Waveguide Phased Array Research Articles

Electron Landau damping of lower hybrid waves

The role of electron Landau damping (ELD) in the lower hybrid resonance region is reviewed. First, it is shown that good matching of waves with parallel index n∥ large enough for efficient ELD from a finite-length antenna is possible only if the antenna is facing a tenuous plasma such that . This situation appears to prevail in recent experiments using phased waveguide arrays as launching structures. Moreover, it is shown that the relevant portion of the spectrum will be depleted by linear wave transformation before suffering appreciable ELD, unless the frequency is at least 1.5 times higher than the resonant frequency in the core of the plasma. Thus, in the case of a phased waveguide array designed for efficient ion heating in the resonance region, hardly more than a few per cent of the power will be absorbed by the electrons through ELD. On the other hand, provided that the antenna design is appropriate, ELD itself can be regarded as a simple and efficient method of heating large plasmas up to thermonuclear temperatures.

Aperture performance of a double-ridge rectangular waveguide in a phased array

Despite its widely recognized broad-band characteristics, the potential of a double-ridge rectangular waveguide as a phased array element has not been systematically explored. An additional benefit in using this waveguide is its reduced size which permits realization of a compact array lattice for wide angle scanning applications. A number of treatments of ridge waveguide propagation characteristics appear in the literature [1] -[5], but an analysis of the performance of a double-ridge waveguide phased array element has only recently been published [6], [7]. The results presented are based on [6], but they include additional material. The unmatched aperture performance of a rectangular ridge-guide in a number of wide-band phased arrays with quarter-hemispherical coverage, and a single narrow-band <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</tex> -plane scan design are examined. A parametric study and comparison of the unmatched aperture performance of a ridged-guide element with that of a rectangular waveguide reflects the capabilities of the double ridged-guide wide-band element in a large phased array. Such parametric study reveals to the designer the active admittance of the unmatched radiating element and leads in a systematic manner to a choice of the ridge-guide geometry and array lattice, to be followed by the determination of a suitable matching structure. This approach contrasts that of [7], which concentrates on demonstrating the feasibility of broad-band matching of a particular dual ridged-element.

Plasma-wave coupling and propagation using phased waveguide arrays

A study of the coupling and propagation of electron plasma waves excited by waveguide arrays is presented. The waves are generated in a low-temperature, linear plasma column in a homogeneous magnetic field. As predicted from a theoretical model, under appropriate conditions efficient coupling to plasma waves can be obtained. These studies are of relevance to plasma heating in that the modes are identical with those that must be generated in any lower hybrid heating experiment. We discuss the implications of these results with respect to future heating experiments on large devices.

Multielement phased array waveguide simulator for circular polarization

An extension of the principles of multimode phased array waveguide simulators to triangular spaced array antennas is presented. It is also shown how such a simulator can be used for any polarization of excitation, if the radiating elements are circular symmetric. Contour plots of the reflection and the transmission coefficients are shown for circular polarization of excitation. The radiating elements are open-ended circular waveguides in a triangular lattice. A comparison between the simulator technique and the small test array technique to approximate the infinite array performance is also given.

Slow-wave launching at the lower hybrid frequency using a phased waveguide array

The coupling efficiency of a phased multi-waveguide structure (the “Grill”) designed to launch HF-waves at the lower hybrid resonance to heat large toroidal plasmas, while satisfying the accessibility condition, is studied. To find the reflection and transmission coefficients, as well as the k‖-spectrum of the excited field, the waveguide field, represented as a superposition of eigenmodes, is matched to the field in the plasma, which is evaluated on the assumption of a linear density profile near the plasma edge. It is found that the reflection coefficient can be made acceptably low and is not sensitively dependent on the plasma parameters. It is concluded that it is possible to design a Grill capable to launch lower hybrid waves at the power level required for the ignition of a reactor plasma.

Ridged waveguide phased array elements

The mutual coupling solution of dual and quad ridged waveguide is described for an infinite array environment. The method of analysis is the numerical solution of integral equations for both the eigen solution and the boundary matching problem. In addition to numerical results, comparison of theory with waveguide simulator measurements is also given.

Penetration of Slow Waves into a Dense Plasma Using a Phased Wave-Guide Array

We report experimental evidence of wave coupling and penetration to the interior of a high-density magnetoplasma using a double-wave-guide antenna as a slow-wave structure. Reflection coefficients as low as 4% were observed. The experiment used 9-cm microwaves with a plasma of 11-cm diam. The relevance to lower-hybrid heating of tokamak fusion plasmas is discussed.

Prediction of active array impedance from simulator measurements using rounded ramp function interpolation

In order to extend the active reflection coefficient of a phased array to general scan angles from measurements on a multielement phased array waveguide simulator, a new interpolation technique using rounded ramp functions (RRPF's) is presented. The interpolation formula is tested on an array, simulated by a 25-element simulator, with stripline-fed slots as radiating elements. Contour plots showing the magnitude and the phase of the active reflection coefficient are included. The described interpolation scheme gives a much smoother behavior than a Fourier series expansion published earlier.

Synthesis of a waveguide phased array element

A synthesis of a simple matching structure for a waveguide phased array element is presented. The matching is in the form of a double-tuned response. Short dielectric discs in combination with a below cutoff section of waveguide approximately realizes the lumped circuit parameters of the ideal double-tuned circuit. The departure from the ideal realization is explained in terms of the dispersive character of the structure and the interdependence of the resonator circuits. Design examples of linearly polarized and wide-scan ( 75\deg cone) polarization diverse arrays are carried out for bandwidths greater than 10 percent. The completed designs are evaluated considering the multimode nature of the aperture discontinuity.

Wideband wide-angle impedance matching and polarization characteristics of circular waveguide phased arrays

A systematic procedure for matching the active element impedance over a wide scan angle for a wide band of frequencies is given. The application of this procedure is illustrated in a dual-polarization array designed to scan a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">60\deg</tex> half-angle cone over a 16-percent bandwidth. The accuracy of this computation has been verified by simulator measurements.

Quadruple ridge-loaded circular waveguide phased arrays

An equivalent circuit representation of quadruple ridge-loaded waveguide arrays is presented which is useful for synthesis and optimization of array performance. The validity of this technique has been verified by simulator measurement.

Broad-band impedance matching of rectangular waveguide phased arrays

A method for wide-band wide-angle impedance matching of rectangular waveguide phased arrays is presented. A maximum VSWR of 2.3:1 is achieved over a 50 percent bandwidth with a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">60\deg</tex> half-angle conical coverage using an element spacing six percent less than the condition required for grating lobe suppression. A further reduction in element spacing, bandwidth, or scan volume results in an even better impedance match. Simplicity and high radiation efficiency are the unique features of this matching technique.

Computer aided impedance matching of an interleaved waveguide phased array

The active admittance of a reduced-size dielectric-loaded waveguide in an interleaved phased array has a low conductance component and a high VSWR. Matching the impedance of such an element poses a difficult problem, in particular if it is desired to achieve matching over a wide frequency band. In this communication, a method to design an impedance transformer for matching such a load based on an optimization approach is presented. The computer results show that a load with a VSWR of 7 to 8 across a 10 percent bandwidth can be matched to achieve a VSWR of about 1.25 across the same band.

On the Design of Optimum Dual-Series Feed Networks

A computer-implemented procedure is presented for the design of optimally efficient dual-series feed networks for use in waveguide phased arrays where the network directional couplers are limited in their values of maximum coupling by geometrical and bandwidth requirements. The theory of the design procedure is outlined and results for the design of sum and difference pattern element excitations for typical coupler limitations are presented.

On the suppression of radiation nulls and broadband impedance matching of rectangular waveguide phased arrays

Numerical solutions are obtained for the problem of radiation from an infinite array of rectangular waveguides, each of which is loaded with iris at the array aperture. It is shown that the introduction of aperture irises can remove a radiation null in the active element pattern and significantly improve the array performance over a wide frequency band.

Characteristics of dielectric loaded and covered circular waveguide phased arrays

The use of dielectric materials for the hardening and matching of phased-array antennas in recent years has shown that a more complete understanding of the effects of these materials upon the array performance is necessary. The characteristics of fully loaded, plugged, and sheath covered circular waveguide phase arrays are analyzed and discussed. Numerical solutions of the boundary-value problem are verified by experimental and convergence tests. Particular emphasis is placed on the study of (forced) surface wave resonance effects. Three different cases for surface wave resonances were obtained. These include the case in which surface wave resonances are present in the absence of dielectrics, the case in which they are trapped by the presence of dielectric plugs, as well as the case in which waves are trapped by the presence of a dielectric sheath. The surface wave resonance due to the plug is shown to vanish for certain "bandpass" ranges of plug thickness which repeat periodically for a single trapped waveguide mode. On the other hand, the surface wave trapped in the sheath exhibits no "bandpass" characteristics. Instead, multiple surface wave resonances occur with increasing sheath thickness. Finally, the surface wave resonances observed here appear at isolated points in the scan plane.

Commission 6: Progress in Radio Waves and Transmission of Information: 1. Radio Waves

In this area, by far the greatest effort has been focused on arrays, particularly phased arrays; the results have been summarized in three books [Hansen, 1966; King et al., 1968] and two special journal issues [Radio Science, 1968; IEEE, 1968]. Complete design formulas for scannable Baklanov‐Chebyshev arrays [Tseng and Cheng, 1968] and new approximations for long Dolph‐Chebyshev arrays [Drane, 1968] were developed. Infinite array models dominated in numerous studies of large phased arrays. Grating lobe effects were investigated by the induced emf method [Stark, 1966] and by use of impedance craters [Wheeler, 1966] Important and unexpected element pattern nulls not attributable to grating lobes have been observed and explained as coupling accumulation [Lechtreck, 1968] and as external resonances in dielectric sheets [Knittel et al., 1968; Wu and Galindo, 1968]. They have also been observed as mismatches in array simulators [Hannan, 1967a]. Proof of the possibility of impedance matching for all scan angles has been offered [Hannan, 1967b] and contested [Varon and Zysman, 1968] Limited control of coupling for wide angle impedance matching has been achieved by means of dielectric sheets [Magill and Wheeler, 1966], hole coupling of waveguides [Amitay, 1966], multiple modes in waveguides [Tang and Wong, 1968], and parasitic chokes [Dufort, 1968], and the form of asymptotic decay of coupling with distance has been established [Galindo and Wu, 1968]. Systematic procedures for the design of phased array elements have appeared [Wheeler, 1968; Amitay et al., 1968], as have methods of analysis of waveguide phased arrays without [Farrell and Kuhn, 1968], and/or with [Borgiotti, 1968a] dielectric sheets. Finally, there was developed an important geometrical description of phased array behavior, based on the fundamental principle of planar apertures, that unifies much of the existing knowledge of infinite arrays [Diamond, 1968]. A thorough application of this development to arrays of rectangular waveguides shows clearly the individual roles of the lattice and the elements [Ehlenberger et al., 1968]. The same principle was used to compute mutual admittances between slots [Borgiotti, 1968b], and formulas for observable stored energies of planar apertures have been derived from it [Rhodes, 1966] and contested [Borgiotti, 1967; Collin, 1967].

A Modified Residue-Calculus Technique for Solving a Class of Boundary Value Problems-Part II: Waveguide Phased Arrays, Modulated Surfaces, and Diffraction Gratings

The modified residue-calculus technique (MRCT) described in a companion paper may be combined with scattering matrix, multiple-reflection techniques to provide solutions in scattering matrix form to thick-wall waveguide phased array, modulated surface, and strip grating geometries. Each of these geometries may be regarded as a periodic array of thin plates modified by dielectric fillings, waveguide steps, and terminations. Solutions to the modified geometries are found by combining the exact solution to the thin-wall array problem with approximate solutions to certain waveguide discontinuity problems found by the MRCT. In particular, a value of the dominant mode reflection coefficient versus scan angle for the thick-wall array may be found accurate to two or three significant figures without need for matrix inversion. In general, reduction of matrix size by a factor of 5 or more over conventional methods with equivalent accuracy may be realized.

A note on the radiation characteristics and forced surface wave phenomena in triangular-grid circular waveguide phased arrays

Forced surface wave resonances are shown to occur in dielectric-free 45-degree triangular-grid circular waveguide phased arrays. Similar surface wave phenomena were observed in an identical grid array of rectangular waveguides in the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</tex> -plane of scan. In the circular waveguide array, however, the resonance is observed in the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</tex> -plane and is shown to be an isolated point. This isolation is further illustrated by observing certain vector symmetries in the radiation patterns.

Dielectric Loaded and Covered Rectangular Waveguide Phased Arrays

This study examines the effects of loading or covering a phased array with dielectric materials. It studies in detail the effect of dielectric geometry, dielectric constant, and sheath thickness on the wide angle array performance of an array of rectangular waveguides in the H and quasi-E plane modes of scan. We obtain numerical solutions of the integral equations describing an array covered with thick dielectric material. The results show that we can obtain a match over a wide scan angle for the array by appropriate use of dielectric geometries, and we discuss the advantages and disadvantages of several geometries.