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

Spin squeezing of atomic ensembles by multi-colour quantum non-demolition measurements

We analyze the creation of spin squeezed atomic ensembles by simultaneous dispersive interactions with several optical frequencies. A judicious choice of optical parameters enables optimization of an interferometric detection scheme that suppresses inhomogeneous light shifts and keeps the interferometer operating in a balanced mode that minimizes technical noise. We show that when the atoms interact with two-frequency light tuned to cycling transitions the degree of spin squeezing $\xi^2$ scales as $\xi^2\sim 1/d$ where $d$ is the resonant optical depth of the ensemble. In real alkali atoms there are loss channels and the scaling may be closer to $\xi^2\sim 1/\sqrt d.$ Nevertheless the use of two-frequencies provides a significant improvement in the degree of squeezing attainable as we show by quantitative analysis of non-resonant probing on the Cs D1 line. Two alternative configurations are analyzed: a Mach-Zehnder interferometer that uses spatial interference, and an interaction with multi-frequency amplitude modulated light that does not require a spatial interferometer.Comment: 7 figure

Evidence cross-validation and Bayesian inference of MAST plasma equilibria

In this paper, current profiles for plasma discharges on the Mega-Ampere Spherical Tokamak (MAST) are directly calculated from pickup coil, flux loop and Motional-Stark Effect (MSE) observations via methods based in the statistical theory of Bayesian analysis. By representing toroidal plasma current as a series of axisymmetric current beams with rectangular cross-section and inferring the current for each one of these beams, flux-surface geometry and q-profiles are subsequently calculated by elementary application of Biot-Savart's law. The use of this plasma model in the context of Bayesian analysis was pioneered by Svensson and Werner on the Joint-European Tokamak (JET) [J. Svensson and A. Werner. Current tomography for axisymmetric plasmas. Plasma Physics and Controlled Fusion, 50(8):085002, 2008]. In this framework, linear forward models are used to generate diagnostic predictions, and the probability distribution for the currents in the collection of plasma beams was subsequently calculated directly via application of Bayes' formula. In this work, we introduce a new diagnostic technique to identify and remove outlier observations associated with diagnostics falling out of calibration or suffering from an unidentified malfunction. These modifications enable good agreement between Bayesian inference of the last closed flux-surface (LCFS) with other corroborating data, such as such as that from force balance considerations using EFIT++ [L. Appel et al., Proc. 33rd EPS Conf., Rome, Italy, 2006]. In addition, this analysis also yields errors on the plasma current profile and flux-surface geometry, as well as directly predicting the Shafranov shift of the plasma core.This work was jointly funded by the Australian Government through International Science Linkages Grant No. CG130047, the Australian National University, the United Kingdom Engineering and Physical Sciences Research Council under Grant No. EP/G003955, and by the European Communities under the contract of Association between EURATOM and CCFE

Model Data Fusion: developing Bayesian inversion to constrain equilibrium and mode structure

Recently, a new probabilistic "data fusion" framework based on Bayesian principles has been developed on JET and W7-AS. The Bayesian analysis framework folds in uncertainties and inter-dependencies in the diagnostic data and signal forward-models, together with prior knowledge of the state of the plasma, to yield predictions of internal magnetic structure. A feature of the framework, known as MINERVA (J. Svensson, A. Werner, Plasma Physics and Controlled Fusion 50, 085022, 2008), is the inference of magnetic flux surfaces without the use of a force balance model. We discuss results from a new project to develop Bayesian inversion tools that aim to (1) distinguish between competing equilibrium theories, which capture different physics, using the MAST spherical tokamak; and (2) test the predictions of MHD theory, particularly mode structure, using the H-1 Heliac.Comment: submitted to Journal of Plasma Fusion Research 10/11/200

Surprises in the suddenly-expanded infinite well

I study the time-evolution of a particle prepared in the ground state of an infinite well after the latter is suddenly expanded. It turns out that the probability density $|\Psi(x, t)|^{2}$ shows up quite a surprising behaviour: for definite times, {\it plateaux} appear for which $|\Psi(x, t)|^{2}$ is constant on finite intervals for $x$. Elements of theoretical explanation are given by analyzing the singular component of the second derivative $\partial_{xx}\Psi(x, t)$. Analytical closed expressions are obtained for some specific times, which easily allow to show that, at these times, the density organizes itself into regular patterns provided the size of the box in large enough; more, above some critical time-dependent size, the density patterns are independent of the expansion parameter. It is seen how the density at these times simply results from a construction game with definite rules acting on the pieces of the initial density.Comment: 24 pages, 14 figure

A low-loss, broadband antenna for efficient photon collection from a coherent spin in diamond

We report the creation of a low-loss, broadband optical antenna giving highly directed output from a coherent single spin in the solid-state. The device, the first solid-state realization of a dielectric antenna, is engineered for individual nitrogen vacancy (NV) electronic spins in diamond. We demonstrate a directionality close to 10. The photonic structure preserves the high spin coherence of single crystal diamond (T2>100us). The single photon count rate approaches a MHz facilitating efficient spin readout. We thus demonstrate a key enabling technology for quantum applications such as high-sensitivity magnetometry and long-distance spin entanglement.Comment: 5 pages, 4 figures and supplementary information (5 pages, 8 figures). Comments welcome. Further information under http://www.quantum-sensing.physik.unibas.c

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

Quantum coherence and carriers mobility in organic semiconductors

We present a model of charge transport in organic molecular semiconductors based on the effects of lattice fluctuations on the quantum coherence of the electronic state of the charge carrier. Thermal intermolecular phonons and librations tend to localize pure coherent states and to assist the motion of less coherent ones. Decoherence is thus the primary mechanism by which conduction occurs. It is driven by the coupling of the carrier to the molecular lattice through polarization and transfer integral fluctuations as described by the hamiltonian of Gosar and Choi. Localization effects in the quantum coherent regime are modeled via the Anderson hamiltonian with correlated diagonal and non-diagonal disorder leading to the determination of the carrier localization length. This length defines the coherent extension of the ground state and determines, in turn, the diffusion range in the incoherent regime and thus the mobility. The transfer integral disorder of Troisi and Orlandi can also be incorporated. This model, based on the idea of decoherence, allowed us to predict the value and temperature dependence of the carrier mobility in prototypical organic semiconductors that are in qualitative accord with experiments

Developments in Rare Kaon Decay Physics

We review the current status of the field of rare kaon decays. The study of rare kaon decays has played a key role in the development of the standard model, and the field continues to have significant impact. The two areas of greatest import are the search for physics beyond the standard model and the determination of fundamental standard-model parameters. Due to the exquisite sensitivity of rare kaon decay experiments, searches for new physics can probe very high mass scales. Studies of the k->pnn modes in particular, where the first event has recently been seen, will permit tests of the standard-model picture of quark mixing and CP violation.Comment: One major revision to the text is the branching ratio of KL->ppg, based on a new result from KTeV. Several references were updated, with minor modifications to the text. A total of 48 pages, with 28 figures, in LaTeX; to be published in the Annual Review of Nuclear and Particle Science, Vol. 50, December 200