Full-wave Calculations Research Articles

Full-wave calculations in flux coordinates for toroidal geometry

A new 2-D full-wave code, HYPERION, employing a poloidal and toroidal mode expansion and including the toroidal terms arising in the wave equation has been developed. It is based on the existing modules developed for the MHD stability codes and uses as input the tokamak equilibria calculated with the RSTEQ code. At present the plasma response is described by the collisionally broadened cold plasma conductivity. However, the code is written in straight field line coordinates, this permits the accurate representation of k /sub /parallel// and as a consequence allows the incorporation of the plasma Z functions. This code also retains the E/sub /parallel// component of the electric field which will allow the study of the low density region of the plasma. We have done detailed benchmarking of the HYPERION code in the cold plasma limit with the existing finite difference ORION full-wave code. The agreement is very good.

Ion cyclotron emission from energetic fusion products in tokamak plasmas—A full-wave calculation

A full-wave ion cyclotron resonant heating (ICRH) code has been modified to allow calculation of cyclotron emission from energetic ions in tokamaks. The immediate application is to fusion alpha particles in near-ignition devices. This permits detailed evaluation of proposed alpha particle diagnostics [Proceedings of the Thirteenth European Conference on Controlled Fusion and Plasma Heating, Schliersee, Federal Republic of Germany, 1986, edited by G. Briffod and M. Kaufmann (European Physical Society, Petit-Lancy, Switzerland, 1986), Part 1, Vol. 2, p. 37.] This full-wave approach automatically takes into account wall reflections, standing waves, and plasma absorption and overcomes the difficulties inherent in attempting to apply conventional geometrical optics to long wavelengths. By calculating the coherent radiation field caused by an ensemble of localized current sources (and retaining the phase information), the directivity of pickup antennas is correctly represented. This method also promises to be useful for studying other kinds of plasma radiation, such as that produced by instabilities.

Vector coupled-mode analysis of coupling between two identical optical fiber cores

The vector coupled-mode analysis considering the exact HE(11) modes is applied to two single-mode coupled optical fiber cores, including the strongly guiding fibers. The accuracy of the conventional coupled-mode theory and the recently formulated new theory as applied to the two-core system is examined. Array modes of different polarization states are considered. It is shown that the full-wave coupled-mode calculations behave well in predicting the array-mode propagation constants beyond the weakly guiding regime and that the simpler conventional theory can provide satisfactory results when applied in the vectorial form.

Full-wave, finite element analysis of irregular microstrip discontinuities

Finite-element expansion currents are used to formulate a full-wave analysis of microstrip discontinuities. With this approach, a rigorous analysis of fairly irregular structures is possible, including radiation and surface wave effects as well as coupling between closely spaced junctions. The step, stub, and bent-stub discontinuities are analyzed using this technique. Measurements are made of three stub structures. Measured resonant frequencies agree with full-wave calculations to within 2% when the nominal measured dielectric constant and structure dimensions are used as input. Using the absolute worst case dielectric constants and dimensions as input gives an error of 3% for the low-frequency stub and less than that for the other stubs.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Full-wave calculations of the O-X mode conversion process

A two-point boundary-value problem has been formulated that describes the conversion between ordinary (O) and extraordinary (X) wave modes in a cold inhomogeneous plasma. Numerical solutions to this problem have been obtained for various values of the WKB parameter k0L; where k0 is the vacuum wavenumber and L the density-gradient scale length. The results are compared with three different theoretical expressions for the O-X mode conversion efficiency derived by others in the WKB limit of k0 L ≫ l. Most of the results presented in this paper are obtained for a collisionless plasma with finite density near the plasma cut-off density. However, some examples are also given of wave propagation from vacuum. In these examples, collision effects are added to the equations in order to remove the singularity otherwise present at the position of the upper hybrid resonance layer.

Surface and near-surface effects on seismic waves—theory and borehole seismometer results

AbstractA simple plane wave model is adequate to explain many surface versus borehole seismometer data sets. Using such a model, we present a series of examples which demonstrate the effects of the free-surface, near-surface velocity gradients, and low impedance surface layers on the amplitudes of upcoming body waves. In some cases, these amplitudes are predictable from simple free-surface and impedance contrast expressions. However, in other cases these expressions are an unreliable guide to the complete response, and the full plane wave calculation must be performed. Large surface amplifications are possible, even without focusing due to lateral heterogeneities or nonlinear effects. Both surface and borehole seismometer site responses are almost always frequency-dependent.Ocean bottom versus borehole seismic data from the 1983 Ngendei Seismic Experiment in the southwest Pacific are consistent with both a simple plane wave model and a more complete synthetic seismogram calculation. The borehole seismic response to upcoming P waves is reduced at high frequencies because of interference between the upgoing P wave and downgoing P and SV waves reflected from the sediment-basement interface. However, because of much lower borehole noise levels, the borehole seismometer enjoys a P-wave signal-to-noise advantage of 3 to 7 dB over nearby ocean bottom instruments.

Comparison of measured and predicted field strengths of medium frequency sky waves over short distances in Japan

Nighttime sky waves of four medium frequencies were observed at distances of not larger than about 300 km in Japan for one to two years of high and low solar activities. The sporadic E (Es) layer always appeared with high probability. Analyzing these data, the following results were obtained: 1) the measured median field strengths are different by at least more than 7 dB from full wave predicted values for the international reference ionosphere (IRI) without the Es-layer. But these agree fairly well with the full wave calculation for IRI with the Es-layer, 2) the field strength approximates the Rayleigh distribution, 3) according to the data for high solar activity, the sky wave appears rapidly after sunset, and during the two to six hours after sunset all median field strengths are about constant.

ICRF wave propagation and absorption in tokamak and mirror magnetic fields — A full-wave calculation

Global solutions for the ion cyclotron resonant frequency (ICRF) wave fields in a straight tokamak with rotational transform and a poloidally symmetric mirror are calculated in the cold plasma limit. The component of the wave electric field parallel to B is assumed zero. Symmetry in each problem allows Fourier decomposition in one ignorable coordinate, and the remaining set of two coupled, two-dimensional partial differential equations is solved by finite differencing. Energy absorption and antenna impedance are calculated using a simple collisional absorption model. When large gradients in ‖ B‖ along B are present in either geometry, ICRF heating at the fundamental ion cyclotron resonance is observed. For the mirror, such gradients are always present. But for the tokamak, the rotational transform must be large enough that B·▿B ⪆ 0(1) . For smaller transforms more typical of real tokamaks, only heating at the two-ion hybrid resonance is observed. This suggests that direct resonant absorption at the fundamental ion cyclotron resonance may be possible in stellarators where B·▿ B ≈ 0(1) naturally.

Numerical solutions of the coupled equations for acoustic-gravity waves in the upper thermosphere

A full wave calculation has been made for the acoustic-gravity waves in an inhomogeneous and viscous atmosphere approximated by a number of horizontal thin slabs. A propagation matrix within a slab is assumed to be in the form of a polynomial function of height. In the derivation of a linearized wave equation, the height derivatives of ambient atmospheric parameters are taken into account. It is revealed that the large-scale gravity waves undergo significant partial downward reflections caused by increasing kinematic viscosity in the upper part of the thermosphere, in addition to the well-known total reflection due to the sharp rise of atmospheric temperature near the thermospheric base. As a consequence of these reflections, some part of the wave energy conveyed from the lower ionosphere is trapped within the region around the F2-peak. Efficiency of energy trapping largely depends on the horizontal phase velocity.

A method of estimating the electron density profile of the D layer from a knowledge of the VLF reflection coefficients

A technique for calculating an estimate of the lower ionospheric electron density profile from a knowledge of the VLF radio wave reflection coefficients is studied. The conditions of success of this technique are discussed in detail. Numerical simulation of this method has been carried out on the basis of a full wave calculation. It was confirmed that the deduced profile converged well to the specified profile after only a few iterations. Some numerical results are presented.

Analytic eikonal model for intermediate energy stripping and pickup reactions

We have developed an analytic eikonalized amplitude for the intermediate energy ($p$,$d$) reaction based on the distorted wave Born approximation. Eikonalization of the distorted waves naturally separates the important dynamical quantity, the momentum transfer, into longitudinal and transverse components. Upon evaluation of the amplitude using techniques similar to those employed by Amado, Dedonder, and Lenz for elastic scattering, we find the dependence of the transverse momentum transfer to be dominated by distortion effects. Consequently the shapes of the angular distributions are similar to those for elastic scattering. The geometry of the binding well of the picked-up neutron determines most of the dependence of the longitudinal momentum transfer. This fixes the dependence on bombarding energy. Many simple systematic features of these reactions are predicted using the analytic eikonalized amplitude and are observed in full partial wave calculations.

A Full Wave Calculation of VLF Waves in Auroral Zone (c. Wave-Particle Interactions in the Magnetosphere) (Proceedings of the Second Symposium on Coordinated Observations of the Ionosphere and Magnetosphere in the Polar Regions : Part I)

A Full Wave Calculation of VLF Waves in Auroral Zone (c. Wave-Particle Interactions in the Magnetosphere) (Proceedings of the Second Symposium on Coordinated Observations of the Ionosphere and Magnetosphere in the Polar Regions : Part I)

Comparison of three different types of VLF direction‐finding techniques

Three different types of VLF direction‐finding techniques (goniometer, tracker, and University of Tokyo type) were tested by using whistler mode VLF signals from Siple. The tests were carried out by simulating each type of direction finder (DF) in a digital computer. The results are as follows: (1) the difference between the azimuth angle obtained by the tracker DF and that obtained by the University of Tokyo type DF is smaller than the difference between the azimuths given by the goniometer and by the University of Tokyo type DF; and (2) in some periods all three DF techniques give nearly equal azimuth angles, and the wave polarization agrees with that expected from the full wave calculations, but in other periods all three techniques give considerably different azimuth angles, and the wave polarizations do not agree with the theoretical ones.

Omega Signal Coverage Prediction

a set of coverage prediction diagrams is presented for the 10.2 kHz signal from each OMEGA transmitter. The diagrams show the −20 dB signal-to-noise ratio contours (in a 100 Hz noise bandwidth) for both local noon and local midnight. Composite diagrams are also presented on which all individual −20 dB contours are plotted for the current transmitter network for local noon and for local midnight. Similar diagrams are presented for the planned full OMEGA operational network. A full-wave signal propagation computer program was employed to generate signal strength profiles along radial paths from each transmitter. Noise values from the CCIR noise map were applied to the profiles. Sensitivity tables showing the shifts that result from email changes in transmitted power or from seasonal variations in the noise power are also included.

Penetration and reflection of VLF waves through the ionosphere: Full wave calculations with ground effect

Numerical calculations of the full-wave treatment are made for VLF electromagnetic waves that are incident on to the plane-stratified ionosphere both from below and above. For the both cases, special attention is paid to the variation of penetration and reflection coefficients with wave frequency, angle of incidence, magnetic dip angle and various model of the ionospheric structure. The effect of conductive ground is taken into account in the calculation of the penetration and reflection coefficients of the waves incident from above. The modifications due to the presence of ground reflection are 1. (1) both penetration and reflection coefficients vary considerably with angle of incidence as a result of the interference between the upward and the downward propagating waves. 2. (2) reflection coefficient in the nighttime ionosphere is large enough to account for common type of repeated whistler echo trains. A new reciprocity relation is established which is related to the reflection coefficients of the waves incident onto the ionosphere from above.

Numerical calculation of gravity wave propagation in a realistic thermosphere

This paper describes a full wave calculation of gravity wave propagation in a realistic thermospheric model, including the effects of height dependent temperature and winds, of Coriolis force, viscosity, thermal conduction, and ion drag. In order to integrate the hydrodynamic equations, the height dependent coefficients are approximated by piecewise constant ones, taking into account also terms which involve vertical derivatives. Numerically calculated results are compared with observational data deduced from ionograms.

Orthogonality of VLF Height Gains in the Earth Ionosphere Waveguide

Orthogonality conditions satisfied by the height gain functions governing VLF fields in the vertically inhomogeneous, anisotropic earth ionosphere waveguide are discussed. It is pointed out that these orthogonality conditions which in general involve both the height gains for the given waveguide and those of an appropriate ‘adjoint’ waveguide can serve as a sensitive test for numerical consistency in full wave calculations of waveguide parameters.

Model ionosphere for D region at summer noon during sunspot maximum

A model ionosphere, comprising electron-density and collision-frequency distributions for the midlatitude D region at summer noon during sunspot-maximum conditions, has been produced which will give satisfactory results for propagation at low and very low frequencies. The electron-density distribution above 68 km was based on a distribution, measured in a rocket, which was altered until fullwave calculations using it gave propagation parameters in agreement with the average observed values. Below 68 km, a C layer was found necessary to give the best fit to measured ground-interference patterns at 16 kHz. A comparison is also shown between a measured pattern of this kind and one calculated from the rocket distribution, which was obtained on the same day.

Full wave calculations of gravity wave propagation through the thermosphere

Full wave calculations have been performed within the frequency range of gravity waves (10−3 ≤ ω ≤ 10−2 sec−1) for a thermospheric model between 150 and 500 km altitude. In this altitude range gravity waves are coupled with heat conduction waves. Reflection, transmission, conversion, and coupling from one wave type into the other one is described by the elements of the scattering matrix. The dependence of these elements on height and angle of incidence is discussed. The transmission coefficients of gravity waves calculated by full wave theory are compared with simple ray calculations and show that ray treatment is a sufficient approximation for obliquely upward propagating gravity waves and that gravity waves predominate throughout the thermosphere. The thermosphere reacts like a selective filter with respect to upward propagating gravity waves with optimal transmission at kx ∼ ω/C (ω = angular frequency; C = velocity of sound; kx = horizontal wave number).

D region electron-density distributions from propagation data

By using a fullwave computer program, Deeks was able to find an electron-density distribution in the D region which would account for certain v.l.f. and l.f. propagation results. Here, more extensive experimental results are employed for this purpose; in particular, ground-interference patterns on 16 and 21 kHz. Stationary-phase techniques are developed to enable such patterns to be calculated from an assumed distribution. It is found that, to get the best fit, Deeks&apos;s distribution has to be modified appreciably; the required change can be described roughly as reducing its height by about 6 km.