Resolving velocity space dynamics in continuum gyrokinetics

Many plasmas of interest to the astrophysical and fusion communities are weakly collisional. In such plasmas, small scales can develop in the distribution of particle velocities, potentially affecting observable quantities such as turbulent fluxes. Consequently, it is necessary to monitor velocity space resolution in gyrokinetic simulations. In this paper, we present a set of computationally efficient diagnostics for measuring velocity space resolution in gyrokinetic simulations and apply them to a range of plasma physics phenomena using the continuum gyrokinetic code GS2. For the cases considered here, it is found that the use of a collisionality at or below experimental values allows for the resolution of plasma dynamics with relatively few velocity space grid points. Additionally, we describe implementation of an adaptive collision frequency which can be used to improve velocity space resolution in the collisionless regime, where results are expected to be independent of collision frequency.Comment: 20 pages, 11 figures, submitted to Phys. Plasma

Pair distribution function and structure factor of spherical particles

The availability of neutron spallation-source instruments that provide total scattering powder diffraction has led to an increased application of real-space structure analysis using the pair distribution function. Currently, the analytical treatment of finite size effects within pair distribution refinement procedures is limited. To that end, an envelope function is derived which transforms the pair distribution function of an infinite solid into that of a spherical particle with the same crystal structure. Distributions of particle sizes are then considered, and the associated envelope function is used to predict the particle size distribution of an experimental sample of gold nanoparticles from its pair distribution function alone. Finally, complementing the wealth of existing diffraction analysis, the peak broadening for the structure factor of spherical particles, expressed as a convolution derived from the envelope functions, is calculated exactly for all particle size distributions considered, and peak maxima, offsets, and asymmetries are discussed.Comment: 7 pages, 6 figure

The exact evaluation of the corner-to-corner resistance of an M x N resistor network: Asymptotic expansion

We study the corner-to-corner resistance of an M x N resistor network with resistors r and s in the two spatial directions, and obtain an asymptotic expansion of its exact expression for large M and N. For M = N, r = s =1, our result is R_{NxN} = (4/pi) log N + 0.077318 + 0.266070/N^2 - 0.534779/N^4 + O(1/N^6).Comment: 12 pages, re-arranged section

Accurate Transfer Maps for Realistic Beamline Elements: Part I, Straight Elements

The behavior of orbits in charged-particle beam transport systems, including both linear and circular accelerators as well as final focus sections and spectrometers, can depend sensitively on nonlinear fringe-field and high-order-multipole effects in the various beam-line elements. The inclusion of these effects requires a detailed and realistic model of the interior and fringe fields, including their high spatial derivatives. A collection of surface fitting methods has been developed for extracting this information accurately from 3-dimensional field data on a grid, as provided by various 3-dimensional finite-element field codes. Based on these realistic field models, Lie or other methods may be used to compute accurate design orbits and accurate transfer maps about these orbits. Part I of this work presents a treatment of straight-axis magnetic elements, while Part II will treat bending dipoles with large sagitta. An exactly-soluble but numerically challenging model field is used to provide a rigorous collection of performance benchmarks.Comment: Accepted to PRST-AB. Changes: minor figure modifications, reference added, typos corrected

On the degrees of freedom of a semi-Riemannian metric

A semi-Riemannian metric in a n-manifold has n(n-1)/2 degrees of freedom, i.e. as many as the number of components of a differential 2-form. We prove that any semi-Riemannian metric can be obtained as a deformation of a constant curvature metric, this deformation being parametrized by a 2-for

Massive Quiescent Cores in Orion. -- II. Core Mass Function

We have surveyed submillimeter continuum emission from relatively quiescent regions in the Orion molecular cloud to determine how the core mass function in a high mass star forming region compares to the stellar initial mass function. Such studies are important for understanding the evolution of cores to stars, and for comparison to formation processes in high and low mass star forming regions. We used the SHARC II camera on the Caltech Submillimeter Observatory telescope to obtain 350 \micron data having angular resolution of about 9 arcsec, which corresponds to 0.02 pc at the distance of Orion. Our analysis combining dust continuum and spectral line data defines a sample of 51 Orion molecular cores with masses ranging from 0.1 \Ms to 46 \Ms and a mean mass of 9.8 \Ms, which is one order of magnitude higher than the value found in typical low mass star forming regions, such as Taurus. The majority of these cores cannot be supported by thermal pressure or turbulence, and are probably supercritical.They are thus likely precursors of protostars. The core mass function for the Orion quiescent cores can be fitted by a power law with an index equal to -0.85$\pm$0.21. This is significantly flatter than the Salpeter initial mass function and is also flatter than the core mass function found in low and intermediate star forming regions. Thus, it is likely that environmental processes play a role in shaping the stellar IMF later in the evolution of dense cores and the formation of stars in such regions.Comment: 30 pages, 10 figures, accepted by Ap

A High-Mass Protobinary System in the Hot Core W3(H2O)

We have observed a high-mass protobinary system in the hot core W3(H2O) with the BIMA Array. Our continuum maps at wavelengths of 1.4mm and 2.8mm both achieve sub-arcsecond angular resolutions and show a double-peaked morphology. The angular separation of the two sources is 1.19" corresponding to 2.43X10^3 AU at the source distance of 2.04 kpc. The flux densities of the two sources at 1.4mm and 2.8mm have a spectral index of 3, translating to an opacity law of kappa ~ nu. The small spectral indices suggest that grain growth has begun in the hot core. We have also observed 5 K components of the CH3CN (12-11) transitions. A radial velocity difference of 2.81 km/s is found towards the two continuum peaks. Interpreting these two sources as binary components in orbit about one another, we find a minimum mass of 22 Msun for the system. Radiative transfer models are constructed to explain both the continuum and methyl cyanide line observations of each source. Power-law distributions of both density and temperature are derived. Density distributions close to the free-fall value, r^-1.5, are found for both components, suggesting continuing accretion. The derived luminosities suggest the two sources have equivalent zero-age main sequence (ZAMS) spectral type B0.5 - B0. The nebular masses derived from the continuum observations are about 5 Msun for source A and 4 Msun for source C. A velocity gradient previously detected may be explained by unresolved binary rotation with a small velocity difference.Comment: 38 pages, 9 figures, accepted by The Astrophysical Journa