of a transmission line of length ℓ. It is shown that, depending on the terminations of the line, resonances can occur even for ℓ/λ⪡1, with λ the wavelength of a fluctuation in the transmission line. A lumped-circuit model based on the approach of Heeter et al. [R. F. Heeter, A. F. Fasoli, S. Ali-Arshad, and J. M. Moret. Rev. Sci. Instrum.71, 4092 (2000)] is extended to enable the inclusion simultaneously of both serial resistance and parallel conductance elements. As originally proposed by Heeter et al. the lumped-circuit model offers the advantage of remote calibration; this may be of particular value when upgrading existing systems to operate at frequencies above the original design specification. It is formally shown that the transmission line equations for the transfer function and measured impedance reduce to those of the lumped circuit model of Heeter et al. under specific conditions. The result extends the use of the lumped-circuit model of Heeter et al., which can be used to extract the transfer function from measurement of the impedance, beyond the case of an open-circuit termination. Although the numerical procedure does exhibit some problems associated with non-uniqueness, it provides a simple calibration method for systems that are not well defined. Using typical parameters for a high-frequency Mirnov coil installed on the Joint European Torus (JET) tokamak, the lumped-circuit approximation agrees with the steady-state transmission line model to within 0.015° in phase and 22% in amplitude for frequencies up to 1 MHz. A matched termination, though eliminating line resonances and reducing the length of time for the system to reach steady state, is inappropriate for the JET-type coils which exhibit significant temperature-dependent resistance. Finally, for fluctuations of finite duration, a method of computing the discrepancy due to the simplifying assumption of Fourier-stationary conditions is described.This work was funded jointly by the United Kingdom Engineering and Physical Sciences Research Council and by EURATOM

A high resolution Mirnov array for the Mega Ampere Spherical Tokamak

Over the past two decades, the increase in neutral-beam heating and alpha particle production in magnetically confined fusion plasmas has led to an increase in energetic particle driven mode activity, much of which has an electromagnetic signature which can be detected by the use of external Mirnov coils. Typically, the frequency and spatial wave number band of such oscillations increase with increasing injection energy, offering new challenges for diagnostic design. In particular, as the frequency approaches the megahertz range, care must be taken to model the stray capacitance of the coil, which limits the resonant frequency of the probe; model transmission line effects in the system, which if unchecked can produce system resonances; and minimize coil conductive shielding, so as to minimize skin currents which limit the frequency response of the coil. As well as optimizing the frequency response, the coils should also be positioned to confidently identify oscillations over a wide wave number band. This work, which draws on new techniques in stray capacitance modeling and coil positioning, is a case study of the outboard Mirnov array for high-frequency acquisition in the Mega Ampere Spherical Tokamak, and is intended as a roadmap for the design of high frequency, weak field strength magnetic diagnostics.This work was partly funded by the Australian National University, the United Kingdom Engineering and Physical Sciences Research Council, and by the European Communities under the contract of Association between EURATOM and CCFE

Stochastic parareal: an application of probabilistic methods to time-parallelisation

Parareal is a well-studied algorithm for numerically integrating systems of time-dependent differential equations by parallelising the temporal domain. Given approximate initial values at each temporal sub-interval, the algorithm locates a solution in a fixed number of iterations using a predictor-corrector, stopping once a tolerance is met. This iterative process combines solutions located by inexpensive (coarse resolution) and expensive (fine resolution) numerical integrators. In this paper, we introduce a stochastic parareal algorithm with the aim of accelerating the convergence of the deterministic parareal algorithm. Instead of providing the predictor-corrector with a deterministically located set of initial values, the stochastic algorithm samples initial values from dynamically varying probability distributions in each temporal sub-interval. All samples are then propagated by the numerical method in parallel. The initial values yielding the most continuous (smoothest) trajectory across consecutive sub-intervals are chosen as the new, more accurate, set of initial values. These values are fed into the predictor-corrector, converging in fewer iterations than the deterministic algorithm with a given probability. The performance of the stochastic algorithm, implemented using various probability distributions, is illustrated on systems of ordinary differential equations. When the number of sampled initial values is large enough, we show that stochastic parareal converges almost certainly in fewer iterations than the deterministic algorithm while maintaining solution accuracy. Additionally, it is shown that the expected value of the convergence rate decreases with increasing numbers of samples

Polaron Transport in the Paramagnetic Phase of Electron-Doped Manganites

The electrical resistivity, Hall coefficient, and thermopower as functions of temperature are reported for lightly electron-doped Ca(1-x)La(x)MnO(3)(0 <= x <= 0.10). Unlike the case of hole-doped ferromagnetic manganites, the magnitude and temperature dependence of the Hall mobility for these compounds is found to be inconsistent with small-polaron theory. The transport data are better described by the Feynman polaron theory and imply intermediate coupling (alpha \~ 5.4) with a band effective mass, m*~4.3 m_0, and a polaron mass, m_p ~ 10 m_0.Comment: 7 pp., 7 Fig.s, to be published, PR

Selectivities of K/Ca and K/Pb Exchange in Two Tropical Soils

Measurement of cation selectivity in soils provides important information about the affinity and binding strength of a particular cation on soil surfaces. Gaines-Thomas (KGT) selectivity coefficients were determined for a variety of K/Ca and K/Pb ratios on an Oxisol and Ultisol soil from Puerto Rico. The calculated KGT values indicated a preference for K+ over Ca2+ or Pb2+. The selectivity for Pb2+ was significantly greater than that for Ca2+ due to the larger hydrated charge density of Pb2+ relative to that of Ca2+. The patterns of selectivity were independent of metal type. The selectivity of the Oxisol for Ca2+ or Pb2+ exhibited no trend/did not change with changes in divalent metal surface coverage indicating exchange sites had similar affinities for Ca2+ and Pb2+. The Ultisol displayed a decrease in selectivity for Ca2+ and Pb2+ with increasing surface coverage of these ions. This was attributed to the presence of smectite in the Ultisol which was able to partially collapse when K+ saturated. Some of the Pb sorption in the soils was due to chemisorption. The Oxisol chemisorbed ~ 3000 ppm Pb while that value for the Ultisol was ~ 1900 ppm. The differences were due to the greater quantities of Fe/Al oxides and organic matter in the Oxisol relative to the Ultisol. SEM-EDX spectroscopy detected discrete Pb-C phases in both soils. The C was from organic matter as PbCO3 was not stable under experimental conditions. It was possible Pb was associated with organic sulfhydral groups. The selectivity exhibited by soil systems for various nutrient and heavy metals is important in elucidating how available these metals will be for plant/animal uptake as well as their mobility and stability in the soil environment

Stochastic Cutoff Method for Long-Range Interacting Systems

A new Monte-Carlo method for long-range interacting systems is presented. This method consists of eliminating interactions stochastically with the detailed balance condition satisfied. When a pairwise interaction $V_{ij}$ of a $N$-particle system decreases with the distance as $r_{ij}^{-\alpha}$, computational time per one Monte Carlo step is ${\cal O}(N)$ for $\alpha \ge d$ and ${\cal O}(N^{2-\alpha/d})$ for $\alpha < d$, where $d$ is the spatial dimension. We apply the method to a two-dimensional magnetic dipolar system. The method enables us to treat a huge system of $256^2$ spins with reasonable computational time, and reproduces a circular order originated from long-range dipolar interactions.Comment: 18 pages, 9 figures, 1 figure and 1 reference are adde

GParareal: A time-parallel ODE solver using Gaussian process emulation

Sequential numerical methods for integrating initial value problems (IVPs) can be prohibitively expensive when high numerical accuracy is required over the entire interval of integration. One remedy is to integrate in a parallel fashion, "predicting" the solution serially using a cheap (coarse) solver and "correcting" these values using an expensive (fine) solver that runs in parallel on a number of temporal subintervals. In this work, we propose a time-parallel algorithm (GParareal) that solves IVPs by modelling the correction term, i.e. the difference between fine and coarse solutions, using a Gaussian process emulator. This approach compares favourably with the classic parareal algorithm and we demonstrate, on a number of IVPs, that GParareal can converge in fewer iterations than parareal, leading to an increase in parallel speed-up. GParareal also manages to locate solutions to certain IVPs where parareal fails and has the additional advantage of being able to use archives of legacy solutions, e.g. solutions from prior runs of the IVP for different initial conditions, to further accelerate convergence of the method -- something that existing time-parallel methods do not do

Immobilized photocatalyst on stainless steel woven meshes assuring efficient light distribution in a solar reactor

An immobilized TiO₂ photocatalyst with a high specific surface area was prepared on stainless steel woven meshes in order to be used packed in layers for water purification. Immobilization of such a complex shape needs a special coating technique. For this purpose, dip coating and electrophoretic deposition (EPD) techniques were used. The EPD technique gave the TiO₂ coating films a better homogeneity and adhesion, fewer cracks, and a higher ^·OH formation than the dip coating technique. The woven mesh structure packed in layers guaranteed an efficient light-penetration in water treatment reactor. A simple equation model was used to describe the distribution of light through the mesh layers in the presence of absorbing medium (e.g., colored water with humic acids). Maximum three or four coated meshes were enough to harvest the solar UV light from 300 nm to 400 nm with a high penetration efficiency. The separation distance between the mesh layers played an important role in the efficiency of solar light penetration through the coated mesh layers, especially in case of colored water contaminated with high concentrations of humic acid

Understanding the Mechanisms of Lead, Copper, and Zinc Retention by Phosphate Rock

The solid-liquid interface reaction between phosphate rock (PR) and metals (Pb, Cu, and Zn)was studied. Phosphate rock has the highest affinity for Pb, followed by Cu and Zn, with sorption capacities of 131, 114, and 83.2 mmol kg-1 PR, respectively. In the Pb-Cu-Zn ternary system, competitive metal sorption occurred with sorption capacity reduction of 15.2%, 48.3%, and 75.6% for Pb, Cu, and Zn, respectively. A fractional factorial design showed the interfering effect in the order of Pb\u3eCu\u3eZn. Desorption of Cu and Zn was sensitive to pH change, increasing with pH decline, whereas Pb desorption was decreased with a strongly acidic TCLP extracting solution (pH=2.93). The greater stability of Pb retention by PR can be attributed to the fact that P-induced formation of fluoropyromorphite [Pb10(PO4)6F2] (i.e. irreversibly chemisorbed) was primarily responsible for Pb immobilization (up to 78.3%), which was confirmed by XRD and SEM. The other 21.7% of Pb retained by PR was via surface adsorption or complexation, compared to 74.5% for Cu and 96.7% for Zn. Solution pH reduction during metal retention and flow calorimetry analysis both supported the hypothesis of retention of Pb, Cu, and Zn by surface adsorption or complexation. Flow calorimetry indicated that Pb and Cu adsorption onto PR was exothermic, while Zn sorption was endothermic. Our research further demonstrated that PR could be used effectively to remove Pb from wastewater or remediate Pb-contaminated soil and sediments

Non-Destructive Probing of Rabi Oscillations on the Cesium Clock Transition near the Standard Quantum Limit

We report on non-destructive observation of Rabi oscillations on the Cs clock transition. The internal atomic state evolution of a dipole-trapped ensemble of cold atoms is inferred from the phase shift of a probe laser beam as measured using a Mach-Zehnder interferometer. We describe a single color as well as a two-color probing scheme. Using the latter, measurements of the collective pseudo-spin projection of atoms in a superposition of the clock states are performed and the observed spin fluctuations are shown to be close to the standard quantum limit.Comment: 4 pages, 4 figures, accepted for publication in Physical Review Letter