Radial Separation Research Articles

Stacking with stochastic cooling

Accumulation of large stacks of antiprotons or ions with the aid of stochastic cooling is more delicate than cooling a constant intensity beam. Basically the difficulty stems from the fact that the optimized gain and the cooling rate are inversely proportional to the number of particles ‘seen’ by the cooling system. Therefore, to maintain fast stacking, the newly injected batch has to be strongly ‘protected’ from the Schottky noise of the stack. Vice versa the stack has to be efficiently ‘shielded’ against the high gain cooling system for the injected beam. In the antiproton accumulators with stacking ratios up to 105 the problem is solved by radial separation of the injection and the stack orbits in a region of large dispersion. An array of several tapered cooling systems with a matched gain profile provides a continuous particle flux towards the high-density stack core. Shielding of the different systems from each other is obtained both through the spatial separation and via the revolution frequencies (filters). In the ‘old AA’, where the antiproton collection and stacking was done in one single ring, the injected beam was further shielded during cooling by means of a movable shutter. The complexity of these systems is very high. For more modest stacking ratios, one might use azimuthal rather than radial separation of stack and injected beam. Schematically half of the circumference would be used to accept and cool new beam and the remainder to house the stack. Fast gating is then required between the high gain cooling of the injected beam and the low gain stack cooling. RF-gymnastics are used to merge the pre-cooled batch with the stack, to re-create free space for the next injection, and to capture the new batch. This scheme is less demanding for the storage ring lattice, but at the expense of some reduction in stacking rate. The talk reviews the ‘radial’ separation schemes and also gives some considerations to the ‘azimuthal’ schemes.

Equilibrium Density Distribution of a Two-Species Plasma with a Single Sign of Charge

The equilibrium density distribution of a nonneutral plasma consisting of two species of particles is studied theoretically on a basis of a cold two-fluid model. We request an equilibrium state with rigid rotation and seek the distribution with minimum energy satisfying the conservation of the particle numbers and the canonical angular momentum. The analysis indicates that the overlapping of the distributions of the fluids is allowed only while the total density is below the Brillouin density limit of the heavier fluid. With increasing number of the lighter particles the heavier fluid is pushed out and surrounds the lighter fluid with increasing radial separation. The rotation of the heavier fluid changes from the low frequency branch to the upper branch as the density of lighter particles further increases. When the number of the heavier particles rotating in the low branch is increased, the inner edge of the heavier fluid shrinks to compress the lighter fluid, but when the rotation is switched to the upper branch the outer edge of the lighter fluid expands.

Apparatus and method incorporating an ultrasound transducer onto a delivery member

A medical device assembly and method provides an ultrasound transducer mounted onto a catheter shaft. The ultrasound transducer is mounted such that there is a radial separation between the transducer and the underlying catheter shaft. The transducer is mounted on support structures which do not bridge the gap between the transducer and delivery member. The location of the support structures provides for an “airbacked” transducer that is very efficient and prevents heat build-up in the materials in contact therewith.

The concomitants of a prehomogeneous vector space

The classical method of radial separation of variables is applied to gain some information about the concomitants, also known as relatively equivariant polynomial maps or covariants, of a class of prehomogeneous vector spaces. Particular attention is payed to concomitants that are themselves prehomogeneous. The results are applied to classify all prehomogeneous concomitants of several examples of interest in arithmetic.

Accurate cylindricity evaluation with axis-estimation preprocessing

Evaluating cylindricity is a very important application in metrology. In this paper, we focus on cylindricity evaluation based on radial form measurements. The standard characterization of cylindricity is the notion of zone cylinder, i.e. the cylindrical crown contained between two coaxial cylinders with minimum radial separation and containing all the data points. Unfortunately, the construction of the zone cylinder is a very complex geometric problem, which can be formulated as a nonlinear optimization. Recently a new method (referred to here as the hyperboloid method) has been discussed, which avoids the direct construction of the zone cylinder of a point set, but approximates it with guaranteed accuracy through a computationally very efficient iterative process based on a linearization of the underlying problem. The iterations can be viewed as the construction of a sequence of “zone hyperboloids” tending to the desired “zone cylinder.” An important requirement of the method, however, is that the initial position of the cylindrical specimen axis be nearly vertical, since significant deviations from this condition essentially invalidate the process. It is the purpose of this paper to remove this shortcoming of the hyperboloid technique by providing a simple procedure for appropriately initializing the data (axis estimation). Axis estimation and the hyperboloid technique constitute an integrated methodology for cylindricity evaluation, which is currently the most effective. The theoretical foundations of the method are reviewed from a viewpoint that highlights its essential features and intuitively explains its effectiveness. The analytical discussion is complemented by experimental data concerning a few significant samples.

Magnetic Structure of a Dark Bok Globule

The thermal dust continuum emission at 848 μm from the globule CB 068, a Class 0 young stellar object (YSO), reveals strong linear polarization percentage values (up to 11%) in two polarized-intensity regions located on either side of the center, away from the twin CO outflows. At the 5% polarized intensity level, the two highly polarized regions have a radial separation of 0.01 pc from the center of the Bok globule. The two polarized regions are located on either side of the axis of the twin CO outflows, with polarization contours paralleling the outflows. The linear polarization orientation leads us to deduce that, in the inner part of the polarized-intensity regions, the electric field vector roughly follows the boundary of a pseudodisk or bar (the pseudodisk or bar was previously detected both in dust and in ammonia emission). The linear polarization orientation, within a radius of 0.03 pc, can be matched roughly to an infalling halo-to-disk magnetic field morphology, excluding the regions of the external envelope and near the CO outflows. On a 0.04 pc scale, our model predictions for CB 068 give a pseudodisk diameter of about 8800 AU. We predict a magnetic field strength (over 0.03 pc) of about 150 μG, which comes about from the Chandrasekhar-Fermi method (via the ratio of the line of sight velocity dispersion to the polarization angle dispersion).

Coorbital Periodic Orbits in the Three Body Problem

We consider the dynamics of coorbital motion of two small moons about a large planet which have nearly circular orbits with almost equal radii. These moons avoid collision because they switch orbits during each close encounter. We approach the problem as a perturbation of decoupled Kepler problems as in Poincare's periodic orbits of the first kind. The perturbation is large but only in a small region in the phase space. We discuss the relationship required among the small quantities (radial separation, mass, and minimum angular separation). Persistence of the orbits is discussed.

Edge turbulence during ergodic divertor operation in Tore Supra

We report new measurements of turbulence during ergodic divertor (ED) operation. At low density, some de-correlation of the turbulence is observed with a decrease of the long timescale structures. It is shown that the typical time involved is compatible with a de-correlation mechanism through radial separation of the B field lines by the ED, with an associated parallel length of the order of the distance between two modules of the ED. This observation reinforces the conclusion drawn in [1] and based on computer simulations. The situation changes when the density is increased: the turbulence level is found to increase. At the highest density, the structure of the turbulent signal is modified and the bursty behaviour suppressed by the ED at low density reappears. These observations lead to the conclusion that the turbulence measured at high density is not sensitive to the ED stabilization effect. This indicates that it could be carried by the ions.

In K-edge extended X-ray absorption fine structure of InGaN epilayers and quantum boxes

Extended X-ray absorption fine structure (EXAFS) above the In K-edge of luminescent InGaN heterostructures provides a unique probe of local structure on an atomic length scale. Through a process of fitting the experimental spectrum, we can refine a model of the probable configuration (the atom type, co-ordination number and radial separation) of the first few shells of neighbouring atoms in the vicinity of a selected probe atom. We present here, for the first time, the In K-edge EXAFS spectrum of an ultrathin, uncapped ‘quantum box’ (QB) sample and compare it to results we have obtained previously on thick luminescent InGaN epilayers with a range of composition. While the epilayers resemble simple alloys, more or less, the QB sample reveals itself to consist of a two-phase mixture of InN and dilute InGaN alloy. The use of EXAFS to distinguish the local In environments of different InGaN-based heterostructures is likely to provide key information to unlock the puzzle of the origin of luminescence in these important commercial semiconductors.

Stellar orbits near Sagittarius A

The SHARP/NTT stellar proper motion data now cover an interval from 1992 to 2000 and allow us to determine orbital accelerations for some of the most central stars of the Galaxy. We confirm the stellar acceleration measurements obtained by Ghez et al. with NIRC at the Keck telescope. Our analysis differs in three main points from that of Ghez et al.: (1) we combine the high-precision but shorter time-scale NIRC/Keck data with the lower precision but longer time-scale SHARP/NTT data set; (2) we statistically correct the observed accelerations for geometrical projection effects; (3) we exclude star S8 from the analysis of the amount and position of the central mass. From the combined SHARP/NTT and NIRC/Keck data sets we show that the stars S2, and most likely S1 and S8 as well, are on bound, fairly inclined (60°<i<80°), and eccentric (0.4<e<0.95) orbits around a central dark mass. The combination of both data sets results in a position of this central mass of and of the nominal radio position of Sgr A*. The mean statistically corrected enclosed mass derived from accelerations is Macc=(5±3)×106 M⊙ with current radial separations of S1 and S2 from Sgr A* of about 8–10 mpc. This enclosed mass estimate is derived from individual stellar orbits as close to the massive black hole at the centre of the Milky Way as currently possible. Although the uncertainties are large, this estimate is fully consistent with the enclosed mass range of (2.6–3.3)×106 M⊙ derived by Genzel et al. from radial and/or proper motion velocities of a homogenized sample of sources. Star S8 was excluded from the analysis, since for the current proper motion velocity and radial separation from the centre we find that the measured acceleration requires orbital motion around a compact object with a mass in excess of 3×106 M⊙. The data suggest either that this star was or is subject to a close interaction with a different object or that its position measurements are influenced by the emission of a different cluster star. Therefore we base the analysis of the enclosed mass solely on the available data for stars S1 and S2. We also discuss two late-type stars with projected separations from Sgr A* of about 0.5 and 1 arcsec. In addition to proper motions, these stars have known radial velocities. Orbit calculations indicate that such stars are very likely at larger physical distances from the centre and part of the larger scale central stellar cluster with a core radius of approximately 0.3 pc.

MeV carbon cluster-induced pulse height defect in a surface barrier detector

The pulse height defect (PHD) of surface barrier detectors (SBDs) bombarded by carbon clusters C n ( n=2–10) with energies of 1 and 2 MeV per carbon atom was measured. At the same projectile velocity the difference between residual cluster PHD and the n-fold PHD of each of the n cluster constituents is found to be proportional to n( n−1). This difference decreases when the thickness of the gold entrance window of the detector is increased. This is due to the smaller energy deposited in the depletion zone of the detector and not due to the separation of the cluster constituents while passing the window. Large radial separation distances of the cluster constituents must be achieved before the PHD vanishes. The model of Finch et al. [Nucl. Instr. and Meth. 163 (1979) 467] developed for atomic ions reproduces the data qualitatively.

A new strategy for circularity problems

The evaluation of circularity based on the minimum zone criterion as a non-linear and non-convex problem, which requires a substantial amount of computational effort in general, is investigated. A new strategy for improving the computational efficiency by collecting data points at the farthest and nearest locations from current minimum radial separation center until all collected data points meet the optimum criterion is proposed. A number of mathematical models developed in this paper indicate that the minimum circularity can be determined by using a small number of critical data points. The validated results show that the proposed strategy offers an effective way to identify the critical data points at the early stage of computation and gives an efficient approach to solve the circularity problems, especially when the number of data point is large.

An optimum feedback coil position for active stabilization of resistive wall modes

A study on the feedback stabilization of resistive wall modes in a cylindrical geometry is presented. The effect of radial separation of feedback coils from sensor loops is investigated. It is shown that there is an optimum radial position for feedback coils where sideband mode coupling parameter is minimized, hence enhancing the efficacy of a system of coils for feedback stabilization of resistive wall modes.

Sphericity error evaluation: theoretical derivation and algorithm development

Several methods for the evaluation of sphericity error exist. The Minimum Radial Separation (MRS) spheres method is a method that has been studied by several researchers. In the MRS criterion, two concentric spheres at minimum radial separation must be found such that they contain all points on the actual spherical surface. The existing procedures for finding MRS spheres are either too complex and time consuming or do not provide an optimal solution to the sphericity error evaluation problem. In this paper, mathematical optimization concepts are utilized to develop a theory and an algorithm for the evaluation of sphericity error based on MRS criterion. Results indicate that the algorithm is fast and accurate in providing optimal solution to the sphericity error evaluation problem.

Structural Properties of Two-Component Coulomb Crystals in Linear Paul Traps

We report on structural properties of two-component Coulomb crystals in a linear Paul trap. The crystals consist of two laser cooled ion species, 24Mg+ and 40Ca+. The lighter 24Mg+ ions form an inner cylindrical crystal structure surprisingly similar to that of an infinitely long single component crystal, while the outermost shell of the surrounding 40Ca+ ions have a spheroidal shape, which is highly insensitive to the presence of the 24Mg+ ions. Observed changes in the radial separation of the two ion species with the radius of the inner cylindrical crystal is explained by a simple model.

Sphericity error evaluation: theoretical derivation and algorithm development

Several methods for the evaluation of sphericity error exist. The Minimum Radial Separation (MRS) spheres method is a method that has been studied by several researchers. In the MRS criterion, two concentric spheres at minimum radial separation must be found such that they contain all points on the actual spherical surface. The existing procedures for finding MRS spheres are either too complex and time consuming or do not provide an optimal solution to the sphericity error evaluation problem. In this paper, mathematical optimization concepts are utilized to develop a theory and an algorithm for the evaluation of sphericity error based on MRS criterion. Results indicate that the algorithm is fast and accurate in providing optimal solution to the sphericity error evaluation problem.

Contribution to the minimax evaluation of circularity error

The measurement of form and profile errors of mechanical parts involves the fitting of continuous surfaces, curves or lines to a set of coordinate points returned by inspection instrumentation. For circularity, both ASME (Y14.5M - 1994 [1995]) and ISO (1R 1001, 1983) prescribe the fitting of a pair of concentric circles with minimum radial separation to a set of discrete coordinate points sampled around the periphery of a surface of revolution at a plane perpendicular to the axis of revolution. This criterion is often referred to as the minimax or minimum zone criterion. The contribution of this paper is to provide a refinement to the basic results of both Ventura and Yeralan and Etesami and Qiao as an improved path to the optimum solution to the minimax roundness problem. The proposed solution applies the Voronoi diagram approach to the P2( k ) problem to show that the optimum solution can only reside at a particular type of vertex of the MAX region. This particular type of vertex corresponds to one of the possible type (ii) solutions of Ventura and Yeralan's P2( k ) problem. In other words, Etesami and Qiao's approach need not examine all vertices of the MAX region and Ventura and Yeralan's P2( k ) solution need not examine any type (i) solutions. This results in a substantial saving in time required to identify the optimum solution and would be useful for applications that return a large number of points such as dedicated roundness testers, axis of rotation analysers or telescopic ball bars.

Plasma and magnetic field correlations in the solar wind

Data from multiple spacecraft are used to determine solar wind plasma and interplanetary magnetic field (IMF) correlation coefficients. These correlation coefficients provide information on solar wind scale lengths and the predictive capability of upstream monitors for space weather purposes. Previous work has looked at plasma and IMF correlation coefficients independently and used much smaller databases than those used in this study. We use data sets from 1977–1984 and 1994–1998 and calculate plasma and IMF correlation coefficients. The IMF correlation coefficients are, on average, slightly higher than those for plasma. Dependence of the correlation coefficients on the spatial separation of the spacecraft is important for placement of upstream monitors; we find a small dependence on the radial separation of the spacecraft but a very strong dependence on spacecraft separation in the YZ (GSE) plane. Scale lengths perpendicular to the flow are about 45 Earth radii (RE) for the IMF components, 70 RE for the speed and IMF magnitude, and over 100 RE for the density. Radial scale lengths are of the order of 400 RE. The plasma and IMF correlation coefficients are larger when values of the density standard deviation are high and when the IMF direction is perpendicular to X (GSE). Front orientations are similar for both plasma and IMF features and are more perpendicular than the average field direction.

Discovery of a Pair of [CLC][ITAL]z[/ITAL][/CLC] = 4.25 Quasars from the Sloan Digital Sky Survey

We report the discovery of a pair of z = 4.25 quasars with a separation of 33''. The brighter of the two objects was identified as a high-redshift quasar candidate from Sloan Digital Sky Survey multicolor imaging data, and the redshift was measured from a spectrum obtained with the Hobby-Eberly Telescope. The slit orientation of this observation by chance included another quasar, approximately 1 mag fainter and having the same redshift as the target. This is the third serendipitous discovery of a z > 4 quasar. The differences in the relative strengths and profiles of the emission lines suggest that this is a quasar pair and not a gravitational lens. The two objects are likely to be physically associated; the projected physical separation is approximately 210 h kpc and the redshifts are identical to ≈0.01, implying a radial physical separation of 950 h kpc or less. The existence of this pair is strong circumstantial evidence that z ~ 4 quasars are clustered.

Determining a Pair of Concentric Spheres for Assessing Sphericity Errors Using Discrete Voronoi Diagrams

In this paper, we propose a new procedure for computing a pair of concentric spheres with a minimum radial separation for assessing sphericity errors by constructing discrete farthest and nearest Voronoi diagrams. The properties of 3D Voronoi diagrams are exploited to determine a pair of concentric spheres with minimum radial separation such that all the data points are bounded by these two spheres. A voxel map is used to construct a discrete Voronoi diagram. The convergence of the proposed procedure to the true global minimum sphericity error is guaranteed. This procedure works for various forms of spherical measurement data, including scattered measurement points. The proposed procedure is simple in implementation and effective in computation.