Backward Wave Mode Research Articles

Application of Algebraic Function Theory to Backward Wave Problems

The problem of studying backward wave mode characteristics of metallic waveguides filled with inhomogeneous and/or anisotropic media, is equivalent to understanding properties of the propagation constant of the guiding structure. In this paper we focus on metallic waveguides filled with inhomogeneous and/or anisotropic media that do not couple transverse to longitudinal field components and note that the propagation constant of such structures is the solution of an algebraic equation. This feature permits application of the well developed theory of algebraic functions to understanding of the backward wave mode behavior of the propagation constant. We show that the problem of assessment of backward wave modes for such guides fits exactly in this theory, and using this fact, numerous results are derived which may be used in the design of backward wave systems.

On The Existence of Backward Waves In Metallic Waveguides

A proof is provided for the fact that whenever there is a frequency region of a backward wave in metallic waveguides filled with media which do not induce coupling between transverse and longitudinal fields, then there exists an adjacent region with a complex propagation constant. This proof is based on the Method of Moments approach used in converting the problem of calculating the modal fields of the inhomogeneous and/or anisotropic waveguide, to a matrix eigenvalue problem. It is also shown that for those structures which are additionally frequency independent, a necessary condition for the existence of backward waves is that TE-TM modes of the empty waveguide whose eigenfunctions are used in the representation of the fields in application of the Method of Moments, be coupled. In other words the waveguide must be inhomogeneous or anisotropic or both for a backward wave mode to exist.

NECESSARY AND SUFFICIENT CONDITIONS FOR THE EXISTENCE OF BACKWARD WAVES IN METALLIC WAVEGUIDES

A novel expression has been obtained for the group velocity in metallic waveguides which are filled with media which do not induce coupling between transverse and longitudinal fields. It is shown that utilizing the expression derived for the group velocity one can express the necessary and sufficient conditions for the existence of backward waves in these waveguides. The criteria developed for the existence of backward waves do not involve evaluation of derivatives even though a backward wave mode by definition is one which has opposite signs for the propagation constant and its derivative with respect to frequency.

YIG 단결정 박막에 대한 정자파의 온도의존성 연구

LPE(liquid phase epitaxy)방법으로 제작한 YIG 단결정 박막의 정자파(MSW; magnetostatic wave) 모드의 온도의존성을 조사하기 위하여 온도를 -14<TEX>$0^{\circ}C$</TEX>에서 20<TEX>$0^{\circ}C$</TEX>까지 2<TEX>$0^{\circ}C$</TEX>간격으로 변화하면서 강자성공명 실험을 하였다. 시편면과 외부자기장을 평행하게 가할 때 모든 온도에서 주기적인 신호로 나타나는 정자표면파와 정자역체적파 모드를 관측하였다 온도가 감소함에 따라 정자파 모드들은 저자장쪽으로 이동하고 세기가 감소하였고, 각 모드들 사이의 간격은 증가하였다. 온도변화에 따른 정자파 모드를 Walker와 Damon-Eshbach 이론으로 분석한 결과 잘 일치하였다. 온도별로 계산한 포화자화값은 온도가 감소함에 따라 증가하였다. 관측된 정자파 모드의 선폭은 온돈가 감소함에 따라 다양하게 변화하였다. In order to study the temperature dependence of the magnetostatic wave modes for an YIG thin film, grown by a liquid phase epitaxy method, The ferromagnetic resonance was performed by an FMR spectrometer in the temperature range -140<TEX>$\^{C}$</TEX>∼200<TEX>$\^{C}$</TEX>. The magnetostatic surface wave and backward volume wave modes show periodic excitations in parallel configuration. The resonance fields of all modes and intensities decreased with decreasing the temperature. All magnetostatic modes can be well explained by the Walker and Damon-Eshbach theory. The calculated saturation magnetization Ms of the YIG thin film was increased with decreasing the temperature. The line widths of magnetostatic modes changed in various trends with decreasing the temperature.

Chatter Instability in Milling Systems with Flexible Rotating Spindles—A New Theoretical Approach

The stability characteristics of a milling system are investigated in this paper. A model is developed that includes the gyroscopic effects of the rotating spindle and on the basis of this model new insight into the physics of chatter instability is obtained. In the analysis the basic Fourier series method for solving a harmonically time-varying system without time lag is extended to obtain a finite-order characteristic equation for the milling system in terms of the system matrices. The complex eigenvalues of the resulting characteristic equation can be efficiently predicted by using Mu¨ller’s optimization algorithm with deflation, and the stability lobes can be predicted by using a nonlinear optimization procedure at different rotating speeds based on the Nyquist stability criterion. In this study it was found that including the gyroscopic effects of the rotating spindle increases the real parts of the eigenvalues of the system. This reduces the critical axial depth of cut. It is also found that the milling forces primarily excite the backward-wave modes but stabilize the forward-wave modes of the rotating spindle.

Efficiency enhancement in high power backward-wave oscillators

High power microwave (HPM) sources based on the backward-wave oscillator (BWO) have been investigated for the past two decades primarily because of their potential for very high efficiency (15 to 40%) operation. Several different effects have been proposed to explain this high efficiency compared to conventional BWOs. One of the major contributors to the high efficiency of the plasma-filled Pasotron HPM BWO source is the presence of optimally phased end reflections. The Pasotron uses a long-pulse (/spl ges/100 /spl mu/s) plasma-cathode electron-gun and plasma filled slow-wave structure to produce microwave pulses in the range of 1 to 10 MW without the use of externally produced magnetic fields. The efficiency of the Pasotron can be enhanced by up to a factor of two when the device is configured as a standing-wave oscillator in which properly phased reflections from the downstream collector end of the finite length SWS constructively interfere with the fundamental backward-wave modes and improve the coupling of the beam to the circuit. Operation in this configuration increases the efficiency up to 30% but causes the frequency to vary in discrete steps and the output power to change strongly with beam parameters and oscillation frequency.

Results from gyrotron backward wave oscillator experiments utilizing a high-current high-voltage annular electron beam

We report the first gyrotron-backward-wave oscillator experiments which utilize a high-current (1-4 kA) high-voltage (300-500 keV) annular electron beam. The experiment was designed to operate in the TE/sub 01/ backward wave mode. Radio frequency extracted power was 0.1-4 MW, with pulselengths of 80-500 ns. Experimental results suggest the possibility of competition with the TE/sub 21/ backward wave mode. Frequency spectrum measurements have shown a wide content of frequencies during the voltage pulse, an undesirable result for use in narrow-band devices.

Wave dispersion and growth analysis of low-voltage grating Čerenkov amplifiers

A theoretical and computational investigation of an electron sheet beam propagating over a grating structure in a rectangular waveguide is carried out. Regimes for low voltage Čerenkov amplifier operation are sought by examining the complex dispersion relation for hybrid waveguide modes in the slow wave structure, which includes sheet beam space-charge effects. A computer code is developed to examine the complex dispersion relation and growth rates for the wave modes. Mode competition is considered and methods to reduce it are presented. Briggs’ criteria is utilized to examine absolute and convective wave growth for the forward wave, backward wave, and transition mode regimes of operation as a function of the beam, hybrid mode, and slow wave grating characteristics. An examination of the effects of beam spread on absolute and convective wave growth to determine regimes for amplifier operation is carried out. A modest Maxwellian beam spread is found to yield a regime of effective backward convective amplification, in addition to the purely convective growth characteristics for the forward wave mode case.

Parasitic oscillation in and suppression of a gyrotron backward wave mode in a low-Q 8 GHz gyrotron

The parasitic oscillation of the TE degrees /sub 21/ gyrotron backward-wave (gyro BW) mode is observed in a low-Q, 8 GHz TE degrees /sub 011/, gyrotron. At low power (P/sub BW/<5 kW), the oscillation of the gyro BW mode, simultaneously with the gyrotron mode, results in a maximum TE degrees /sub 011/, mode efficiency of less than 0.25. The parasitic oscillation is suppressed by operating the gyrotron with a negative magnetic field gradient along the electron beam, which allows the maximum efficiency to reach 0.40 and the output power to be multiplied by a factor varying from 1.4 to 1.7. The optimum efficiency curve of the TE degrees /sub 011/ mode indicates that the low-Q cavity behaves as a much higher Q/sub diff/ cavity. Excessive values of magnetic field gradient and alpha favor the TE degrees /sub 012/, longitudinal mode, which oscillates in place of the TE degrees /sub 011/ mode and limits its maximum output power. This competitive process is responsible for the high-Q-like behavior of the optimum efficiency curve.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Photothermal investigation of magnetostatic modes in yttrium iron garnet at high microwave power levels

Laterally resolved magnetostatic mode spectra in an yttrium-iron-garnet single-crystal (0.98 mm*8.40 mm*4.40 mm) were obtained by microwave spectroscopy using the photothermal laser beam deflection technique. For a microwave frequency of 9.33 GHz and a power of 2.2 W, both magnetostatic surface and magnetostatic backward volume wave modes were observed. The lateral variation of these modes can be explained by a modified WKB approximation for the magnetostatic potential and by taking into account the presence of an inhomogeneous demagnetization field inside the sample. At high incident microwave power, a foldover effect in the range of the surface wave modes and one distinctly larger volume wave mode peak occur. The photothermal signal phase provides information on the penetration depth of the surface wave modes.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Complex and Backward-Wave Modes in Inhomogeneously and Anisotropically Filled Waveguides

A rigorous analysis of lossless inhomogeneously and anisotropically filled waveguides of arbitrarily shaped cross section is presented. The mode propagation constants squared appear as eigenvalues of a real infinite-dimensional characteristic matrix, which is, in the general case, nonsymmetric. Complex conjugate pairs of eigenvalues are then possible, which give rise to complex modes. Modes at cutoff are shown to be either TE or TM with real cutoff frequencies. An investigation of the power flow shows that backward-wave modes may exist as well. Different orthogonality relations are derived from which the power coupling between complex modes is investigated.

Formulation of the Singular Integral Equation Technique for Planar Transmission Lines

The singular integral equation technique is used to determine the normal modes of propagation in general planar transmission lines. Taking finlines as, an example, it is demonstrated how high-order modes can effectively and accurately be calculated. It is also shown that complex and backward-wave modes, which are known to exist in rectangular and circular waveguides with dielectric inserts, can also exist in finlines. Besides a discussion of their characteristic features, this paper describes the conditions under which complex and backward-wave modes are found in finlines.

Electronically variable time delays using cascaded magnetostatic delay lines

A magnetostatic wave (MSW) variable time delay device with a phase deviation from linearity of less than 20 deg over a bandwidth of 300 MHz centered at 3 GHz has been demonstrated. The device consists of two cascaded delay lines. One delay line is biased to operate in the surface wave (MSSW) mode to provide a positive slope delay versus frequency characteristics, while the other operates in the backward volume wave (MSBVW) mode to provide a dispersive characteristic with negative slope. Both dispersions have been linearized by modifying the spacing between the propagation medium (YIG film) and the ground plane. The net device dispersion is the sum of the dispersive characteristics of the individual delay lines, and delay variability is achieved by varying the bias field of one of these components. A bias field change of 100 G will change the total delay by more than 40 ns.

A Finite Element Model for Temperature Induced Electrohydrodynamic Pumping in Horizontal Pipes

The electrohydrodynamic (EHD) pumping created by an axially traveling electric wave superimposed on a dielectric fluid with a transverse temperature field has been investigated using a finite element technique. Both forward wave (cooled wall) and backward wave (heated wall) modes of operation have been considered. The secondary flow generated by buoyancy effects in the cross section were included in the calculations. The driving effects of the traveling wave were calculated by assuming that only the average electric shear stress produced movement while the sinusoidally varying transient effects cancelled out. The results show that effective pumping can be achieved without the use of a grounding electrode along the axis of the tube but the design parameters have to be carefully selected. Increasing the diameter-to-wavelength ratios increases the velocities. The flow rate is maximum at an optimum frequency, about 0.8 Hz in our typical cases, but it drops off rather quickly as the frequency is either decreased or increased. The velocities were much less sensitive to heating/cooling rates (i.e., Rayleigh numbers) or changes in the magnitude of the electrical conductivity values. Although the pumping effect increases approximately as the square of the maximum applied electric potential, in practice, the electric gradients are limited by the dielectric strength of the fluid. The results indicate the EHD heat exchanger/pumps can be feasible alternatives to mechanical pumps in certain circumstances when dielectric liquids require both heat tranfer and circulation.

Improved orotron performance in the 50- to 75-GHz frequency region

New experimental results for the Harry Diamond Laboratories (HDL) orotron, a Smith-Purcell free-electron laser, have been obtained. Emphasis was placed on improving the 100-mW output power previously obtained with this device by using a new, more powerful ribbon-beam electron gun and a new open resonator. The orotron was tuned continuously from about 50 to 75 GHz on a TEM <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">208</inf> Fabry-Perot mode; more than a watt of output power was measured on this mode. Considerably more power, approximately 5 W, was obtained at 65.65 GHz on a TEM <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">209</inf> mode. Oscillation of the orotron was also observed on backward wave modes. In addition, it was found that improvements in beam quality lead to higher power orotron operation.

Nonlinear Wave Interactions on a Discrete Transmission Line

On a discrete transmission line which admits both the forward and backward wave modes, the following four kinds of weakly nonlinear wave interactions are investigated theoretically: (i) the three-wave interaction, (ii) the second harmonic resonance, (iii) the interaction between a pair of waves with equal group velocities and (iv) the interaction between a long wave and a short wave where the phase velocity of the former is equal to the group velocity of the latter. In each case, it is shown by using the derivative expansion method that the original differential-difference equation for the transmission line can be reduced to a simple set of interaction equations which are similar in form to those obtained so far in water waves, plasma waves, nonlinear optics, and other fields.

Circuit properties of coupled dispersive transmission lines

A circuit model is used to present the basis forthe existence of complex propagation constants and backward wave modes in lossless coupled dispersive transmission lines. In particular, for the 2-line lossless case, conditions for realizing complex modes, as well as the possible forms for the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\omega-\beta</tex> diagram are given. Methods for approximating the mode behavior of lossless waveguide systems, uniform in the propagation direction, but with transverse plane inhomogeneities, are presented using coupled-line models. These methods are derived from the Schelkunoff representation of such a waveguide structure by an infinite set of coupled TE and TM dispersive transmission lines. The techniques used in this paper depend on an approximation which reduces the infinite number of lines to a finite number. One approximation method interpolates the parameters of a realizable 2-line system to approximate the behavior of the infinite line system up to a frequency in the vicinity of the secondlowest eigenmode. A second method is a systematic network procedure for eliminating coupling ports of the infinite structure so as to obtain a finite number of coupled lines to approximate the mode behavior. These two methods are illustrated by 2-line models for round waveguide loaded with a dielectric rod. The mode behavior of the loaded guide is surprisingly well approximated by both the 2-line models.

Proposed microwave delay lines for pulse-compression radar

The letter discusses some properties of dispersive delay lines suitable for use in pulse-compression radar systems with pulse bandwidth of up to 600 Mc/s. The lines employ the backward-wave mode of propagation in dielectric-loaded waveguide.

A Backward-Wave Surface Mode in a Plasma Waveguide

The phase characteristics of a backward-wave pass-band mode have been measured in a plasma waveguide, consisting of a circular waveguide that is coaxial with the positive column of a mercury-vapor discharge. The mode has been identified as an n = 1 surface mode similar to that described by Trivelpiece. It is shown that zero-temperature plasma-waveguide theory predicts this mode accurately. This theory predicts that a simple relation exists between the lower cutoff frequency of the n = 1 mode and the electron plasma frequency. It is demonstrated that the calculated electron plasma frequency obtained from this relation, where the cutoff frequency is determined from a measurement of the phase characteristics, agrees well with an independent measurement of electron plasma frequency by the well-known cavity-perturbation method. Both the n = 1 and symmetric n = 0 modes were excited by a novel coupler called the double-ring coupler. Noise measurements on the n = 1 and symmetric n = 0 modes indicate that the output signal-to-noise ratio is independent of input signal power and is about 7 dB for the n = 1 mode and varies from about 7 to greater than 30 dB for the n = 0 mode. A simple model of the plasma is proposed which explains all the noise observations reported here. Crawford and Lawson independently proposed a similar model.

Wave Propagation in a Tubular Plasma

The configuration consisting of a dielectric rod, surrounded by a plasma shell and a concentric outer conducting cylinder, is investigated theoretically and experimentally for its propagation characteristics. It is predicted from the theory that such a configuration will support propagation in a backward wave mode (oppositely directed phase and group velocities). These backward waves were observed in experiments using a configuration essentially identical to the above (the dielectric rod had an air space down the center used to insert a probing antenna), with the plasma provided by a cesium discharge. Agreement between these observations and calculations is excellent. A forward wave was also observed at low frequencies, and is attributed to the influence of the sheath at the plasma-conductor interface. The observed dispersion curve for this forward wave is also in good agreement with that calculated using the expected sheath size of the cesium plasma-metal interface.