Transverse Spread Research Articles

Non-diffusive corrections to the long-scale behaviour of ensembles of turbulent magnetic lines: application of the functional method

The transverse spreading of magnetic field lines in a turbulent plasma is investigated analytically in order to obtain a statistical characterization at large spatial scales. We develop a functional-integral method that allows us to calculate in a systematic way statistical averages of physical quantities that depend on the fluctuating field. The known magnetic diffusion coefficient for the shear-free case is corrected with a term arising from the assumption of a finite transverse correlation length. For the case with magnetic shear the functional method provides the appropriate framework for a perturbative approach based on diagram series.

Quantum-nondemolition measurement of atomic momentum.

We present a quantum-nondemolition measurement scheme in which one component of the momentum of an atom traversing a propagating light wave is measured by monitoring a quandrature phase of the field. We show how a selective version of the measurement may be used to reduce the transverse momentum spread of an atomic beam and we suggest how this scheme could be used to transversely cool a beam of atoms in the absence of spontaneous emission.

Simple formulae for the optimization of the FEL gain length including the effects of emittance, betatron oscillations and energy spread

Simple analytical formulae are presented for a quick optimization of the free electron laser (FEL) gain length for given values of radiation wavelength, electron beam current, normalized transverse emittance and energy spread. The optimization parameters include the gap size of the wiggler, the wiggler period and the betatron wavelength (in the case of external focusing). The method is based on the handy formulae for the FEL gain of a Gaussian beam [Y.H. Chin et al., Nucl. Instr. and Meth. A318 (1992) 481] including the effects of energy spread, emittance, and betatron oscillations of the electron beam. We have found a simple relation between the maximum FEL gain length and the optimum betatron wavelength for given energy spread, emittance, and gap size of the wiggler. When the emittance is about the radiation wavelength divided by 4π and the energy spread is negligible, this relation shows that the gain length is optimized if the betatron wavelength is chosen so that the betatron phase advances by a half radian in the gain length.

Containment of a high-temperature plasma in a cylindrical heavy shell with a solenoidal magnetic field

The authors consider questions connected with the behavior of a plasma in a magnetic field. The plasma studied, with its spaciotemporal parameters, occupies a position intermediate between stationary toroidal systems and pulsed spherical ones. The authors consider targets that incorporate elements of limiting systems, but occupy an intermediate position (except for the magnetic field). The behavior of a high-temperature plasma contained in a heavy cylindrical shell, which contains the transverse spreading, is investigated. The advantages of this system are explored. A simple theoretical model is developed using simple analytical equations that permits the lifetime of the plasma and the geometry of the target to be functions of the total energy, initial temperature, and initial plasma density. Conditions for a possible experiment validating this model are described. 4 refs., 1 fig.

Development of satellite mill and trial rolling of profiled metal strip

A new type of compact continuous mill called the “Satellite mill” has been developed to produce profiled metal strip from flat strip. This mill consists of one large-diameter driven roll (central roll) and five smaller rolls (satellite rolls) arranged along the periphery of the central roll. A strip is continuously rolled at five gaps between the central roll and the satellite rolls. All rolls are driven at an equal roll peripheral speed to promote transverse metal flow or lateral spread. Guide shoes are provided between the adjacent satellite rolls and are supported with two adjacent satellite rolls. They prevent a strip from bulging or buckling. A test mill was constructed, and rolling experiments have been performed on the production of T-shaped or U-shaped profiled aluminum strip. The deformation- load characteristics were investigated and compared with those of conventional rolling. As a result, in the satellite mill rolling operation, elongation was suppressed. Lateral spread was enhanced, and the profile of the product cross section was significantly improved. Consequently, the new rolling process was found to be forming of profiled metal strip.

Surface Electromigration and Diffusion of Ag on Ge(111)

Spread of a deposited Ag patch with coverage of several monolayers over Ge(111)-c(2×8) was observed with scanning Auger electron spectroscopy when the Ge substrate was heated by DC current. The spread-out Ag layer was uniform in coverage (1.0 monolayer) and structure (√3×√3-R30°) with a sharp leading edge. The longitudinal spread parallel to the current, dominated by the electromigration, was preferential towards the cathode with linear proportionality to the time of the DC power supply, while the transverse spread was well balanced and proportional to the square root of the time, consistently with the surface diffusion. The transverse spread exhibited a temperature dependence with the thermal activation energy of 0.50±0.1 eV. Theoretical expressions for the spreads were derived and compared with the data. The effective charge of the Ag adatom was as large as +(13±2)q.

Tracer dispersion in stratified porous media: influence of transverse dispersion and gravity

We have studied tracer dispersion in stratified media made of alternating layers of glass beads with different permeabilities. Both transmission experiments and echo experiments, in which the tracer is first injected into the sample and then pumped back through a detector, have been used. When there is no exchange between layers, the transmission dispersion curves give the permeability contrast, while the echo curves give the dispersivity of individual layers (namely their grain size if they are homogenous). If the transverse transport between layers homogenizes the concentration across the sample, echo and transmission dispersivities are identical and related to the layer thickness and the transverse dispersivity. We observed the transition between both regimes as the flow velocity decreases in thin-layered samples. In samples with thicker layers, transverse tracer spreading requires more time; in addition, strong gravity effects associated to very small density variations with the tracer concentration were observed.

Spread in sheet rolling: A comparison using experiments, analytical solutions and numerical techniques

Two models have been developed to predict transverse deformation and spread during sheet rolling. The asymptotic model (ASY) is an approximate method that yields analytical results, but contains a number of modeling restrictions. Short computation time is the primary advantage of the asymptotic solution. The lateral flow model (LFM) is a more robust numerical method, in the sense that more general constitutive and interface behavior can be considered. The two models are briefly described, compared to each other and to experimental data. The comparisons exhibit good agreement between the two models and between models and experimental data.

A method of studying the influence of fertilizer particle size on the distribution from a twin-disc spreader

The object of this work was to study the influence of fertilizer particle size on the distribution from a typical spreader design. The fertilizer, spread from a stationary twin-disc spreader, was collected in square trays positioned in a regular pattern in the field covered by the spreader. Collected samples were weighed, and the particle shape and size determined by an image processing technique. Based on these results the spatial distributions of mass and particle size were determined. It is shown that the shape of the transverse spread pattern calculated from the spatial mass distribution coincides well with the corresponding shape from a moving spreader. The measured particle diameters were sorted into particle classes covering five commonly used size intervals. From the spatial mass distribution the corresponding transverse spread pattern was calculated for each of four dominating classes. A method of predicting the transverse spread pattern for a mixture of particle classes isdescribed and an example is given. To obtain continuous distributions, interpolation was performed. The distribution of particles of different sizes is visualized using three-dimensional graphics.

Effects of Banded Post‐Tensioning in Prestressed Concrete Flat Slab

This study investigates strain distribution in regions immediately adjacent to the transverse post-tensioning bands in a new class of flat slab reinforced concrete bridges employing bidirectional post-tensioning. While longitudinal post-tensioning is uniform, transverse strands are concentrated in the vicinity of column lines. The currently applied design assumes that the transverse post-tensioning effect spreads along straight lines at a specified angle. Size of a laboratory model slab is chosen so that this assumption may be checked for validity. A load schedule is used to study strain distribution for a variety of tendon and load patterns. Values of strain at gage locations as predicted by a finite element analysis are compared to the actual data collected. Reasonably good correlation between laboratory data and the computer program allows increased confidence in numerical simulation. Following testing and analysis of elastic loads, the slab is loaded to impose a punch-through shear failure. Shear formulas recommended by the American Concrete Institute and other researchers are compared with experimental failure and reserve capacity loads.

Shape forming and lateral spread in sheet rolling

An approximate theory to describe transverse flow and lateral spread in sheet rolling is developed using asymptotic methods. The formulation is based on the thin sheet approximation. The approach is relevant for analysing spread in conventional rolling and also for shape rolling. Predictions from the theory are illustrated with a few examples. This includes: (1) a thorough study of lateral effects in conventional rolling, (2) a model of deformed rolls and (3) rib-rolling. The theory shows that the spread formula depends on the front and back tensions. This is a new feature. The dependence on the roll friction is also identified.

Quantitative, three‐dimensional analysis of granule cell dendrites in the rat dentate gyrus

The three-dimensional organization of dentate granule cell dendritic trees has been quantitatively analyzed with the aid of a computerized microscope system. The dendrites were visualized by iontophoretic injection of horseradish peroxidase into individual granule cells in the in vitro hippocampal slice preparation. Selection criteria insured that the analyzed cells were completely stained and that only neurons with two or fewer cut dendrites in the distal portion of the molecular layer were analyzed. Twenty-nine of the 48 sampled granule cells had no cut dendrites. The granule cells had between one and four primary dendrites. Granule cell dendritic branches were covered with spines and most extended to the hippocampal fissure or pial surface. The mean total dendritic length was 3,221 microns with a range from 2,324 microns to 4,582 microns. The dendrites formed an elliptical plexus with the transverse spread averaging 325 microns and the spread in the septotemporal axis averaging 176 microns. On individual neurons, the maximum branch order ranged from four to eight and the number of dendritic segments ranged from 22 to 40. Approximately 63% of the dendritic branch points occurred in a zone that included the granule cell layer and the inner one-third of the molecular layer. The dendritic tree was organized so that, on average, 30% of the length was in the granule cell layer and proximal third of the molecular layer, 30% was in the middle third, and 40% was in the distal third. Comparisons were made between the dendrites of granule cells in the suprapyramidal and infrapyramidal blades of the dentate gyrus. Suprapyramidal cells had a significantly greater total dendritic length than infrapyramidal cells, their transverse spread was higher, and they had a greater number of dendritic segments. When neurons in the suprapyramidal blade were further subdivided on the basis of somal position within the depth of the cell body layer, superficial neurons were found to have a greater number of primary dendrites, more elliptical trees, and larger transverse spreads of their dendrites. There were no significant differences in dendritic segment number or total dendritic length between superficial and deep cells.

Effect of Buoyancy on Transverse Mixing in Streams

A dye tracer study has been conducted in a large recirculating flume for the purpose of examining the influence of buoyancy on transverse mixing in streams. Using Rhodamine WT dye, the transverse spread of a freshwater discharge into a saline receiving stream was measured downstream from the release point. The discharge emanated from a circular pipe 2.54 cm in diameter, aligned parallel to the stream flow and located at mid‐depth at the flume sidewall. Fluo‐rometer samples were obtained throughout the cross section at downstream stations spaced 18‐24 m apart. The transverse variance of the depth‐averaged concentration distribution was determined at each station. Using a dimensionless parameter reflecting the ratio of the buoyancy input to the stream turbulent intensity, we present findings as to when the effects of buoyancy must be included in the analysis of transverse mixing. These findings illustrate the potential for greatly enhanced transverse mixing in cases of buoyant discharges, with a good deal of variability depending on discharge and stream characteristics.

Modification of the NPE computer code to describe the propagation of axisymmetric sound beams in infinite media

NPE is a nonlinear progressive wave equation computer code developed by McDonald and Kuperman [Comp. Math. Appl. 11, 843–851 (1985)] to evaluate transient propagation in acoustic waveguides. It is suitable for two-dimensional phenomena, as well as for radial propagation of azimuthally symmetric waves. The present study describes the modifications required to employ NPE for the evaluation of axially propagation axisymmetric waves, particularly those associated with sound beams radiated by a baffled piston. In addition to implementing a formulation in which the propagation is essentially parallel to the axis of a set of cylindrical coordinates, it is necessary to account for the transverse spreading of the beam into an infinite medium. Another issue is the manner in which the initial waveform input to NPE is obtained. The predictions of NPE for a linear sound beam when the input is obtained from the King integral, which is an exact solution in quadrature form, are compared to the results obtained for a simple input based on assumption of planar wave behavior in the vicinity of the transducer. The results in both cases are also compared to the analytical solution for the farfield radiation pattern.

“Diffraction-free” optical beams in inverse free electron laser accelerators

“Diffraction-free” optical beams correspond to exact solutions of the wave equation in free space with the remarkable property that they propagate with negligible transverse spreading for distances much larger than the Rayleigh range. The requirement for this to occur is a large aperture. Using a 2D computer code, we find that these optical beams will also propagate with negligible diffraction even when perturbed by the electron beam in an IFEL; indeed they match well the FEL requirement for the accelerator. The numerical simulations are performed for the proposed facility at Brookhaven in which λs = 10 μm, B = 1.5 T (linearly tapered lw = 1.31−6.28 cm) and the optical beam power is either 8 × 1011 W or 2.3 × 1010 W. Approximately 70% of the electrons constituting a beam of current 5 mA or 15 A, radius 0.14 mm and initial energy of 50 MeV is accelerated at 50 MeV/m.

Confinement and Bed‐Friction Effects in Shallow Turbulent Mixing Layers

The transverse development of the turbulent mixing layers in an open channel flow of shallow water depth was investigated experimentally to study the confinement and bed-friction effects. Mean and r.m.s. velocity profiles were obtained, using a hot-film anemometer, at a number of cross sections downstream of a splitter plate between two streams of different velocities. In the confinement between the free surface and the channel bed, the transverse spreading rate of the shallow mixing layer was initially twice as large as the nominal rate for the free mixing layer. The spreading rate reduces with distance from the splitter plate under the stabilizing influence of bed-friction, and diminishes to zero in the far field region when the bed-friction number exceeds a critical value of about 0.09.

The Heidelberg Heavy Ion Test Storage Ring TSR

The Heavy Ion Test Storage Ring TSR [1] is an experimental facility for accelerator, atomic and nuclear physics studies presently under construction at the Heidelberg Max-Planck-Institute. The storage ring is designed for heavy ions of up ∼ 30 MeV/u at a charge to mass ratio of q A = 0.5 , corresponding to a magnetic rigidity of B ρ = 1.5 Tm. Phase space compression using electron cooling [2] will be applied in the TSR to produce ion beams of extreme quality and at the same time to reduce the large transverse emittances and momentum spread which build up in the sophisticated injection technique used to reach heavy ion currents in the mA range. The beam's equilibrium emittance and momentum distribution after cooling will be limited just by intrabeam scattering and the interaction in an internal target. Furthermore the very broad rigidity acceptance of the TSR will permit operation with simultaneous storage of several neighboring charge states of ions. This report will review the major design features and give the status of the ring project.

An empirical treatment of nonrelattvistic proton beam spreading

Transverse spreading in proton transmission microscopy limits to some degree the amount of resolution that is possible from the beam. A semi-empirical expression is given which estimates the lateral displacement of a proton beam as it passes through a material. The angular deflections are assumed to be primarily due to small angle Coulomb interactions. The expression includes a proportionality constant which is evaluated with the TRIM ion transport code. The results are compared to experimental data when available.

Developmental transitions of myosin isoforms and organisation of the lateral muscle in the teleost Dicentrarchus labrax (L.).

In Dicentrarchus labrax (the sea bass) the differentiation of lateral muscle fibres occurs at different stages and in different ways in the superficial (red), intermediate (pink) and deep (white) regions of the myotome. At hatching the myotomes are composed of presumptive white and red fibres, the latter forming a superficial monolayer present only near the transverse septum. At this stage, differences between the fibre types are mainly ultrastructural. From their different reactions with isoform-specific antibodies to mullet myosin, and the appearance of histochemical mATPase activity, it appears that in both red and white muscle fibres there is a transition in myosin composition from an early larval form (L1R and L1W respectively) to a late larval form (L2R and L2W) and then to the isoforms typical of adult red and white muscle. The transition from L1W to L2W in the deep muscle occurs very rapidly and early in larval life (between 10 and 28 days), whereas the equivalent transition in the superficial muscle (from L1R to L2R) is a gradual process beginning in fibres near the transverse septum and spreading hypo- and epi-axially as this layer grows around the deep muscle. The definitive adult forms (AR and AW), distinguishable by the appearance of characteristic histochemical myosin ATPase activity, are present in the superficial red muscle by 80 days, but later in the deep white muscle (by 20 months), respectively. Compared to the superficial red and deep white muscle, the intermediate (pink) muscle layer first appears relatively late (80 days), but then acquires the histo- and immunohistochemical profile characteristic of the adult form much more rapidly.(ABSTRACT TRUNCATED AT 250 WORDS)

Important aspects of linac beams for food irradiation

Linac based irradiators will require careful design before they can be routinely adopted for the radiation processing of food. The transverse emittance and energy spread from simple injectors provide a significant challenge to the design of a beam delivery system which must handle high power especially in photon mode. Any nonuniform current distribution at the plane of the product is further complicated by large dose variations near the air/product interface, even with simple geometries. The paper describes the use of methods developed at AECL to control and monitor linac behaviour as well as electron interactions at the product surface. It also reports on activation cross-section measurements and particularly on neutron yields from composite targets, designed to monitor the energy of accelerators used in food applications.