Random walk through fractal environments

We analyze random walk through fractal environments, embedded in 3-dimensional, permeable space. Particles travel freely and are scattered off into random directions when they hit the fractal. The statistical distribution of the flight increments (i.e. of the displacements between two consecutive hittings) is analytically derived from a common, practical definition of fractal dimension, and it turns out to approximate quite well a power-law in the case where the dimension D of the fractal is less than 2, there is though always a finite rate of unaffected escape. Random walks through fractal sets with D less or equal 2 can thus be considered as defective Levy walks. The distribution of jump increments for D > 2 is decaying exponentially. The diffusive behavior of the random walk is analyzed in the frame of continuous time random walk, which we generalize to include the case of defective distributions of walk-increments. It is shown that the particles undergo anomalous, enhanced diffusion for D_F < 2, the diffusion is dominated by the finite escape rate. Diffusion for D_F > 2 is normal for large times, enhanced though for small and intermediate times. In particular, it follows that fractals generated by a particular class of self-organized criticality (SOC) models give rise to enhanced diffusion. The analytical results are illustrated by Monte-Carlo simulations.Comment: 22 pages, 16 figures; in press at Phys. Rev. E, 200

Tests of analytical hadronisation models using event shape moments in {\epem} annihilation

Predictions of analytical models for hadronisation, namely the dispersive model, the shape function and the single dressed gluon approximation, are compared with moments of hadronic event shape distributions measured in \epem annihilation at centre-of-mass energies between 14 and 209 GeV. In contrast to Monte Carlo models for hadronisation, analytical models require to adjust only two universal parameters, the strong coupling and a second quantity parametrising nonperturbative corrections. The extracted values of as are consistent with the world average and competitive with previous measurements. The variance of event shape distributions is compared with predictions given by some of these models. Limitations of the models, probably due to unknown higher order corrections, are demonstrated and discussed.Comment: Ref.s [19,36] added and footnote 1 adjuste

Development and Validation of a Tokamak Skin Effect Transformer model

A control oriented, lumped parameter model for the tokamak transformer including the slow flux penetration in the plasma (skin effect transformer model) is presented. The model does not require detailed or explicit information about plasma profiles or geometry. Instead, this information is lumped in system variables, parameters and inputs. The model has an exact mathematical structure built from energy and flux conservation theorems, predicting the evolution and non linear interaction of the plasma current and internal inductance as functions of the primary coil currents, plasma resistance, non-inductive current drive and the loop voltage at a specific location inside the plasma (equilibrium loop voltage). Loop voltage profile in the plasma is substituted by a three-point discretization, and ordinary differential equations are used to predict the equilibrium loop voltage as function of the boundary and resistive loop voltages. This provides a model for equilibrium loop voltage evolution, which is reminiscent of the skin effect. The order and parameters of this differential equation are determined empirically using system identification techniques. Fast plasma current modulation experiments with Random Binary Signals (RBS) have been conducted in the TCV tokamak to generate the required data for the analysis. Plasma current was modulated in Ohmic conditions between 200kA and 300kA with 30ms rise time, several times faster than its time constant L/R\approx200ms. The model explains the most salient features of the plasma current transients without requiring detailed or explicit information about resistivity profiles. This proves that lumped parameter modeling approach can be used to predict the time evolution of bulk plasma properties such as plasma inductance or current with reasonable accuracy; at least in Ohmic conditions without external heating and current drive sources

The 2009 World Average of αs\alpha_s

Measurements of $\alpha_s$, the coupling strength of the Strong Interaction between quarks and gluons, are summarised and an updated value of the world average of $\alpha_s (M_Z)$ is derived. Building up on previous reviews, special emphasis is laid on the most recent determinations of $\alpha_s$. These are obtained from $\tau$-decays, from global fits of electroweak precision data and from measurements of the proton structure function \F_2, which are based on perturbative QCD calculations up to $O(\alpha_s^4)$; from hadronic event shapes and jet production in \epem annihilation, based on $O(\alpha_s^3)$ QCD; from jet production in deep inelastic scattering and from $\Upsilon$ decays, based on $O(\alpha_s^2)$ QCD; and from heavy quarkonia based on unquenched QCD lattice calculations. Applying pragmatic methods to deal with possibly underestimated errors and/or unknown correlations, the world average value of $\alpha_s (M_Z)$ results in $\alpha_s (M_Z) = 0.1184 \pm 0.0007$. The measured values of $\alpha_s (Q)$, covering energy scales from Q \equiv \mtau = 1.78 GeV to 209 GeV, exactly follow the energy dependence predicted by QCD and therefore significantly test the concept af Asymptotic Freedom.Comment: 14 pages, 7 figure

Exploration of the equilibrium operating space for NSTX-Upgrade

This paper explores a range of high-performance equilibrium scenarios available in the NSTX-Upgrade device [J.E. Menard, submitted for publication to Nuclear Fusion]. NSTX-Upgrade is a substantial upgrade to the existing NSTX device [M. Ono, et al., Nuclear Fusion 40, 557 (2000)], with significantly higher toroidal field and solenoid capabilities, and three additional neutral beam sources with significantly larger current drive efficiency. Equilibria are computed with freeboundary TRANSP, allowing a self consistent calculation of the non-inductive current drive sources, the plasma equilibrium, and poloidal field coil current, using the realistic device geometry. The thermal profiles are taken from a variety of existing NSTX discharges, and different assumptions for the thermal confinement scalings are utilized. The no-wall and idealwall n=1 stability limits are computed with the DCON code. The central and minimum safety factors are quite sensitive to many parameters: they generally increases with large outer plasmawall gaps and higher density, but can have either trend with the confinement enhancement factor. In scenarios with strong central beam current drive, the inclusion of non-classical fast ion diffusion raises qmin, decreases the pressure peaking, and generally improves the global stability, at the expense of a reduction in the non-inductive current drive fraction; cases with less beam current drive are largely insensitive to additional fast ion diffusion. The non-inductive current level is quite sensitive to the underlying confinement and profile assumptions. For instance, for BT=1.0 T and Pinj=12.6 MW, the non-inductive current level varies from 875 kA with ITER-98y,2 thermal confinement scaling and narrow thermal profiles to 1325 kA for an ST specific scaling expression and broad profiles. This sensitivity should facilitate the determination of the correct scaling of transport with current and field to use for future fully non-inductive ST devices. Scenarios are presented which can be sustained for 8-10 seconds, or (20-30)τCR, at βN=3.8-4.5, facilitating, for instance, the study of disruption avoidance for very long pulse. Scenarios have been documented which can operate with βT~25% and equilibrated qmin&gt;1. The value of qmin can be controlled at either fixed non-inductive fraction of 100% or fixed plasma current, by varying which beam sources are used, opening the possibility for feedback qmin control. In terms of quantities like collisionality, neutron emission, non-inductive fraction, or stored energy, these scenarios represent a significant performance extension compared to NSTX and other present spherical torii