Freely decaying turbulence in two-dimensional electrostatic gyrokinetics

In magnetized plasmas, a turbulent cascade occurs in phase space at scales smaller than the thermal Larmor radius ("sub-Larmor scales") [Phys. Rev. Lett. 103, 015003 (2009)]. When the turbulence is restricted to two spatial dimensions perpendicular to the background magnetic field, two independent cascades may take place simultaneously because of the presence of two collisionless invariants. In the present work, freely decaying turbulence of two-dimensional electrostatic gyrokinetics is investigated by means of phenomenological theory and direct numerical simulations. A dual cascade (forward and inverse cascades) is observed in velocity space as well as in position space, which we diagnose by means of nonlinear transfer functions for the collisionless invariants. We find that the turbulence tends to a time-asymptotic state, dominated by a single scale that grows in time. A theory of this asymptotic state is derived in the form of decay laws. Each case that we study falls into one of three regimes (weakly collisional, marginal, and strongly collisional), determined by a dimensionless number D*, a quantity analogous to the Reynolds number. The marginal state is marked by a critical number D* = D0 that is preserved in time. Turbulence initialized above this value become increasingly inertial in time, evolving toward larger and larger D*; turbulence initialized below D0 become more and more collisional, decaying to progressively smaller D*.Comment: 12 pages, 12 figures; replaced to match published versio

Optimisation of confinement in a fusion reactor using a nonlinear turbulence model

The confinement of heat in the core of a magnetic fusion reactor is optimised using a multidimensional optimisation algorithm. For the first time in such a study, the loss of heat due to turbulence is modelled at every stage using first-principles nonlinear simulations which accurately capture the turbulent cascade and large-scale zonal flows. The simulations utilise a novel approach, with gyrofluid treatment of the small-scale drift waves and gyrokinetic treatment of the large-scale zonal flows. A simple near-circular equilibrium with standard parameters is chosen as the initial condition. The figure of merit, fusion power per unit volume, is calculated, and then two control parameters, the elongation and triangularity of the outer flux surface, are varied, with the algorithm seeking to optimise the chosen figure of merit. A two-fold increase in the plasma power per unit volume is achieved by moving to higher elongation and strongly negative triangularity.Comment: 32 pages, 8 figures, accepted to JP

Direct Distances to Cepheids in the Large Magellanic Cloud: Evidence for a Universal Slope of the Period-Luminosity Relation up to Solar Abundance

We have applied the infrared surface brightness (ISB) technique to derive distances to 13 Cepheids in the LMC which span a period range from 3 to 42 days. From the absolute magnitudes of the variables calculated from these distances, we find that the LMC Cepheids define tight period-luminosity relations in the V, I, W, J and K bands which agree exceedingly well with the corresponding Galactic PL relations derived from the same technique, and are significantly steeper than the LMC PL relations in these bands observed by the OGLE-II Project in V, I and W, and by Persson et al. in J and K. We find that the tilt-corrected true distance moduli of the LMC Cepheids show a significant dependence on period, which hints at a systematic error in the ISB technique related to the period of the stars. We identify as the most likely culprit the p-factor which converts the radial into pulsational velocities; our data imply a much steeper period dependence of the p-factor than previously thought, and we derive p=1.58 (+/-0.02) -0.15 (+/-0.05) logP as the best fit from our data, with a zero point tied to the Milky Way open cluster Cepheids. Using this revised p-factor law, the period dependence of the LMC Cepheid distance moduli disappears, and at the same time the Milky Way and LMC PL relations agree among themselves, and with the directly observed LMC PL relations, within the 1 sigma uncertainties. Our main conclusion is that the previous, steeper Galactic PL relations were caused by an erroneous calibration of the p-factor law, and that there is now evidence that the slope of the Cepheid PL relation is independent of metallicity up to solar metallicity, in both optical, and near-infrared bands.Comment: ApJ accepte

Distances to six Cepheids in the LMC cluster NGC1866 from the near-IR surface-brightness method

We derive individual distances to six Cepheids in the young populous star cluster NGC1866 in the Large Magellanic Cloud employing the near-IR surface brightness technique. With six stars available at the exact same distance we can directly measure the intrinsic uncertainty of the method. We find a standard deviation of 0.11 mag, two to three times larger than the error estimates and more in line with the estimates from Bayesian statistical analysis by Barnes et al. (2005). Using all six distance estimates we determine an unweighted mean cluster distance of 18.30+-0.05. The observations indicate that NGC1866 is close to be at the same distance as the main body of the LMC. If we use the stronger dependence of the p-factor on the period as suggested by Gieren et al. (2005) we find a distance of 18.50+-0.05 (internal error) and the PL relations for Galactic and MC Cepheids are in very good agreement.Comment: Presented at the conference "Stellar Pulsation and Evolution" in Monte Porzio Catone, June 2005. To appear in Mem. Soc. Ast. It. 76/

Nonlinear phase mixing and phase-space cascade of entropy in gyrokinetic plasma turbulence

Electrostatic turbulence in weakly collisional, magnetized plasma can be interpreted as a cascade of entropy in phase space, which is proposed as a universal mechanism for dissipation of energy in magnetized plasma turbulence. When the nonlinear decorrelation time at the scale of the thermal Larmor radius is shorter than the collision time, a broad spectrum of fluctuations at sub-Larmor scales is numerically found in velocity and position space, with theoretically predicted scalings. The results are important because they identify what is probably a universal Kolmogorov-like regime for kinetic turbulence; and because any physical process that produces fluctuations of the gyrophase-independent part of the distribution function may, via the entropy cascade, result in turbulent heating at a rate that increases with the fluctuation amplitude, but is independent of the collision frequency.Comment: Revtex, 4 pages, 3 figures; replaced to match published versio

Multiscale Gyrokinetics for Rotating Tokamak Plasmas: Fluctuations, Transport and Energy Flows

This paper presents a complete theoretical framework for plasma turbulence and transport in tokamak plasmas. The fundamental scale separations present in plasma turbulence are codified as an asymptotic expansion in the ratio of the gyroradius to the equilibrium scale length. Proceeding order-by-order in this expansion, a framework for plasma turbulence is developed. It comprises an instantaneous equilibrium, the fluctuations driven by gradients in the equilibrium quantities, and the transport-timescale evolution of mean profiles of these quantities driven by the fluctuations. The equilibrium distribution functions are local Maxwellians with each flux surface rotating toroidally as a rigid body. The magnetic equillibrium is obtained from the Grad-Shafranov equation for a rotating plasma and the slow (resistive) evolution of the magnetic field is given by an evolution equation for the safety factor q. Large-scale deviations of the distribution function from a Maxwellian are given by neoclassical theory. The fluctuations are determined by the high-flow gyrokinetic equation, from which we derive the governing principle for gyrokinetic turbulence in tokamaks: the conservation and local cascade of free energy. Transport equations for the evolution of the mean density, temperature and flow velocity profiles are derived. These transport equations show how the neoclassical corrections and the fluctuations act back upon the mean profiles through fluxes and heating. The energy and entropy conservation laws for the mean profiles are derived. Total energy is conserved and there is no net turbulent heating. Entropy is produced by the action of fluxes flattening gradients, Ohmic heating, and the equilibration of mean temperatures. Finally, this framework is condensed, in the low-Mach-number limit, to a concise set of equations suitable for numerical implementation.Comment: 113 pages, 3 figure

Gyrokinetic simulation of entropy cascade in two-dimensional electrostatic turbulence

Two-dimensional electrostatic turbulence in magnetized weakly-collisional plasmas exhibits a cascade of entropy in phase space [Phys. Rev. Lett. 103, 015003 (2009)]. At scales smaller than the gyroradius, this cascade is characterized by the dimensionless ratio D of the collision time to the eddy turnover time measured at the scale of the thermal Larmor radius. When D >> 1, a broad spectrum of fluctuations at sub-Larmor scales is found in both position and velocity space. The distribution function develops structure as a function of v_{perp}, the velocity coordinate perpendicular to the local magnetic field. The cascade shows a local-scale nonlinear interaction in both position and velocity spaces, and Kolmogorov's scaling theory can be extended into phase space.Comment: 8 pages, 10 figures, Conference paper presented at 2009 Asia-Pacific Plasma Theory Conference. Ver.2 includes corrected typos & updated reference

Direct multiscale coupling of a transport code to gyrokinetic turbulence codes

Direct coupling between a transport solver and local, nonlinear gyrokinetic calculations using the multiscale gyrokinetic code TRINITY [M. Barnes, Ph.D. thesis, arxiv:0901.2868] is described. The coupling of the microscopic and macroscopic physics is done within the framework of multiscale gyrokinetic theory, of which we present the assumptions and key results. An assumption of scale separation in space and time allows for the simulation of turbulence in small regions of the space-time grid, which are embedded in a coarse grid on which the transport equations are implicitly evolved. This leads to a reduction in computational expense of several orders of magnitude, making first-principles simulations of the full fusion device volume over the confinement time feasible on current computing resources. Numerical results from TRINITY simulations are presented and compared with experimental data from JET and ASDEX Upgrade plasmas.Comment: 12 pages, 13 figures, invited paper for 2009 APS-DPP meeting, submitted to Phys. Plasma

Effective action for Dirac fields in a constant electromagnetic background

We obtain, through zeta function methods, the one-loop effective action for massive Dirac fields in the presence of a uniform, but otherwise general, electromagnetic background. We show the agreement of our result with previous ones, concerning particular limit cases

Mesoscopic one-way channels for quantum state transfer via the Quantum Hall Effect

We show that the one-way channel formalism of quantum optics has a physical realisation in electronic systems. In particular, we show that magnetic edge states form unidirectional quantum channels capable of coherently transporting electronic quantum information. Using the equivalence between one-way photonic channels and magnetic edge states, we adapt a proposal for quantum state transfer to mesoscopic systems using edge states as a quantum channel, and show that it is feasible with reasonable experimental parameters. We discuss how this protocol may be used to transfer information encoded in number, charge or spin states of quantum dots, so it may prove useful for transferring quantum information between parts of a solid-state quantum computer.Comment: 4 pages, 3 figure