Quasi-optical Beam Research Articles

On O–X mode conversion near the cut-off surfaces in 3D sheared magnetic field

The linear coupling between ordinary and extraordinary electron cyclotron waves in the vicinity of the cut-off plasma density is discussed, taking into account variation of a magnetic field on flux surfaces in tokamaks and stellarators. Previously developed theory of two-dimensional mode conversion is applied to study the effects of the poloidal magnetic field and its shear, in particular, on the efficiency of penetration of quasi-optical beams through the evanescent layer due to transformation into a cross mode.

Compact Gaussian Beam System for S-Parameter Characterization of Planar Structures at Millimeter-Wave Frequencies

This paper describes the design and implementation of a compact quasi-optical Gaussian beam system for measuring the frequency response of millimeter-wave materials, frequency-selective surfaces, and antenna elements in the array environment. The core components of this system are two wideband millimeter-wave focusing array antennas that act as adapters between the coaxial ports of the network analyzer and the wave ports defined at the input and output planes of the device under test. The use of planar focusing arrays for generating the Gaussian beams leads to very compact measurement setups with a total length of only a few centimeters. This paper addresses the design of the Ka/Q-band focusing arrays and demonstrates the utility of the proposed system through experiment. A useful method that allows reproducing two-port S-parameters from one-port measurements will also be introduced.

Analysis and Design of $E$-Plane Scanning Grid Arrays

A quasi-optical beam steering multilayer lens with scanning in E -plane is analyzed. A full-wave mathematical model is developed to predict the scanning characteristics of the lens. The model is used to optimize the performance of a three-bit beam steering lens. It is demonstrated that the calculated conversion coefficients for the optimized lens are better than -2.1 dB in the frequency band from 27.5 to 32.5 GHz for transmission elevation angles up to 28°. A two-bit lens that corrects the phase front at the aperture of a short .E-plane sectoral horn has been designed, fabricated and tested to verify the model. Measured radiation pattern of the E -plane sectoral horn with correcting lens agrees well with the predictions based on the model.

Time-resolved imaging of millimeter waves using visible continuum from the positive column of a Cs–Xe dc discharge

We present a high-sensitivity technique for time-resolved imaging of millimeter waves (MMWs) using the visible continuum (VC) from the positive column (PC) of a medium-pressure Cs–Xe dc discharge. For the MMW imaging application, a uniform plasma slab of the PC of a Cs–Xe discharge with 10×8 cm2 aperture and 2 cm in thickness was generated for 45 Torr xenon. The imaging technique is based on the fact that the intensity of the e-Xe bremsstrahlung continuum from the PC increases in the visible region when the electrons in the plasma are heated by MMWs. It is shown that in the MMW intensity range from zero to the threshold of the microwave-induced plasma breakdown, the intensity of the VC from the PC of a Cs–Xe discharge increases approximately as a second-order polynomial function of the MMW intensity. The obtained experimental data agree well with our calculations of the dependence of the VC intensity on electron temperature. The Ka-band MMW field patterns at the output of conical horn antennas and in the quasioptical beam were imaged using the discharge technique. It is shown that the technique can be used for time-resolved measurement of the profiles of watt- and subwatt-level MMWs. An energy flux sensitivity of the technique of about 10 μJ/cm2 in the Ka-band was demonstrated. The temporal resolution of the technique is about 0.8 μs. Our modeling of the transient behavior of the electron temperature in the PC shows that the time history of the electron temperature variation coincides well with the measured time history of the VC intensity variation.

Investigations of Subcritical Streamer Microwave Discharge in Reverse-Vortex Combustion Chamber

In this paper, we report on the experimental investigations of two innovative technologies combined in one device, namely, the application of an initiated streamer microwave (MW) discharge for ignition and flame control in a reverse-vortex combustion chamber, also known as a Tornado combustor. The pulsed subcritical streamer MW discharge (SSD) in a quasi-optical wave beam was experimentally investigated in the atmospheric-pressure model of a Tornado combustor with transparent dielectric walls. The possibility of a surface MW streamer discharge formation at new conditions, particularly on the dielectric walls of the cylindrical combustion chamber, has been confirmed. The mechanism of SSD realization, at which the discharge development takes place in a volume of the combustion chamber, has been proposed. It was shown that SSD could be applied for ignition of fuel/air mixtures in an axial area of the reverse-vortex combustion-chamber bottom plate, which is normally used for a fuel feeding.

Electrical discharge excited by the deeply undercritical field of a microwave beam in a high-speed jet of air and air-propane mixture

An electrical gas discharge initiated by a tubular linear electromagnetic vibrator is studied. The discharge is excited by the deeply undercritical linearly polarized field of a quasi-optical microwave beam. Experiments are conducted at a flow velocity of several hundreds of meters per second. The discharge region is photographed, and the stagnation temperature of the flow in the wake of the discharge is measured. It is shown that a deeply undercritical microwave discharge may arise in air even at such high flow velocities. Moreover, it is found that the discharge ignites and stabilizes the discharge region in a “lean” air-propane mixture. In such an experimental design, propane completely burns out when the flow velocity is smaller than some threshold value. When the flow velocity is high and the Mach number of the flow approaches unity, throttling effects and “thermal blocking” of the jet are observed.

Deeply undercritical microwave discharge excited by the field of a quasi-optical electromagnetic beam in a supersonic air jet

Electric discharge in a supersonic air jet is studied. It is ignited in a linearly polarized quasi-optical microwave electromagnetic beam the initial field intensity of which is much lower than the breakdown level. Electric breakdown is initiated by a tubular electromagnetic vibrator, one end of which has spikes and is covered by a quartz tube. Atmospheric air enters into a low-pressure working chamber through the inner channel of the vibrator. As a result, an immersed supersonic air jet forms in the chamber at the outlet from the quartz tube. A microwave discharge ignited in this jet is “attached” to aft spikes of the vibrator. The energy deposit into the discharge plasma and the effective area of energy interaction between the discharge and excited microwave field are estimated from the temperature and stagnation pressure distributions in the wake of the discharge.

Theoretical Investigation of Iterative Phase Retrieval Algorithm for Quasi-Optical Millimeter-Wave RF Beams

In this paper, we present a detailed analysis of the iterative phase retrieval approach (IPRA) for determining the phase profile of the output microwave beam of a gyrotron from known intensity patterns emphasizing the field propagation techniques which are used to propagate the RF field of the microwave beam between known intensity planes. The propagation method, based on first Rayleigh-Sommerfeld diffraction integral (RSDI), is solved using fast Fourier transform (FFT) technique and zero padding. It is observed that the use of FFT and, therefore, the discretization of the RSDI propagation kernel introduce aberrations in the propagated field due to the superposition of the original field with its replicated versions. This problem is solved by approximations leading to the Huygens-Fresnel propagation method which further imposes the restrictions on the distances of propagation depending on the size of the transverse plane used to discretize the intensity pattern. This constraint of the distance of propagation causes problem in the iterative phase retrieval approach (IPRA) when more than two intensity planes are used. A method based on interpolation is proposed to overcome this restriction. IPRA is then further discussed to optimize several parameters, such as plane separation, plane dimension, mesh size, and measurement accuracies, which become more of an issue during the measurements of infrared intensity thermograms of the output microwave beam.

Ionization-overheating instability threshold in the electrodeless microwave discharge plasma

Experiments with a pulsed freely localized electrodeless microwave discharge in air under a pressure corresponding to the ascending branch of the pressure dependence of the breakdown field are described. The discharge is initiated in a focused quasi-optical electromagnetic beam. The minimal threshold values of the electromagnetic field (for which a brighter plasma channel extended along the field is formed in the initially spatially homogeneous diffuse discharge plasma) are determined by varying air pressure for several fixed values of this field in the focal region of the beam. In accordance with the prevailing theory, this phenomenon is interpreted as the result of evolution of ionization-overheating instability in the microwave discharge plasma.

On perfect O–X mode conversion near the cut-off surfaces in magnetized plasmas

Recently the theory of linear coupling between the ordinary (O) and extraordinary (X) electron cyclotron waves in the vicinity of critical (cut-off) plasma density was generalized for two-dimensionally inhomogeneous plasma configurations, in particular taking into account the variation of a magnetic field on flux surfaces in tokamaks and stellarators. One of the new features of two-dimensional mode conversion is the existence of optimal quasi-optical beams of a finite aperture exhibiting perfect (no reflection) transformation instead of an optimal plane wave specific for one-dimensional geometry. In this paper such wave structures are analysed in more detail keeping in mind its importance for experiments on electron cyclotron resonance heating and diagnostics of overdense magnetized plasma based on linear mode conversion in modern stellarators and spherical tokamaks.

Microwave breakdown of air initiated by a short electromagnetic vibrator

The electrical breakdown of air (under a pressure from several tens of Torr to several hundreds of Torr) is initiated in a linearly polarized quasi-optical microwave beam using a rounded-end cylindrical metallic electromagnetic vibrator placed parallel to the electric component of the microwave field. The vibrator is much shorter than the wavelength of the field. The field strength at the top of the vibrator as a function of its length is determined. An empiric expression relating the field strength at the top with the vibrator length-to-diameter ratio is found for the vibrator length range studied. The practicability of locally measuring the field in a quasioptical microwave beam is substantiated. The idea is to determine the maximal air pressure at which electrical breakdown of air initiated by a short vibrator placed at a given point of the beam takes place.

Parameterized modelling of mm-wave beam propagation of the ITER ECRH remote steering upper port launcher in CATIA

A 3D model has been developed in CATIA that is capable of accurate visualization of a mm-wave beam along the entire free-space section of a transmission line. This development has been applied to the design of the remote steering ECRH upper port launching system for ITER. Because the model uses parameterized equations to calculate the quasi-optical beam propagation, it can show the effects of a change of any of the transmission line components (location, orientation, or optical properties). Furthermore, it takes into account the effects the square waveguide has on the propagating beams as a function of its steered angle. The beam size at its target area inside the ITER plasma has proven to be a good indicator of the launcher's performance. It has also become clear that the 3D visualisation of the beam propagation in the structural design can result in a much more efficient use of the confined space inside each upper port plug—space that is also needed to locate sufficient neutron shielding and cooling structures, as well as to allow access for remote-handling tools.

Thermal ionization instability of an air discharge plasma in a microwave field

Results are presented from experimental studies of the initial stage of an air discharge initiated in a linearly polarized quasi-optical microwave beam. The discharge was excited at an air pressure at which the electron-neutral collision frequency in the discharge plasma was considerably higher than the circular frequency of the electromagnetic field and at a microwave field amplitude close to the threshold field for air breakdown. The experiments revealed relatively bright plasma channels stretched along the microwave electric field. The development rate of these channels and their characteristic transverse dimensions are estimated. A comparison of the experimental data and theoretical estimates indicates that the channels observed arise due to the onset of thermal ionization instability in the microwave discharge plasma.

Numerical analysis and synthesis of 2D quasi-optical reflectors and beam waveguides based on an integral-equation approach with Nystrom's discretization

Considered is the beam wave guidance and scattering by 2D quasi-optical reflectors modeling the components of beam waveguides. The incident field is taken as the complex-source-point field to simulate a finite-width beam generated by a small-aperture source. A numerical solution is obtained from the coupled singular integral equations (SIEs) for the surface currents on reflectors, discretized by using the recently introduced Nystrom-type quadrature formulas. This analysis is applied to study what effect the edge illumination has on the performance of a chain of confocal elliptic reflectors. We also develop a semianalytical approach for shaped reflector synthesis after a prescribed near-field pattern. Here a new point is the use of auxiliary SIEs of the same type as in the scattering analysis problem, however, for the gradient of the objective function. Sample results are presented for the synthesis of a reflector-type beam splitter.

Domains of existence of various types of microwave discharge in quasi-optical electromagnetic beams

High- and medium-pressure discharges excited by quasi-optical microwave beams in air are classi- fied using experimental data. Diffuse, streamer, overcritical, undercritical, and deeply undercritical discharges are distinguished. The domains of existence of each type of discharge are determined as functions of the air pressure and field strength for two particular electromagnetic wavelengths.

Experimental Verification of Phase Retrieval of Quasi-Optical Millimeter-Wave Beams

The accuracy of a phase-retrieval procedure for microwave beams was analyzed and verified using an 84-GHz quasi-optical beam transmitted by a corrugated waveguide. The output intensity and phase profiles of the beam were directly measured with a microwave receiver. The beam intensity was also measured at several planes and the data were used with a phase-retrieval algorithm to yield an independent estimate of the phase. Moment and matching coefficient methods were used to analyze the retrieved profiles. In the higher order moment analysis, the intensity profiles, which were calculated from the retrieved phase profiles, coincided well with the measured profiles in terms of the beam size, asymmetric property (skewness), and flatness/peakedness (kurtosis) over the entire profile. Analysis indicated that the mode content of the beam obtained by phase retrieval matched that of the direct measurement with a matching coefficient of 0.97 using both the intensity and phase profiles

Quasi-optical Gaussian beam tracing to evaluate Doppler backscattering conditions

Microwave beam backscattering near the cut-off layer appears to be the most interesting diagnostic to observe density fluctuation time evolution for a given localization in the plasma and at a defined wave vector. It also provides perpendicular plasma velocity. Scattering only occurs when the Bragg selection rule is fulfilled, i.e. when the scattering wave vector is almost perpendicular to the magnetic field. In order to evaluate these scattering conditions, ray tracing is required. 3D geometry is necessary to evaluate the angle between the magnetic field and the wave vector at the reflection. The ripple effect on the iso-index layer curve cannot be neglected. Scattering localization and wave vector resolution can be approached if single ray tracing is replaced with quasi-optical beam tracing. Optical propagation is still considered in the WKB approximation but the beam is described as multiple connected rays. The beam radial expansion due to diffraction is well described. This approach allows one to compute beam parameters for all data acquisitions (50 triggers per shot) and all shots (40 shots per day) during the following night on a recent personal computer with MatLab©.

On the influence of 2D inhomogeneity on electromagnetic mode conversion near the cut-off surfaces in magnetized plasmas

Peculiarities of the ordinary to extraordinary wave conversion in the electron cyclotron frequency range near the cut-off surfaces in magnetized plasmas are analysed in a two-dimensionally inhomogeneous simplified tokamak-like geometry. It is demonstrated that the mode conversion may be of essentially two-dimensional nature even neglecting the curvature of the cut-off surfaces; for the latter case a set of reduced wave equations in the transformation region is derived and solved analytically. Transformation coefficients for quasi-optical beams with a finite transverse distribution of rf field are obtained as well as a recipe for synthesis of the optimal (perfectly converted) beam. Applicability limits of a conventional one-dimensional theory are finally discussed.

Excitation of surface wave beams at the interface between linear and nonlinear media

The spatial evolution of quasi-optical electromagnetic-wave beams propagating in the vicinity of an interface between linear and nonlinear media is studied. It is demonstrated that three-dimensional nonlinear surface beams can efficiently be excited by Gaussian beams of optimal shape, incident onto the nonlinear interface at angles exceeding the total internal reflection angle, and that giant nonlinear Goos-Hanchen effect can result from this process.

Gaussian beam mode analysis of standing waves between two coupled corrugated horns

In this paper we present the theoretical analysis of the effects of standing waves between coupled horn antennas that can occur in terahertz quasi-optical systems. In particular we illustrate the approach for the case of two coupled horn antennas as the distance between them is varied. The full mode matching scattering matrix approach is based on combining a standard waveguide mode description of the horn antenna and a quasi-optical Gaussian beam description of the free space propagation. Track is kept of both the backward and forward going components of the propagating fields. We compare theoretical predictions with actual experimental test results for a quasi-optical system operating at a frequency of 0.480 THz.