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in subjects: "Partial Differential Equations"

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Ion optics arithmetic and its implications for the positive ion CTR program

This paper discusses ion extraction optics formulations in which presheath ionization is shown to have a negligible effect on ion optics at optimum perveance; otherwise, the examples shown establish an ionization gradient instability. Infinite slot optics as a function of perveance and potential partitioning is delineated for the TFTR tetrode from 2-D considerations; finite slot optics at optimum perveance is delineated from 3-D considerations. Finally, further 2-D considerations yield an end s… more

Date: January 1, 1980

Creator: Whealton, J.H.

Item Type: Article

Partner: UNT Libraries Government Documents Department

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Electromagnetic fields in axial symmetric waveguides with variable cross section

A new class of separable variables is found which allows one to find an approximate analytical solution of the Maxwell equations for axial symmetric waveguides with slow (but not necessarily small) varying boundary surfaces. An example of the solution is given. Possible applications and limitations of this approach are discussed. 6 refs., 10 figs.

Date: February 15, 1980

Creator: Kheifets, S.

Item Type: Report

Partner: UNT Libraries Government Documents Department

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NUMERICAL ANALYSIS OF FLOWFIELDS GENERATED BY ACCELERATING FLAMES

A numerical technique is presented for the analysis of nonsteady flowfields generated by accelerating flames in gaseous media. The problem is formulated in Eulerian coordinates and the solution is based on the extension of the floating shock-fitting technique to all the discontinuities and their interactions occurring in the flowfield. Besides shock waves, the discontinuities taken into account thus far consist of contact surfaces, deflagration, and detonation fronts. The governing partial diff… more

Date: March 1, 1980

Creator: Kurylo, J.; Dwyer, H.A. & Oppenheim, A.K.

Item Type: Article

Partner: UNT Libraries Government Documents Department

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Hamiltonian theory of guiding-center motion

A Hamiltonian treatment of the guiding center problem is given which employs noncanonical coordinates in phase space. Separation of the unperturbed system from the perturbation is achieved by using a coordinate transformation suggested by a theorem of Darboux. As a model to illustrate the method, motion in the magnetic field B=B(x,y)z is studied. Lie transforms are used to carry out the perturbation expansion.

Date: May 1, 1980

Creator: Littlejohn, R.G.

Item Type: Report

Partner: UNT Libraries Government Documents Department

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Progress report No. 56, October 1, 1979-September 30, 1980. [Courant Mathematics and Computing Lab. , New York Univ]

Research during the period is sketched in a series of abstract-length summaries. The forte of the Laboratory lies in the development and analysis of mathematical models and efficient computing methods for the rapid solution of technological problems of interest to DOE, in particular, the detailed calculation on large computers of complicated fluid flows in which reactions and heat conduction may be taking place. The research program of the Laboratory encompasses two broad categories: analytical… more

Date: October 1, 1980

Item Type: Report

Partner: UNT Libraries Government Documents Department

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Local volume-time averaged equations of motion for dispersed, turbulent, multiphase flows

In most flows of liquids and their vapors, the phases are dispersed randomly in both space and time. These dispersed flows can be described only statistically or in terms of averages. Local volume-time averaging is used here to derive a self-consistent set of equations governing momentum and energy transfer in dispersed, turbulent, multiphase flows. The empiricisms required for use with these equations are the subject of current research.

Date: November 1, 1980

Creator: Sha, W.T. & Slattery, J.C.

Item Type: Report

Partner: UNT Libraries Government Documents Department

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Efficient technique for calculating multiple solutions of electric-field problems. Part I. Final report

The purpose of this report is to present a digital computer program capable of calculating the electrostatic field in an arbitrary two-dimensional configuration. The program was developed as a preliminary result in a project aimed at producing a three-dimensional program. Thus, this report represents an interim report on the entire project.

Date: December 1, 1980

Creator: Lauber, T.S.

Item Type: Report

Partner: UNT Libraries Government Documents Department

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Longitudinal symmetric coupled bunch modes

The theory of longitudinal coupled bunch instabilities is discussed. Although some of the results included are not new, it is useful to summarize them here in a unified fashion.

Date: December 1, 1980

Creator: Wang, J.M.

Item Type: Report

Partner: UNT Libraries Government Documents Department

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Source Effects on Impurity and Heat Transport in a Tokamak

A recently developed generalization of neoclassical theory is extended here to study heat flux contributions to impurity transport, as well as the heat fluxes themselves. The theory accounts for the first four source moments, with external drags, which has been studied previously with either fewer moments or restricted to a collisional plasma. Conditions are established for which a momentum source may be used to modify the particle and heat transport. In the course of this work, the particle an… more

Date: December 1, 1980

Creator: Bennett, R B

Item Type: Report

Partner: UNT Libraries Government Documents Department

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Stability of a Landau damped system

Dispersion relation serves as a base for all the Landau damping theory. In this paper we rederive the dispersion relation for general oscillator systems from a different approach which hopefully gives a little clearer view of the problem. Stability criteria are obtained by mapping technique. Two examples will be discussed to illustrate the sufficient condition for stability. 5 refs., 3 figs.

Date: December 1, 1980

Creator: Yao, C.Y.

Item Type: Report

Partner: UNT Libraries Government Documents Department

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Adaptive-grid methods for time-dependent partial differential equations

This paper contains a survey of recent developments of adaptive-grid algorithms for time-dependent partial differential equations. Two lines of research are discussed. One involves the automatic selection of moving grids to follow propagating waves. The other is based on stationary grids but uses local mesh refinement in both space and time. Advantages and disadvantages of both approaches are discussed. The development of adaptive-grid schemes shows promise of greatly increasing our ability to … more

Date: January 1, 1981

Creator: Hedstrom, G.W. & Rodrique, G.H.

Item Type: Article

Partner: UNT Libraries Government Documents Department

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Algorithms for sparse, symmetric, definite quadratic lambda-matrix eigenproblems

Methods are presented for computing eigenpairs of the quadratic lambda-matrix, M lambda/sup 2/ + C lambda + K, where M, C, and K are large and sparse, and have special symmetry-type properties. These properties are sufficient to insure that all the eigenvalues are real and that theory analogous to the standard symmetric eigenproblem exists. The methods employ some standard techniques such as partial tri-diagonalization via the Lanczos Method and subsequent eigenpair calculation, shift-and- inve… more

Date: January 1, 1981

Creator: Scott, D. S. & Ward, R. C.

Item Type: Article

Partner: UNT Libraries Government Documents Department

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Charged-particle calculations using Boltzmann transport methods

Several aspects of radiation damage effects in fusion reactor neutron and ion irradiation environments are amenable to treatment by transport theory methods. In this paper, multigroup transport techniques are developed for the calculation of charged particle range distributions, reflection coefficients, and sputtering yields. The Boltzmann transport approach can be implemented, with minor changes, in standard neutral particle computer codes. With the multigroup discrete ordinates code, ANISN, d… more

Date: January 1, 1981

Creator: Hoffman, T. J.; Dodds Jr., H. L.; Robinson, M. T. & Holmes, D. K.

Item Type: Article

Partner: UNT Libraries Government Documents Department

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Computation of high Reynolds number internal/external flows. [VNAP2 computer code]

A general, user oriented computer program, called VNAP2, has been developed to calculate high Reynolds number, internal/external flows. VNAP2 solves the two-dimensional, time-dependent Navier-Stokes equations. The turbulence is modeled with either a mixing-length, a one transport equation, or a two transport equation model. Interior grid points are computed using the explicit MacCormack scheme with special procedures to speed up the calculation in the fine grid. All boundary conditions are calc… more

Date: January 1, 1981

Creator: Cline, Michael C. & Wilmoth, Richard G.

Item Type: Article

Partner: UNT Libraries Government Documents Department

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Electrode shapes for spherical Pierce flow

The problem of obtaining the electrode shapes to produce a conically converging proton beam that has constant current density over each spherical surface of convergence is treated in spherical coordinates. A cone is taken from the Langmuir and Blodgett solution for the region within, and at the edge of, the conically converging beam. A solution for the LaPlace equation, required for the region outside the beam, is in terms of a power series in r and the Legendre polynomials of cos phi.

Date: January 1, 1981

Creator: Mueller, D.W.

Item Type: Article

Partner: UNT Libraries Government Documents Department

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Electron-electron correlation in highly charged atoms

The relativistic random-phase approximation (RRPA) is introduced to account for electron-electron correlation in atoms and ions of high nuclear charge where non-relativistic many-body methods are inadequate. To provide a basis for this study of the RRPA, the Dirac-Fock (DF) theory is reviewed. Applications of the DF equations to determine inner-electron binding energies in heavy atoms are given illustrating the influence of relativistic effects in situations where correlations are unimportant. … more

Date: January 1, 1981

Creator: Johnson, W. R. & Cheng, K. T.

Item Type: Article

Partner: UNT Libraries Government Documents Department

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Electron energy-distribution functions in gases

Numerical calculation of the electron energy distribution functions in the regime of drift tube experiments is discussed. The discussion is limited to constant applied fields and values of E/N (ratio of electric field strength to neutral density) low enough that electron growth due to ionization can be neglected. (GHT)

Date: January 1, 1981

Creator: Pitchford, L.C.

Item Type: Article

Partner: UNT Libraries Government Documents Department

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Gyroscopic analog for magnetohydrodynamics

The gross features of plasma equilibrium and dynamics in the ideal magnetohydrodynamics (MHD) model can be understood in terms of a dynamical system which closely resembles the equations for a deformable gyroscope.

Date: January 1, 1981

Creator: Holm, D.D.

Item Type: Article

Partner: UNT Libraries Government Documents Department

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ICRF oscillations of an inhomogeneous plasma cylinder

We have derived a dispersion differential equation suitable for studying free and forced oscillations of a radially inhomogeneous plasma cylinder in the ion cyclotron range of frequencies (ICRF). Solving the differential equation, subject to appropriate boundary conditions, yields global eigenmodes of the cylindrical configuration; thus, our description embraces both the geometry and the physics relevant in the ICRF. The derivation begins with the equations of the Vlasov(ion)-fluid(electron) mo… more

Date: January 1, 1981

Creator: Cayton, T. E. & Lewis, H. R.

Item Type: Article

Partner: UNT Libraries Government Documents Department

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Ion kinetic effects on the tilt mode in FRCs

Theory and simulations have shown that field reversed configurations (FRG's) should be unstable magnetohydrodynamically to the tilting mode, yet tilting seldom is seen in the experiments. Profile effects (within MHD) and ion finite larmor radius (FLR) effects have been prosed to explain the observed stability of FRC's. The present work seeks to test both of these effects.

Date: January 1, 1981

Creator: Schwarzmeier, J. L.; Seyler, C. E. & Barnes, D. C.

Item Type: Article

Partner: UNT Libraries Government Documents Department

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Melting and freezing in two dimensions: a molecular-dynamics study

Using molecular dynamics (MD) technique, we have investigated the nature of melting and freezing transitions as well as structural and dynamical properties of liquid and solid phases in two-dimensional systems interacting via 1/r and 1/r/sup 3/ potentials. From the velocity auto-correlation function (VAF) and dynamic structure factor for the electron liquid, it is shown that the well-defined oscillations in VAF are due to a coupling between the single particle motion and longitudinal excitation… more

Date: January 1, 1981

Creator: Vashishta, P. & Kalia, R.K.

Item Type: Article

Partner: UNT Libraries Government Documents Department

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Numerical Calculation of the Three Dimensional Electrical Field in the Central Region of a Cyclotron

To provide detailed and accurate electric fields in the ion source-puller region and at the dee dummy-dee gap for a cyclotron, a relaxation method solution of Laplace's equation has been used. A conventional difference equation with variation in mesh size and relaxation factor as well as different schemes for boundary corrections have been developed to achieve roughly 1 percent accuracy for a thre-dimensional domain with 10/sup 6/ mesh points. Although the computation requires considerable comp… more

Date: January 1, 1981

Creator: Chen, M. & Lind, D. A.

Item Type: Article

Partner: UNT Libraries Government Documents Department

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Observation of neoclassical effects on neutral beam injected ions in PLT

The horizontally-scanning charge exchange analyzer on the Princeton Large Torus (PLT) was used to measure fast co-moving ions during counter-injection of neutral beams. The large flux of charge exchange neutrals observed under these circumstances exhibited a sharp cutoff as the analyzer was moved toward more parallel radii of tangency. At a fixed angle and beam energy, the cutoff showed a strong dependence on the plasma current. Monte-Carlo calculations using a Fokker-Planck formalism and full … more

Date: January 1, 1981

Creator: Kaita, R.; Goldston, R.J. & Bussac, J.P.

Item Type: Report

Partner: UNT Libraries Government Documents Department

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Octupole focusing in transport and accelerator systems

The radio-frequency quadrupole (RFQ) linac is capable of accelerating high-current, low-velocity ion beams. In accelerator systems comprising an RFQ and higher velocity accelerating structures, the current bottleneck still typically occurs within the RFQ. This limiting current is quite high in most cases, but linacs with even higher currents may be required in the future. We have begun a study of higher multipole systems to determine their capability or focusing and accelerating very high curre… more

Date: January 1, 1981

Creator: Crandall, K. R.; Pabst, M.; Stokes, R. H. & Wangler, T. P.

Item Type: Article

Partner: UNT Libraries Government Documents Department