Modelling RF sources using 2-D PIC codes

In recent years, many types of RF sources have been successfully modelled using 2-D PIC codes. Both cross field devices (magnetrons, cross field amplifiers, etc.) and pencil beam devices (klystrons, gyrotrons, TWT'S, lasertrons, etc.) have been simulated. All these devices involve the interaction of an electron beam with an RF circuit. For many applications, the RF structure may be approximated by an equivalent circuit, which appears in the simulation as a boundary condition on the electric field ( port approximation''). The drive term for the circuit is calculated from the energy transfer between beam and field in the drift space. For some applications it may be necessary to model the actual geometry of the structure, although this is more expensive. One problem not entirely solved is how to accurately model in 2-D the coupling to an external waveguide. Frequently this is approximated by a radial transmission line, but this sometimes yields incorrect results. We also discuss issues in modelling the cathode and injecting the beam into the PIC simulation

Optimization of a lasertron double output cavity

Double output cavities have been used experimentally to increase the efficiency of high-power klystrons. We have used particle-in-cell simulations with the 2 + 1/2 dimensional code MASK to optimize the design of double output cavities for the lasertron under development at SLAC. We discuss design considerations for double output cavities (e.g., optimum choice of voltages and phases, efficiency, wall interception, breakdown). We describe how one calculates the cavity impedance matrix from the gap voltages and phases. Some results of the effect of varying voltage, perveance, and pulse are reported

Impacts of Atmospheric Nitrogen Deposition and Coastal Nitrogen Fluxes on Oxygen Concentrations in Chesapeake Bay

Although rivers are the primary source of dissolved inorganic nitrogen (DIN) inputs to the Chesapeake Bay, direct atmospheric DIN deposition and coastal DIN concentrations on the continental shelf can also significantly influence hypoxia; however, the relative impact of these additional sources of DIN on Chesapeake Bay hypoxia has not previously been quantified. In this study, the estuarine‐carbon‐biogeochemistry model embedded in the Regional‐Ocean‐Modeling‐System (ChesROMS‐ECB) is used to examine the relative impact of these three DIN sources. Model simulations highlight that DIN from the atmosphere has roughly the same impact on hypoxia as the same gram‐for‐gram change in riverine DIN loading, although their spatial and temporal distributions are distinct. DIN concentrations on the continental shelf have a similar overall impact on hypoxia as DIN from the atmosphere (~0.2 mg L−1); however, atmospheric DIN impacts dissolved oxygen (DO) primarily via the decomposition of autochthonous organic matter, whereas coastal DIN concentrations primarily impact DO via the decomposition of allochthonous organic matter entering the Bay mouth from the shelf. The impacts of atmospheric DIN deposition and coastal DIN concentrations on hypoxia are greatest in summer and occur farther downstream (southern mesohaline) in wet years than in dry years (northern mesohaline). Integrated analyses of the relative contributions of all three DIN sources on summer bottom DO indicate that impacts of atmospheric deposition are largest in the eastern mesohaline shoals, riverine DIN has dominant impacts in the largest tributaries and the oligohaline Bay, while coastal DIN concentrations are most influential in the polyhaline region

The Near-Linear Regime of Gravitational Waves in Numerical Relativity

We report on a systematic study of the dynamics of gravitational waves in full 3D numerical relativity. We find that there exists an interesting regime in the parameter space of the wave configurations: a near-linear regime in which the amplitude of the wave is low enough that one expects the geometric deviation from flat spacetime to be negligible, but nevertheless where nonlinearities can excite unstable modes of the Einstein evolution equations causing the metric functions to evolve out of control. The implications of this for numerical relativity are discussed.Comment: 10 pages, 2 postscript figures, revised tex

Dynamics of Gravitational Waves in 3D: Formulations, Methods, and Tests

The dynamics of gravitational waves is investigated in full 3+1 dimensional numerical relativity, emphasizing the difficulties that one might encounter in numerical evolutions, particularly those arising from non-linearities and gauge degrees of freedom. Using gravitational waves with amplitudes low enough that one has a good understanding of the physics involved, but large enough to enable non-linear effects to emerge, we study the coupling between numerical errors, coordinate effects, and the nonlinearities of the theory. We discuss the various strategies used in identifying specific features of the evolution. We show the importance of the flexibility of being able to use different numerical schemes, different slicing conditions, different formulations of the Einstein equations (standard ADM vs. first order hyperbolic), and different sets of equations (linearized vs. full Einstein equations). A non-linear scalar field equation is presented which captures some properties of the full Einstein equations, and has been useful in our understanding of the coupling between finite differencing errors and non-linearites. We present a set of monitoring devices which have been crucial in our studying of the waves, including Riemann invariants, pseudo-energy momentum tensor, hamiltonian constraint violation, and fourier spectrum analysis.Comment: 34 pages, 14 figure

An Axisymmetric Gravitational Collapse Code

We present a new numerical code designed to solve the Einstein field equations for axisymmetric spacetimes. The long term goal of this project is to construct a code that will be capable of studying many problems of interest in axisymmetry, including gravitational collapse, critical phenomena, investigations of cosmic censorship, and head-on black hole collisions. Our objective here is to detail the (2+1)+1 formalism we use to arrive at the corresponding system of equations and the numerical methods we use to solve them. We are able to obtain stable evolution, despite the singular nature of the coordinate system on the axis, by enforcing appropriate regularity conditions on all variables and by adding numerical dissipation to hyperbolic equations.Comment: 19 pages, 9 figure

Symmetry without Symmetry: Numerical Simulation of Axisymmetric Systems using Cartesian Grids

We present a new technique for the numerical simulation of axisymmetric systems. This technique avoids the coordinate singularities which often arise when cylindrical or polar-spherical coordinate finite difference grids are used, particularly in simulating tensor partial differential equations like those of 3+1 numerical relativity. For a system axisymmetric about the z axis, the basic idea is to use a 3-dimensional Cartesian (x,y,z) coordinate grid which covers (say) the y=0 plane, but is only one finite-difference-molecule--width thick in the y direction. The field variables in the central y=0 grid plane can be updated using normal (x,y,z)--coordinate finite differencing, while those in the y \neq 0 grid planes can be computed from those in the central plane by using the axisymmetry assumption and interpolation. We demonstrate the effectiveness of the approach on a set of fully nonlinear test computations in 3+1 numerical general relativity, involving both black holes and collapsing gravitational waves.Comment: 17 pages, 4 figure

Sinking properties of some phytoplankton shapes and the relation of form resistance to morphological diversity of plankton – an experimental study

Form resistance (Phi) is a dimensionless number expressing how much slower or faster a particle of any form sinks in a fluid medium than the sphere of equivalent volume. Form resistance factors of PVC models of phytoplankton sinking in glycerin were measured in a large aquarium (0.6 x 0.6 x 0.95 m). For cylindrical forms, a positive relationship was found between Phi and length/ width ratio. Coiling decreased Phi in filamentous forms. Form resistance of Asterionella colonies increased from single cells up to 6-celled colonies than remained nearly constant. For Fragilaria crotonensis chains, no such upper limit to Phi was observed in chains of up to 20 cells ( longer ones were not measured). The effect of symmetry on Phi was tested in 1 - 6-celled Asterionella colonies, having variable angles between the cells, and in Tetrastrum staurogeniaeforme coenobia, having different spine arrangements. In all cases, symmetric forms had considerably higher form resistance than asymmetric ones. However, for Pediastrum coenobia with symmetric/asymmetric fenestration, no difference was observed with respect to symmetry. Increasing number and length of spines on Tetrastrum coenobia substantially increased Phi. For a series of Staurastrum forms, a significant positive correlation was found between arm-length/cell-width ratio and Phi: protuberances increased form resistance. Flagellates (Rhodomonas, Gymnodinium) had a Phi 1. The highest value ( Phi = 8.1) was established for a 20-celled Fragilaria crotonensis chain. Possible origin of the so-called 'vital component' ( a factor that shows how much slower viable populations sink than morphologically similar senescent or dead ones) is discussed, as is the role of form resistance in evolution of high diversity of plankton morphologies