Proton imaging of stochastic magnetic fields

Recent laser-plasma experiments report the existence of dynamically significant magnetic fields, whose statistical characterisation is essential for understanding the physical processes these experiments are attempting to investigate. In this paper, we show how a proton imaging diagnostic can be used to determine a range of relevant magnetic field statistics, including the magnetic-energy spectrum. To achieve this goal, we explore the properties of an analytic relation between a stochastic magnetic field and the image-flux distribution created upon imaging that field. We conclude that features of the beam's final image-flux distribution often display a universal character determined by a single, field-scale dependent parameter - the contrast parameter - which quantifies the relative size of the correlation length of the stochastic field, proton displacements due to magnetic deflections, and the image magnification. For stochastic magnetic fields, we establish the existence of four contrast regimes - linear, nonlinear injective, caustic and diffusive - under which proton-flux images relate to their parent fields in a qualitatively distinct manner. As a consequence, it is demonstrated that in the linear or nonlinear injective regimes, the path-integrated magnetic field experienced by the beam can be extracted uniquely, as can the magnetic-energy spectrum under a further statistical assumption of isotropy. This is no longer the case in the caustic or diffusive regimes. We also discuss complications to the contrast-regime characterisation arising for inhomogeneous, multi-scale stochastic fields, as well as limitations currently placed by experimental capabilities on extracting magnetic field statistics. The results presented in this paper provide a comprehensive description of proton images of stochastic magnetic fields, with applications for improved analysis of given proton-flux images.Comment: Main paper pp. 1-29; appendices pp. 30-84. 24 figures, 2 table

Advanced photonic routing sub-systems with efficient routing control

In recent years, there has been much interest in the development of optical switches which can route optical signals from different input guides to different outputs based on thermo-optic and electro-optic technologies. Such switches, which can be reconfigured on millisecond and microsecond timescales, have already attracted commercial interest. However switches which are able to reconfigure on the nanosecond timescales required for packet switching have been more challenging and only in recent years, have router concepts been devised to allow lossless routers to be constructed able to switch on nanosecond timescales with more than 16×16 ports. This paper will therefore review the advances that have occurred to allow such operation and then describe recent studies that have begun to determine the electronic control and functionality required to enable full and practical operation of such switches in high performance networks.This research has received funding from the UK Engineering and Physical Sciences Research Council through the INTERNET Project, STAR and COPOS II grants and the European Commission under FP7 grant agreement ICT 257210 PARADIGM.This is the author accepted manuscript. The final version is available from IEEE via http://dx.doi.org/10.1109/ICTON.2015.719339

Low-energy, high-performance lossless 8×8 SOA switch

We demonstrate the first monolithically-integrated active-passive lossless 8×8 SOA switch. A wide IPDR of 14.5dB for penalty <1dB is achieved. The switch paths through the device exhibit excellent uniformity.The research leading to these results has received funding from the UK EPSRC through the INTERNET, STAR and COPOS II grants and the European Commission under FP7 grant agreement ICT 257210 PARADIGM.This is the accepted manuscript. The final version is available from OSA at http://www.opticsinfobase.org/abstract.cfm?uri=OFC-2015-Th4E.6

Demonstration of the feasibility of large-port-count optical switching using a hybrid Mach-Zehnder interferometer-semiconductor optical amplifier switch module in a recirculating loop.

For what we believe is the first time, the feasibility of large-port-count nanosecond-reconfiguration-time optical switches is demonstrated using a hybrid approach, where Mach-Zehnder interferometric (MZI) switches provide low-loss, high-speed routing with short semiconductor optical amplifiers (SOAs) being integrated to enhance extinction. By repeatedly passing signals through a monolithic hybrid dilated 2×2 switch module in a recirculating loop, the potential performance of high-port-count switches using the hybrid approach is demonstrated. Experimentally, a single pass switch penalty of only 0.1 dB is demonstrated for the 2×2 module, while even after seven passes through the switch, equivalent to a 128×128 router, a penalty of only 2.4 dB is recorded at a data rate of 10 Gb/s.This is the author accepted manuscript. The final version is published in Optics Letters - http://www.opticsinfobase.org/ol/abstract.cfm?uri=ol-39-18-5244

Diagonal Ladders: A New Class of Models for Strongly Coupled Electron Systems

We introduce a class of models defined on ladders with a diagonal structure generated by $n_p$ plaquettes. The case $n_p=1$ corresponds to the necklace ladder and has remarkable properties which are studied using DMRG and recurrent variational ansatzes. The AF Heisenberg model on this ladder is equivalent to the alternating spin-1/spin-1/2 AFH chain which is known to have a ferrimagnetic ground state (GS). For doping 1/3 the GS is a fully doped (1,1) stripe with the holes located mostly along the principal diagonal while the minor diagonals are occupied by spin singlets. This state can be seen as a Mott insulator of localized Cooper pairs on the plaquettes. A physical picture of our results is provided by a $t_p-J_p$ model of plaquettes coupled diagonally with a hopping parameter $t_d$. In the limit $t_d \to \infty$ we recover the original $t-J$ model on the necklace ladder while for weak hopping parameter the model is easily solvable. The GS in the strong hopping regime is essentially an "on link" Gutzwiller projection of the weak hopping GS. We generalize the $t_p-J_p-t_d$ model to diagonal ladders with $n_p >1$ and the 2D square lattice. We use in our construction concepts familiar in Statistical Mechanics as medial graphs and Bratelli diagrams.Comment: REVTEX file, 22 pages (twocolumn), 35 figures inserted in text. 12 Table

Lattice-Boltzmann model for axisymmetric thermal flows

In this brief report, a thermal lattice-Boltzmann (LB) model is presented for axisymmetric thermal flows in the incompressible limit. The model is based on the double-distribution-function LB method, which has attracted much attention since its emergence for its excellent numerical stability. Compared with the existing axisymmetric thermal LB models, the present model is simpler and retains the inherent features of the standard LB method. Numerical simulations are carried out for the thermally developing laminar flows in circular ducts and the natural convection in an annulus between two coaxial vertical cylinders. The Nusselt number obtained from the simulations agrees well with the analytical solutions and/or the results reported in previous studies.Comment: 11 pages, 4 figure

Comparison between resistive and collisionless double tearing modes for nearby resonant surfaces

The linear instability and nonlinear dynamics of collisional (resistive) and collisionless (due to electron inertia) double tearing modes (DTMs) are compared with the use of a reduced cylindrical model of a tokamak plasma. We focus on cases where two q = 2 resonant surfaces are located a small distance apart. It is found that regardless of the magnetic reconnection mechanism, resistivity or electron inertia, the fastest growing linear eigenmodes may have high poloidal mode numbers m ~ 10. The spectrum of unstable modes tends to be broader in the collisionless case. In the nonlinear regime, it is shown that in both cases fast growing high-m DTMs lead to an annular collapse involving small magnetic island structures. In addition, collisionless DTMs exhibit multiple reconnection cycles due to reversibility of collisionless reconnection and strong ExB flows. Collisionless reconnection leads to a saturated stable state, while in the collisional case resistive decay keeps the system weakly dynamic by driving it back towards the unstable equilibrium maintained by a source term.Comment: 15 pages, 9 figure

A Real Space Renormalization Group Approach to Field Evolution Equations

A new operator formalism for the reduction of degrees of freedom in the evolution of discrete partial differential equations (PDE) via real space Renormalization Group is introduced, in which cell-overlapping is the key concept. Applications to 1+1-dimensional PDEs are presented for linear and quadratic equations which are first order in time.Comment: 8 pages, 10 ps figures. Accepted for publication in Phys. Rev.

Validation of satellite retrievals of cloud microsphysics and liquid water path using observations from FIRE

Cloud effective radii (r(sub e)) and cloud liquid water path (LWP) are derived from ISCCP spatially sampled satellite data and validated with ground-based pyranometer and microwave radiometer measurements taken on San Nicolas Island during the 1987 FIRE IFO. Values of r(sub e) derived from the ISCCP data are also compared to values retrieved by a hybrid method that uses the combination of LWP derived from microwave measurement and optical thickness derived from GOES data. The results show that there is significant variability in cloud properties over a 100 km x 80 km area and that the values at San Nicolas Island are not necessarily representative of the surrounding cloud field. On the other hand, even though there were large spatial variations in optical depth, the r(sub e) values remained relatively constant (with sigma less than or equal to 2-3 microns in most cases) in the marine stratocumulus. Furthermore, values of r(sub e) derived from the upper portion of the cloud generally are representative of the entire stratiform cloud. When LWP values are less than 100 g m(exp -2), then LWP values derived from ISCCP data agree well with those values estimated from ground-based microwave measurements. In most cases LWP differences were less than 20 g m(exp -2). However, when LWP values become large (e.g., greater than or equal to 200 g m(exp -2)), then relative differences may be as large as 50%- 100%. There are two reasons for this discrepancy in the large LWP clouds: (1) larger vertical inhomogeneities in precipitating clouds and (2) sampling errors on days of high spatial variability of cloud optical thicknesses. Variations of r(sub e) in stratiform clouds may indicate drizzle: clouds with droplet sizes larger than 15 microns appear to be associated with drizzling, while those less than 10 microns are indicative of nonprecipitating clouds. Differences in r(sub e) values between the GOES and ISCCP datasets are found to be 0.16 +/- 0.98 micron

BRST Cohomology of N=2 Super-Yang-Mills Theory in 4D

The BRST cohomology of the N=2 supersymmetric Yang-Mills theory in four dimensions is discussed by making use of the twisted version of the N=2 algebra. By the introduction of a set of suitable constant ghosts associated to the generators of N=2, the quantization of the model can be done by taking into account both gauge invariance and supersymmetry. In particular, we show how the twisted N=2 algebra can be used to obtain in a straightforward way the relevant cohomology classes. Moreover, we shall be able to establish a very useful relationship between the local gauge invariant polynomial $tr\phi^2$ and the complete N=2 Yang-Mills action. This important relation can be considered as the first step towards a fully algebraic proof of the one-loop exactness of the N=2 beta function.Comment: 22 pages, LaTeX, final version to appear in Journ. Phys.