Tape Helix Research Articles

CAD of Tape Helix Circuits for Traveling Wave Tubes by Convolution Methods

This work describes a new general approach to the analysis of periodic tape helix circuits and its application in practical computer programs for numerical design. The procedure is based on transforming the stationary periodic tape helix itself to Fourier space, in the same manner as the RF fields. The interaction between the RF field harmonics and the stationary circuit harmonics is conceptually a convolution process. The mathematical description of this process is done through the intermediary of a convoluting circuit matrix created from the geometrical harmonics of the stationary metallic circuit, representing its Fourier space transform. Similar representations are made of the external dielectric rod and metallic vane system so that the entire configuration is analyzed by the same approach. The procedure separates the overall fields into two orthogonal distributions belonging to the nullspace and the range of the convolution matrices of the relevant circuit regions. All relevant data such as the dispersion relation and fundamental and space harmonic impedances are obtained as part of the nullspace distribution alone. The distributions belonging to the range have the character of independent idler fields playing no part in the solution process. The presented theory is exact for all configurations of tape helix structures and of anisotropic dielectric rods and metallic vanes. In order to benefit from reduced programming efforts, the exact theory is approximated by disregarding certain second-order effects, and implemented into a comprehensive computer program for design of tape helix circuits for traveling wave tubes. A set of computer-generated numerical data compared with experimental results are presented at the end.

Analysis of the Dispersion Characteristic and Interaction Impedance of a Tape Helix Slow Wave Structure with Novel Supporting Mode

In order to enhance the power capability of the helix travelling wave tube, a novel tape helix slow wave structure (SWS), which is supported by helically arrayed radial dielectric-support posts, is developed. Each dielectric post can be easily brazed with the tape helix and the metal envelope by means of a special soldering. This kind of supporting mode can protect the dielectric supporting posts from being broken by the thermal stress in the case of high temperature. A hybrid model is set up in consideration of the influences of both the radial thickness of the tape helix and these discrete dielectric-support posts. The dispersion equation and interaction impedance of the helical SWS are obtained. The calculated results using this hybrid model presented in the paper show good agreements with the HFSS simulation results. All the results presented here can provide a good basis for designing the novel tape helix SWS.

Simplified Approach to the Nonlinear Analysis in Helix Slow-Wave-Structure for a Traveling Wave Tube

A stationary 1-D nonlinear code based on Lagrangian disk model is developed on the basis of a simple set of analytical expressions to study nonlinear dynamics in the helix slow-wave structure used in a traveling wave tube. The loss profiles such as triangular and Gaussian types are modeled as stairsteps and a simple formula is developed to found the loss at a plane for such loss profile. In contrast to the earlier works in nonlinear theory, at present, no numerical method is used at any stage. The method, introduced in this work, is general in nature because it can handle (a) multi-section structure with sever, (b) different loss profiles, namely, center (Gaussian) and tip (triangular: increasing or decreasing), (c) space charge effect on the electrons, (d) backward waves arising due to reflections, etc. Accuracy of the theory and code is verified with comparison of the computed present results with the results from simulation code MAGIC and published elsewhere and found to be in good agreement. The generation and suppression of the harmonic power are studied for a typical structure. It is found that the introduction of resynchronization section of the reduced pitch enhances the fundamental power with the reduction of the second harmonic power. In addition, the method can be used for any helix slow-wave-structure consisting of homogeneous/inhomogeneous dielectric support rods in isotropic/anisotropic overall metallic enclosure, because the axial propagation constant and interaction impedance obtained for any structure and model such as sheath and tape helix approximations or from any simulation codes can be used as the input in the program to make the code more general.

Dynamics of a magnetic flux jump in a composite superconductor

An attempt is made at direct experimental verification of the theory of thermomagnetic instability in composite superconductors under conditions of external magnetic field or transport current variations. The development of thermomagnetic instability in the form of a magnetic flux jump is experimentally studied in a bulk low-temperature composite niobium-tin superconductor. The liquid-helium-cooled sample representing a compressed tape helix (helicoid) is placed in an external magnetic field orthogonal to the turn plane and varying with a constant rate. For the first time, both the magnetic induction inside the sample and its temperature are simultaneously detected in experiments. The sample overheat preceding the magnetic flux jump is measured to be 0.23 + 0.02 K. This value is found to be independent of the rate of the external magnetic field variation and the value of the jump itself and coincides, within the experimental accuracy, with the temperature parameter of electric field buildup involved in the general exponential I-V characteristic of the composite superconductor, which depends on temperature and magnetic induction.

A heuristic analysis for an inhomogeneously loaded tape helix used in a practical travelling wave tube

The analysis of an inhomogeneously loaded helix in the tape model, reported elsewhere, considering the effect of space harmonics as well as the different radial propagation constants over the different structure regions, is quite tedious and rigorous. So, to avoid the rigorous analysis here, a heuristic analysis has been developed by combining the results of the tape model analysis of a helix in free space with those of the sheath helix model analysis of a loaded helix. The results presented here in terms of dispersion characteristics have been compared with those results obtained from a rigorous approach (both for homogeneously and inhomogeneously loaded structures) in the tape helix model. However, the results obtained from this approach agree closely with those of the rigorous approach for a practical situation in which the discrete supports are smoothed out into a single continuous region. The approach is valid for an inhomogeneously loaded helix for optimum conditions of structure parameters, namely, helix pitch angle, helix to barrel gap, support material and inhomogeneity. Moreover, the results predicted by this heuristic approach have also been validated with those experimental results published in the literature and are found to be in good agreement.

Tape helix perturbation including 3-D dielectrics for TWTs

A perturbation technique described in a previous paper has been applied to the tape helix model of a traveling wave tube (TWT). The perturbation technique employs two solutions; the unperturbed solution is that for a helix in a conducting sleeve, suspended in vacuum, and the perturbed solution is with the above configuration, but with the introduction of dielectric support rods. Usually the perturbed solution is not known and is approximated by the homogeneous dielectric solution. Then in three-dimensional (3-D) fashion, the perturbation technique weights the dielectric with an energy-like term that is only evaluated within the discrete dielectric. Therefore, the model accounts for the distribution of dielectric material. Extending the perturbation to the tape helix, the current density is accurately portrayed in space. In all cases, the perturbed tape helix solution has a lower least square error in normalized phase velocity than the unperturbed tape helix solution. It had a lower error than the perturbed sheath helix solution of the previous paper, which in turn had a lower least square error than the Naval Research Laboratory's (NRL's) Small Signal Gain (SSG) Program. An initial discussion of the tape helix is presented and the calculated dispersion relation given. This solution incorporates a conducting backwall or shield with a homogeneous dielectric between it and the helix, using n=-6 to n=+6 space harmonics. Then the perturbation theory is applied, first for uniform support rods, and then to include notched rods. The resultant simulations produce phase velocity and coupling impedance data. Deviation from theory to experiment is reported by comparing the square root of the average sum of the squares difference, divided by an average phase velocity, between calculated phase velocities and a second order least squares fit of the measured data. Experimental data on the dispersion properties of four helices came from Northrop. The average error in phase velocity for four cases was 0.95%. For uniform rods the perturbation theory lowers the phase velocity, but doesn't significantly alter the dispersion. However, for notched rods, the perturbation theory raises the phase velocity and flattens the dispersion, in agreement with experiment. Computations can be performed in 1/2 min for a ten-frequency-step problem on a Pentium II processor.

A three-dimensional multifrequency large signal model for helix traveling wave tubes

A three-dimensional (3D) multifrequency large signal model of the beam wave interaction in a helix TWT is described. The beam is divided into a set of discrete rays, or beamlets, instead of the disks or rings used in one-dimensional (1-D) or two-dimensional (2-D) models. The RF fields supported by the helix are represented by a tape helix model that uses a modal expansion including the full (Bessel function) radial dependence of the fields; both forward and backward synchronous space harmonics are included in the model. RF space charge fields are obtained from solutions of the Helmholtz equations for the RF electric and RF magnetic fields, using the beam current and charge densities as sources. The dc space charge electric field is similarly obtained from a solution of Poisson's equation. This model has been implemented in a code called CHRISTINE 3D, a generalization of the one dimensional CHRISTINE code. The full three dimensional treatment permits the accurate computation of large signal gain and efficiency, taking into account the self-consistent variation of beam radius along the interaction space. The code also computes helix interception current and transverse beam distributions at the entrance to the collector-important design data that are unavailable from a 1D model. Results from the CHRISTINE 3D code are shown to compare very favorably with measurements of output power, efficiency, and interception current vs. drive power. Its predictions for spent beam distributions also compare very well with measurements. Run times for the code are problem dependent, but for a single case of interest are typically 1 to 5 min on a 450 MHz PC, orders of magnitude shorter than that required for a comparable 3D particle-in-cell simulation.

The coupling impedance of vane-loaded tape helix slow-wave structure

Based on the actual vane-loaded tape helix slow wave structure, a new theoretical analytic model for calculating coupling impedance is proposed by Chen Qingyou, et al.(1999) with calculated values of dispersion in good agreement with measured ones. In this paper, it is continued to use this model to calculate the coupling impedance of such a structure, and analyze the effects of the propagation power within vane gaps and the helix gap on the coupling impedance. As a result, the theoretical values are found to be in good agreement with the measured ones, with the maximum difference less than ±18%.

Time-dependent simulation of helix traveling wave tubes

A time-dependent nonlinear analysis of a helix traveling wave tube (TWT) is presented for a configuration where an electron beam propagates through a three-dimensional tape helix surrounded by a conducting wall. The effects of dielectric- and vane-loading are included as is efficiency enhancement by tapering the helix pitch and external focusing by means of either a uniform solenoidal magnetic field or a periodic field produced by a periodic permanent magnet stack. Dielectric-loading is described under the assumption that the gap between the helix and the wall is uniformly filled by a dielectric material. Vane-loading describes the insertion of an arbitrary number of vanes running the length of the helix. The electromagnetic field is represented as a superposition of waves in a vacuum tape helix. The propagation of each wave as well as the interaction of each wave with the electron beam is included by allowing the amplitudes of the waves to vary in z and t. The field equations are solved in conjunction with the three-dimensional Lorentz force equations for an ensemble of electrons. Collective effects are included by both a finite-difference grid formulation of Poisson’s equation and an analysis based upon a modal superposition of solutions of the Helmholtz equation. The time-dependent simulation is compared with a steady-state simulation for a model corresponding to a TWT built at Northrop–Grumman Corporation.

Sensitivity analysis of TWT's small signal gain based on the effect of rod shape and dimensions

An extensive study aiming at analyzing the effect of rod shapes and dimensions on the gain of helix traveling wave tubes (TWTs) is performed. The evaluation of tube small-signal gain is obtained by making use of a rigorous field analysis which takes into account the helix tape model and the dielectric inhomogeneous loading conditions. Computing time to perform the analysis is extremely low compared with the time required in the case of a full wave, three-dimensional (3-D) electromagnetic simulator. The accuracy of the simulation approach has been extensively verified in a previous paper. A novel expression for the attenuation constant has been introduced in the model to improve the quality of results. The proposed study allows a better understanding of tube behavior before fabrication highlighting the contribution of the shape, the mechanical tolerances and the /spl epsiv//sub r/ variation of the rods to the small-signal gain.

Three-dimensional nonlinear theory of helix traveling-wave tubes

A three-dimensional (3-D) nonlinear helix traveling-wave tube (TWT) analysis in the frequency domain is presented for a tape helix surrounded by a conducting wall. Dielectric- and vane-loading of the helix are included, as is circuit tapering and external focusing, by either a solenoid or a field produced by a periodic permanent magnet (PPM) stack. A complete tape helix dispersion equation is derived by an eigenvector analysis. The electromagnetic field is treated as a superposition of eigenvectors at different frequencies whose amplitudes and phases vary slowly in z. The nonlinear field equations are solved in conjunction with the three-dimensional Lorentz force equations for an ensemble of electrons. Beam space-charge waves are included using a superposition of solutions of the Helmholtz equation. The DC self-fields of the beam are also included. The three-dimensional simulation is compared with a previous 2.5 dimensional simulation using a sheath helix model, each of which is compared with a tube built at Northrop-Grumman Corp. The tape helix model is shown to be in substantially better agreement with the experiment than the sheath helix model.

A comparison of L-band helix TWT experiments with CHRISTINE, a 1-D multifrequency helix TWT code

Extensive experimental measurements were carried out to test the accuracy of the parametric helix traveling-wave tube (TWT) code, CHRISTINE. The model is one-dimensional, with beam electrons represented as rigid disks. Multifrequency interactions are supported and the RF circuit can be optionally represented with cold-test data, a sheath helix model, or a recently implemented tape helix model. Simulations using the tape helix model are shown to be in good agreement with experimental measurements of an L-band TWT over a broad (250-MHz) frequency range. In the intermediate and saturated power regimes, the modeled and measured TWT gain versus frequency agree to better than 0.4 dB, with deviations explained by strong reflections at the output window that are not accounted for in the code. Single-tone experimental and simulated drive curves agree to better than 1 dB in the small- and large-signal regimes; relative phase shift simulations agree to within experimental measurement accuracy in the small-signal regime and to within 75% in the large-signal regime. Two-tone experimental and modeled data exhibit similarly good agreement, with CHRISTINE accurately predicting the effect of frequency-dependent gain variations on the TWT output response and third- and fifth-order intermodulation products.

Exact treatment of the dispersion and beam interaction impedance of a thin tape helix surrounded by a radially stratified dielectric

An exact dispersion relation is obtained for electromagnetic waves propagating on a thin metallic tape helix of arbitrary width, supported by a radially stratified dielectric layer and enclosed by a metallic shell. By expanding the surface currents on the tape in a series of Chebyshev polynomials, the unquantifiable assumptions made in all previously published analyzes of the tape helix regarding the forms of the surface current on the tape, or the electric fields at the radius of the tape, are avoided. The power flow and interaction impedance are exactly computed. The dispersion relation is solved numerically for slow waves and the resulting phase velocity and interaction impedance are compared to those computed using the frequently made assumptions of constant current along the tape and zero current across the tape. It is found that for wide tapes significant errors are made in both the phase velocity and interaction impedance when neglecting the transverse variation of the longitudinal current and neglecting the transverse current. For narrow tapes, the two approaches agree to good accuracy. Plots of the surface currents for wide and narrow tapes are presented. The longitudinal current shows a significant variation across the tape. An example is given showing the existence of an optimum tape width, at which the on-axis interaction impedance is maximized. It is separately shown how an approximate, but useful model of metallic vanes may be incorporated in the analysis by the modification of certain boundary conditions. In all cases, computations of phase velocity and impedance across a wide frequency band take well under a minute on a modern workstation.

Interaction Impedance of a Practical Helix Slow-Wave Structure using Tape Helix Model

An expression for interaction impedance of a practical helix slow-wave structure used in a high power, broad-band Travelling Wave Tube, based on tape helix model is derived. The method is validated by comparing the theoretical values of axial propagation constant and the interaction impedance with the experimental data for typical structures.

Accurate analysis of helix slow-wave structures

In this paper, the helix slow wave structure (SWS) of traveling wave tubes (TWT's) has been analyzed. Dielectric supporting rods of arbitrary cross section have been considered in this analysis. The inhomogeneous dielectric loading factor has been accounted for by modeling the discrete support with a number of continuous dielectric tubes of appropriate effective dielectric permittivity. The helix tape model has been used for the field analysis. Furthermore the thickness of the helix tape has been considered. A rigorous solution of the field equations, including the contribution of the space harmonics, was performed to evaluate the phase velocity and the interaction impedance up to millimeter-wave frequencies. The nonuniformity of radial propagation constant over the structure cross section has been also included. With respect to other approaches, a closed-form expression of the field constants has been obtained. A study to choose the optimum number of space harmonics and dielectric tubes to be used in the analysis, has shown how the results are more sensitive to the number of space harmonics than to the number of dielectric tubes, beyond a certain number of the latter. The validity of this theory has been proved by comparison between measurements and simulations for helix SWS with different dimensions, rod shapes and operating frequency band.

Rigorous tape analysis of inhomogeneously-loaded helical slow-wave structures

The inhomogeneously-loaded helical slow-wave structure is field analyzed by azimuthally smoothing out the discrete supports into a number of continuous dielectric tube regions of appropriate permittivity values. The analysis is made rigorous by removing the usual approximation of considering the radial propagation constant to be the same in the different structure regions; moreover, a tape-helix instead of a simpler sheath-helix model has been used to consider the space-harmonic effects. This renders the present analysis more general, accurate and capable of dealing with a wide range of structure parameters, and particularly makes it valid for large values of helix pitch angle, inhomogeneity and separation between the helix and the metal envelope of the structure. Further, structured expressions amenable to easy computation are presented with the help of the recurrence relations for various structure regions, and methods to use them effectively in an iterative cycle for the desired accuracy are suggested. The developed analytical expressions have also been checked by seeing that they pass on, as special cases, to those obtained earlier by making simplifying assumptions. In this comparison, care has been taken to account for the helix tape thickness by considering a free-space gap equal to the difference between the mean helix radius and the inner radius of the dielectric helix support. The results for the propagation characteristics of an inhomogeneously-loaded helical structure presented here are rather general and can readily be used for the structure design, performance evaluation, and control of any space harmonic of interest in a practical device.

Field analysis of a tape helix with embedded bio-media for microwave hyperthermia.

A general field theory has been developed for the EM wave propagation on a tape helix with embedded bone, muscle, fat and skin co-axial biological layers in a multilayered dielectric environment. The electric and magnetic fields in every biological/dielectric layer is formulated in terms of complex modified Bessel functions and complex exponentials, i.e. in terms of complex radial and axial propagation constants for the azimuthally symmetric and higher order spatial harmonics. A complete dispersion relation is derived by substituting the field expressions into as many boundary conditions as there are unknown constants. The dispersion relation is numerically solved for the complex axial propagation constant and hence for the phase velocity and depth of penetration for n = 0 and 1 modes propagating along three dielectric loaded tape helices of different dimensions at several spot frequencies within the range of 300 MHz to 3.00 GHz. The results for variations in normalized phase velocity and depth of penetration with frequency for these modes separately and for the combined mode are presented. The patterns of specific absorption rate (SAR) across the cross-section of the dielectric loaded helices are also computed and presented. The variations with frequency, and cross-sectional dimension of the helix of the normalized phase velocity, axial depth and SAR across the cross-section of each of the helices are discussed for the modes considered. The theoretical results for the propagation constant obtained by using a tape helix model for the azimuthally symmetric mode propagating along a wire helix loaded with a phantom muscle sample of known dielectric constant are compared with experimental results and with those obtained theoretically employing a sheath helix model at 2.45 and 2.55 GHz. The use of a helix for human limb hyperthermia is also discussed.

Design of traveling wave tubes based on field theory

A method is described for the design of helix traveling wave tubes (TWT) which is based on the linear field analysis of the coupled beam-wave system. The dispersion relations are obtained by matching of radial admittances at boundaries instead of the individual field components. This approach provides flexibility in modeling various beam and circuit configurations with relative ease by choosing the appropriate admittance functions for each case. The method is illustrated for the case of a solid beam inside a sheath helix which is loaded externally by lossy dielectric material, a conducting cylinder, and axial vanes. Extension of the analysis to include a thin tape helix model is anticipated in the near future. The TWT model may be divided into axial regions to include velocity tapers, lossy materials and severs, with the helix geometry in each region varied arbitrarily. The relations between the AC velocities, current densities, and axial electric fields are used to derive a general expression for the new amplitudes of the three forward waves at each axial boundary. The sum of the fields for the three forward waves (two waves in a drift region) is followed to the circuit output. Numerical results of the field analysis are compared with the coupled-mode Pierce theory. A method is suggested for applying the field analysis to accurate design of practical TWT's that have a more complex circuit geometry, which starts with a simple measurement of the dispersion of the helix circuit. The field analysis may then be used to generate a circuit having properties very nearly equivalent to those of the actual circuit.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Characteristics of a helical tape antenna embedded in a multilayer dielectric coated cylinder

The dispersion relation and radiation characteristics of a tape helix with two layers of dielectric substrates and one layer of dielectric superstrate is derived and analyzed. The derivation is based on the hybrid mode field expressions in cylindrical coordinates with unknown expansion coefficients. The application of the appropriate boundary conditions and the point matching technique is used to determine the expansion coefficients. It is assumed that the tape current has only one component along the length of the tape for small values of tape width. The dispersion relation is obtained based on an approximate representation of the current on a narrow tape helix. The k-β diagram is then obtained from the solution of the complex dispersion relation. The radiation patterns of the first and second propagating modes, for a finite number of turns of the tape helix, are presented for different geometrical and electrical parameters.

Quasi-three-dimensional perturbation technique, including dielectrics for TWT's

A perturbation technique is described for finding phase velocities and coupling impedances in a traveling wave tube for an arbitrary distribution of dielectric material. A model of the sheath helix is presented. Tape helix results will be presented in a separate paper. In all cases presented, without adjusting the dielectric constant, the calculated perturbed phase velocity provided a better answer than the homogeneous dielectric solution, or Naval Research Laboratories' Small Signal Gain Program. Deviation from theory versus experiment is reported by stating the average sum of the squares difference between theoretical calculations and a second order least squares fit of the measured data. Phase velocities can be calculated for uniform dielectric support rods where the average sum of the squares /spl les/1.19/spl times/10/sup /spl minus/5/. For cases with notched dielectric support rods phase velocities can be calculated where the average sum of the squares /spl les/1.94/spl times/10/sup /spl minus/5/. For NRL's SSG program the average sum of the squares was /spl les/1.01/spl times/10/sup /spl minus/4/ by comparison. For uniform dielectric support rods the perturbation does not significantly alter the basic shape of the predicted dispersion curve. For notched dielectric support rods applying the perturbation does alter and flatten the shape of the predicted dispersion curve in agreement with experiment.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>