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At least 37 records · Page 2

Further study of a new dispersion relation for electron-atom scattering

A recently proposed dispersion relation (DR) is tested for e-He scattering; the results show that the new DR is not satisfied. Therefore, the analytic structure of the difference amplitude, previously assumed to be nonsingular, is investigated on the negative scattering energy axis. Even under severe approximations, the difference amplitude contains both poles and branch points. This suggests, however, a useful approximation of these contributions to the DR which gives very satisfactory agreement in both e-H and e-He scattering.

Bhatia, A. K.↗

A new dispersion relation for electron-atom scattering

A new forward-angle dispersion relation (DR) for electron-atom scattering is proposed. It is based on a subtraction of the static-exchange amplitude from the exact elastic scattering amplitude. Arguments are advanced to explain why this should obviate the difficulties associated with the Gerjuoy-Krall DR, specifically with the exchange Born amplitude. The new DR is tested in the elastic energy range for e-H scattering and compared with the GKDR.

Temkin, A.↗

Dispersion-relation-preserving finite difference schemes for computational acoustics

Time-marching dispersion-relation-preserving (DRP) schemes can be constructed by optimizing the finite difference approximations of the space and time derivatives in wave number and frequency space. A set of radiation and outflow boundary conditions compatible with the DRP schemes is constructed, and a sequence of numerical simulations is conducted to test the effectiveness of the DRP schemes and the radiation and outflow boundary conditions. Close agreement with the exact solutions is obtained.

Tam, Christopher K. W.↗

The Dispersion Relation for the 1/sinh(exp 2) Potential in the Classical Limit

The dispersion relation for the inverse hyperbolic potential is calculated in the classical limit. This is shown for both the low amplitude phonon branch and the high amplitude soliton branch. It is shown these results qualitatively follow that previously found for the inverse squared potential where explicit analytic solutions are known.

Campbell, Joel↗

Partial Wave Dispersion Relations: Application to Electron-Atom Scattering

In this Letter we propose the use of partial wave dispersion relations (DR's) as the way of solving the long-standing problem of correctly incorporating exchange in a valid DR for electron-atom scattering. In particular a method is given for effectively calculating the contribution of the discontinuity and/or poles of the partial wave amplitude which occur in the negative E plane. The method is successfully tested in three cases: (i) the analytically solvable exponential potential, (ii) the Hartree potential, and (iii) the S-wave exchange approximation for electron-hydrogen scattering.

Temkin, A.↗

Interpretation of dispersion relations for bounded systems.

Treatment of the problem of constructing normal modes for an arbitrarily bounded system from roots of the linear dispersion relation D(omega, k) = 0 for the corresponding infinite or periodically bounded system. For a system described by continuous macroscopic variables, and of general cylindrical form, each transverse eigenmode gives rise to a set of axial normal modes constructed from a pair of dominant roots of D = 0 satisfying the boundary conditions which are characterized by complex reflection coefficients for the dominant waves. The implications of the results for the interpretation of experiments on plasma waves and instabilities on finite cylinders are discussed, with particular reference to the effects of end-plate damping and axial current on Q-machines.

Rognlien, T. D.↗

Investigation of dispersion-relation-preserving scheme and spectral analysis methods for acoustic waves

Important characteristics of the aeroacoustic wave propagation are mostly encoded in their dispersion relations. Hence, a computational aeroacoustic (CAA) algorithm, which reasonably preserves these relations, was investigated. It was derived using an optimization procedure to ensure, that the numerical derivatives preserved the wave number and angular frequency of the differential terms in the linearized, 2-D Euler equations. Then, simulations were performed to validate the scheme and a compatible set of discretized boundary conditions. The computational results were found to agree favorably with the exact solutions. The boundary conditions were transparent to the outgoing waves, except when the disturbance source was close to a boundary. The time-domain data generated by such CAA solutions were often intractable until their spectra was analyzed. Therefore, the relative merits of three different methods were included in the study. For simple, periodic waves, the periodogram method produced better estimates of the steep-sloped spectra than the Blackman-Tukey method. Also, for this problem, the Hanning window was more effective when used with the weighted-overlapped-segment-averaging and Blackman-Tukey methods gave better results than the periodogram method. Finally, it was demonstrated that the representation of time domain-data was significantly dependent on the particular spectral analysis method employed.

Vanel, Florence O.↗

Exchange Forces in Dispersion Relations Investigated Using Circuit Relations

We propose a novel method to compute in an exact manner the left-hand cut discontinuity of the electron-Atom partial wave scattering amplitude in the complex energy plane within the static stage approximation. Zero energy dispersion relations for electron-Hydrogen scattering are computed numerically for illustration.

Vrinceanu, D.↗

Conversion of electrostatic plasma waves into electromagnetic waves - Numerical calculation of the dispersion relation for all wavelengths.

The dispersion curves have been computed for a wide range of wavelengths from electromagnetic waves to electrostatic waves in a magnetoactive warm plasma with a Maxwellian velocity distribution function. The computation was carried out mainly for the perpendicular propagation mode. The upper hybrid resonance is the connection point of the electrostatic waves and the electromagnetic waves. The electrostatic waves not associated with the upper hybrid resonance are subjected to electron cyclotron damping when the wavelength becomes long. Oblique propagation is allowed for the electrostatic waves in a frequency range from the plasma frequency to the upper hybrid resonance frequency in the long-wavelength region where Landau damping can be neglected and where the electrostatic mode smoothly connects to the electromagnetic X-mode. In a slightly inhomogeneous plasma, the Bernstein-mode electrostatic wave can escape by being converted into the O-mode electromagnetic wave; two reflections take place during this escape process.

Oya, H.↗

Computation of Transonic Nozzle Sound Transmission and Rotor Problems by the Dispersion-Relation-Preserving Scheme

The transonic nozzle transmission problem and the open rotor noise radiation problem are solved computationally. Both are multiple length scales problems. For efficient and accurate numerical simulation, the multiple-size-mesh multiple-time-step Dispersion-Relation-Preserving scheme is used to calculate the time periodic solution. To ensure an accurate solution, high quality numerical boundary conditions are also needed. For the nozzle problem, a set of nonhomogeneous, outflow boundary conditions are required. The nonhomogeneous boundary conditions not only generate the incoming sound waves but also, at the same time, allow the reflected acoustic waves and entropy waves, if present, to exit the computation domain without reflection. For the open rotor problem, there is an apparent singularity at the axis of rotation. An analytic extension approach is developed to provide a high quality axis boundary treatment.

Tam, Christopher K. W.↗

A perpendicular ion beam instability - Solutions to the linear dispersion relation

A 200-eV Xe(+) ion beam directed perpendicular to the terrestrial magnetic field in the F region ionosphere produced very narrow band electrostatic emissions just above multiples of the hydrogen cyclotron frequency. Although the plasma conditions associated with the ion beam were undoubtedly very complex, a simple ion beam in a background ionosphere is considered first. The dispersion relation for flute mode waves and an unmagnetized perpendicular ion beam is solved for a diffuse H(+) plasma and then for a combination of dense O(+) and diffuse H(+). These solutions account for most of the wave properties, including the observation of narrow spectral peaks separated by the hydrogen cyclotron frequency and the observation of no spectral peaks below 2000 Hz. We cannot dismiss field-aligned currents associated with the Xe(+) beam as an alternate source of free energy for the narrow band emissions. However, our intention here is to examine closely the Xe(+) beam as a source for directly exciting the plasma waves.

Kintner, P. M.↗

Optical dispersion relations for diamondlike carbon films

Ellipsometric measurements on plasma deposited diamondlike amorphous carbon (a-C:H) films were taken in the visible, (E=1.75 to 3.5 eV). The films were deposited on Si and their properties were varied using high temperature (up to 750 C) anneals. The real (n) and imaginary (k) parts of the complex index of refraction N were obtained simultaneously. Following the theory of Forouhi and Bloomer, a least squares fit was used to find the dispersion relations n(E) and k(E). Reasonably good fits were obtained, showing that the theory can be used for a-C:H films. Moreover, the value of the energy gap (Eg) obtained in this way was compared to the Eg value using conventional Tauc plots and reasonably good agreement was obtained.

Alterovitz, Samuel A.↗

Optical dispersion relations for diamondlike carbon films

Ellipsometric measurements on plasma deposited diamondlike amorphous carbon (a-C:H) films were taken in the visible, (E = 1.75 to 3.5 eV). The films were deposited on Si and their properties were varied using high temperature (up to 750 C) anneals. The real (n) and imaginary (k) parts of the complex index of refraction, N, were obtained simultaneously. Following the theory of Forouhi and Bloomer, a least squares fit was used to find the dispersion relations n(E) and k(E). Reasonably good fits were obtained, showing that the theory can be used for a-C:H films. Moreover, the value of the energy gap, Eg, obtained in this way was compared the the Eg value using conventional Tauc plots and reasonably good agreement was obtained.

Alterovitz, Samuel A.↗

Optical dispersion relations for 'diamondlike' carbon films

Ellipsometric measurements on plasma deposited diamondlike amorphous carbon (a-C:H) films were taken in the visible, (E = 1.75 to 3.5 eV). The films were deposited on Si and their properties were varied using high temperature (up to 750 C) anneals. The real (n) and imaginary (k) parts of the complex index of refraction N were obtained simultaneously. Following the theory of Forouhi and Bloomer, a least squares fit was used to find the dispersion relations n(E) and k(E). Reasonably good fits were obtained, showing that the theory can be used for a-C:H films. Moreover, the value of the energy gap (Eg) obtained in this way was compared to the Eg value using conventional Tauc plots and reasonably good agreement was obtained.

Alterovitz, Samuel A.↗