Turbulent transport in tokamak plasmas with rotational shear

Nonlinear gyrokinetic simulations have been conducted to investigate turbulent transport in tokamak plasmas with rotational shear. At sufficiently large flow shears, linear instabilities are suppressed, but transiently growing modes drive subcritical turbulence whose amplitude increases with flow shear. This leads to a local minimum in the heat flux, indicating an optimal E x B shear value for plasma confinement. Local maxima in the momentum fluxes are also observed, allowing for the possibility of bifurcations in the E x B shear. The sensitive dependence of heat flux on temperature gradient is relaxed for large flow shear values, with the critical temperature gradient increasing at lower flow shear values. The turbulent Prandtl number is found to be largely independent of temperature and flow gradients, with a value close to unity.Comment: 4 pages, 5 figures, submitted to PR

PEPSI deep spectra. III. A chemical analysis of the ancient planet-host star Kepler-444

We obtained an LBT/PEPSI spectrum with very high resolution and high signal-to-noise ratio (S/N) of the K0V host Kepler-444, which is known to host 5 sub-Earth size rocky planets. The spectrum has a resolution of R=250,000, a continuous wavelength coverage from 4230 to 9120A, and S/N between 150 and 550:1 (blue to red). We performed a detailed chemical analysis to determine the photospheric abundances of 18 chemical elements, in order to use the abundances to place constraints on the bulk composition of the five rocky planets. Our spectral analysis employs the equivalent width method for most of our spectral lines, but we used spectral synthesis to fit a small number of lines that require special care. In both cases, we derived our abundances using the MOOG spectral analysis package and Kurucz model atmospheres. We find no correlation between elemental abundance and condensation temperature among the refractory elements. In addition, using our spectroscopic stellar parameters and isochrone fitting, we find an age of 10+/-1.5 Gyr, which is consistent with the asteroseismic age of 11+/-1 Gyr. Finally, from the photospheric abundances of Mg, Si, and Fe, we estimate that the typical Fe-core mass fraction for the rocky planets in the Kepler-444 system is approximately 24 per cent. If our estimate of the Fe-core mass fraction is confirmed by more detailed modeling of the disk chemistry and simulations of planet formation and evolution in the Kepler-444 system, then this would suggest that rocky planets in more metal-poor and alpha-enhanced systems may tend to be less dense than their counterparts of comparable size in more metal-rich systems.Comment: in press, 11 pages, 3 figures, data available from pepsi.aip.d

Zero-Turbulence Manifold in a Toroidal Plasma

Sheared toroidal flows can cause bifurcations to zero-turbulent-transport states in tokamak plasmas. The maximum temperature gradients that can be reached are limited by subcritical turbulence driven by the parallel velocity gradient. Here it is shown that q/\epsilon (magnetic field pitch/inverse aspect ratio) is a critical control parameter for sheared tokamak turbulence. By reducing q/\epsilon, far higher temperature gradients can be achieved without triggering turbulence, in some instances comparable to those found experimentally in transport barriers. The zero-turbulence manifold is mapped out, in the zero-magnetic-shear limit, over the parameter space (\gamma_E, q/\epsilon, R/L_T), where \gamma_E is the perpendicular flow shear and R/L_T is the normalised inverse temperature gradient scale. The extent to which it can be constructed from linear theory is discussed.Comment: 5 Pages, 4 Figures, Submitted to PR

Experimental Signatures of Critically Balanced Turbulence in MAST

Beam Emission Spectroscopy (BES) measurements of ion-scale density fluctuations in the MAST tokamak are used to show that the turbulence correlation time, the drift time associated with ion temperature or density gradients, the particle (ion) streaming time along the magnetic field and the magnetic drift time are consistently comparable, suggesting a "critically balanced" turbulence determined by the local equilibrium. The resulting scalings of the poloidal and radial correlation lengths are derived and tested. The nonlinear time inferred from the density fluctuations is longer than the other times; its ratio to the correlation time scales as $\nu_{*i}^{-0.8\pm0.1}$, where $\nu_{*i}=$ ion collision rate/streaming rate. This is consistent with turbulent decorrelation being controlled by a zonal component, invisible to the BES, with an amplitude exceeding the drift waves' by $\sim \nu_{*i}^{-0.8}$.Comment: 6 pages, 4 figures, submitted to PR

Transport Bifurcation in a Rotating Tokamak Plasma

The effect of flow shear on turbulent transport in tokamaks is studied numerically in the experimentally relevant limit of zero magnetic shear. It is found that the plasma is linearly stable for all non-zero flow shear values, but that subcritical turbulence can be sustained nonlinearly at a wide range of temperature gradients. Flow shear increases the nonlinear temperature gradient threshold for turbulence but also increases the sensitivity of the heat flux to changes in the temperature gradient, except over a small range near the threshold where the sensitivity is decreased. A bifurcation in the equilibrium gradients is found: for a given input of heat, it is possible, by varying the applied torque, to trigger a transition to significantly higher temperature and flow gradients.Comment: 4 pages, 4 figures, submitted to PR

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

Statistics of anomalously localized states at the center of band E=0 in the one-dimensional Anderson localization model

We consider the distribution function $P(|\psi|^{2})$ of the eigenfunction amplitude at the center-of-band (E=0) anomaly in the one-dimensional tight-binding chain with weak uncorrelated on-site disorder (the one-dimensional Anderson model). The special emphasis is on the probability of the anomalously localized states (ALS) with $|\psi|^{2}$ much larger than the inverse typical localization length $\ell_{0}$. Using the solution to the generating function $\Phi_{an}(u,\phi)$ found recently in our works we find the ALS probability distribution $P(|\psi|^{2})$ at $|\psi|^{2}\ell_{0} >> 1$. As an auxiliary preliminary step we found the asymptotic form of the generating function $\Phi_{an}(u,\phi)$ at $u >> 1$ which can be used to compute other statistical properties at the center-of-band anomaly. We show that at moderately large values of $|\psi|^{2}\ell_{0}$, the probability of ALS at E=0 is smaller than at energies away from the anomaly. However, at very large values of $|\psi|^{2}\ell_{0}$, the tendency is inverted: it is exponentially easier to create a very strongly localized state at E=0 than at energies away from the anomaly. We also found the leading term in the behavior of $P(|\psi|^{2})$ at small $|\psi|^{2}<< \ell_{0}^{-1}$ and show that it is consistent with the exponential localization corresponding to the Lyapunov exponent found earlier by Kappus and Wegner and Derrida and Gardner.Comment: 25 pages, 9 figure

Disrupting the wall accumulation of human sperm cells by artificial corrugation

Many self-propelled microorganisms are attracted to surfaces. This makes their dynamics in restricted geometries very different from that observed in the bulk. Swimming along walls is beneficial for directing and sorting cells, but may be detrimental if homogeneous populations are desired, such as in counting microchambers. In this work, we characterize the motion of human sperm cells $60 \mu m$ long, strongly confined to $25 \mu m$ shallow chambers. We investigate the nature of the cell trajectories between the confining surfaces and their accumulation near the borders. Observed cell trajectories are composed of a succession of quasi-circular and quasi-linear segments. This suggests that the cells follow a path of intermittent trappings near the top and bottom surfaces separated by stretches of quasi-free motion in between the two surfaces, as confirmed by depth resolved confocal microscopy studies. We show that the introduction of artificial petal-shaped corrugation in the lateral boundaries removes the tendency of cells to accumulate near the borders, an effect which we hypothesize may be valuable for microfluidic applications in biomedicine.Comment: 9 pages, latex. In accepted version on April 14, v2: abstract modified, information added to Sec. II.A and experiments added to Sec. III.A and Fig.3. Sec. III.C was deleted. Requested references adde