Tape Helix Research Articles

Comparative Study of Guided Electromagnetic Wave Propagation for Two Models of an Open Tape Helix

Rigorous methods to solve the homogeneous boundary value problems and the techniques to resolve illposed mathematical issues arising in the problem formulation of electromagnetic wave propagation of an Open tape helix slow wave structure with anisotropically conducting and completely conducting model is presented. The dispersion equation of both the models require convergent coeefficients of the infinte linear homogeneous equations whose determinant of the coefficent matrix is zero. The coefficient matrix of the anisotropically conducting model is rapidly convergent, while in the case of completely conducting model, the matrix entries which are infinite summation series representations turns out to be divergent, the not so well-posed boundary value problem is regularised with the method of mollification functions. The dispersion characteristics are plotted after truncating the infinite series expansions to adequate number of terms and summing the terms of converging series expansions(after regularization in the case of the completely conducting tape-helix model) in dispersion equations. The tape-current distribution for both models are estimated from the null-space vector of the truncated coefficient matrix corresponding to a particular (β <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> – <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> ) root of the dispersion equation. A comparison of the numerical results for both models show that the neglect of the perpendicular tape-current density component entails a substantial modification of the dispersion characteristics of guided waves supported by an open tape helix.

Dispersion Analysis of a Planar Rectangular Tape Helix Slow Wave Structures Supported by Dielectric Rods

Dispersion Analysis of a Planar Rectangular Tape Helix Slow Wave Structures Supported by Dielectric Rods

Heat Transfer of rGO/CO3O4 Hybrid Nanomaterial-Based Nanofluids and Twisted Tape Configurations in a Tube

Abstract The friction factor, thermal performance, and heat transfer are experimentally analyzed for reduced-graphene oxide/cobalt oxide (rGO/CO3O4) hybrid nanomaterial-based nanofluid circulating in a plain tube with and without twisted tape inserts having different pitches. The reduced-graphene oxide/cobalt oxide (rGO/CO3O4) hybrid nanomaterial is prepared using in situ/chemical reduction technique and then characterized with transmission electron microscope, X-ray diffraction, and magnetometry. The experiments were conducted with different values of particle loading (0.05%, 0.1%, and 0.2%) and Reynolds number (2000–2,020,000). Three twisted tape inserts of helixes 285 mm, 190 mm, and 95 mm were used. The nanofluids was produced from the addition of the hybrid nanomaterial to water yield an increase, as compared to the basefluid (water), of the Nusselt number, which is further enhanced by increasing the nanoparticle loading. Therefore, when compared to water, the Nusselt number is enhanced by 25.65%, with no twisted tape and by 79.16% with twisted tape with helix of 95 mm for the nanofluid of 0.2% volume concentration. However, when compared to water, there is a slight friction factor penalty with the 0.2% particle loading of 1.11-times and 1.49-times for the plain tube and for the 95-mm twisted tape helix, respectively. The thermal performance factor gets enhanced by increasing the nanoparticles concentration of the hybrid nanofluids with or without twisted tape inserts, and it is always higher than one. Based on the experimental data, regression equations were developed for the Nusselt number and friction factor.

Theory of Traveling-Wave Tube Including Space Charge Effects on the Circuit Mode and Distributed Cold Tube Loss

This article presents a small-signal theory of a tape helix traveling-wave tube (TWT) with distributed cold tube loss, including the recently discovered space charge effects on the circuit mode that was obtained from the exact dispersion relation of the corresponding lossless tube. The classical values of Pierce’s parameter ${C}$ and ${Q}$ are modified in this new formulation, while the cold tube loss will enter in a similar way as in Pierce. Realistic examples are given, including tubes with uniform circuit loss and with a spatial sever, and compared with the Pierce’s classical theory.

The winding mechanical behavior of conductor on round core cables

In the process of the HTS cable structure cabling, the HTS tape is subjected to the combined deformation caused by tension, bending, and torsion. The electro-mechanical behaviors and the degradation mechanism of HTS cable are remain elusive. In the present paper, a numerical model is built in ABAQUS software to analyze the winding mechanical behavior of the CORC cable. Then, the critical current degradation is calculated and the effects of the tape width, substrate thickness, pre-stress, winding pitch and helix angle are investigated. The results show that it should be avoid selecting a roller with a much small radius to produce a large strain. The critical current degradation of the cable is minimal when the helix angle equals to 45°, which is the best choice to winding the tape to form the CORC cable. A smaller winding radius can be choose when the thickness of the substrate is in the small strain region of 10–20 µm. This study helps understand the deformation of the HTS tape during the winding process and provides a winding optimization for the CORC cable.

Modification of Pierce’s Classical Theory of Traveling-Wave Tubes

For a realistic case of an electron beam interacting with the electromagnetic fields supported by a thin perfectly conducting tape helix, we derive the exact dispersion relation, from which an unambiguous determination of Pierce's space-charge parameter Q is made. In the process of doing so, we discover that the circuit mode in the equivalent three-wave theory of Pierce must be modified at high beam current, an aspect not included in Pierce's original analysis. We quantify this circuit mode modification by a new parameter that we call q, introduced here for the first time in traveling-wave tube theory. In a realistic example, we find that the effect of q is equivalent to a modification of the circuit phase velocity by as much as two percent, which is a significant effect equivalent-to a detune of two percent.

Large-signal field analysis of a linear beam travelling wave tube amplifier for the anisotropically conducting tape helix slow-wave structure supported by dielectric rods

The large-signal behavior of traveling wave tube amplifier for a linear beam dielectric loaded anisotropically conducting tape helix slow wave structure (SWS) is realized through a swift and reliable field analysis. Using Green’s function sequence, the field components in the SWS are designated as nonlinear functionals of electron arrival time. The electron arrival time in the beam region is formulated into a nonlinear operator in the Banach space mapping form by substituting the axial electric field component into the electron ballistic equation. The nonlinear beam–wave interaction is then obtained by determining the electron arrival time through extensive successive approximations, and thus exact electric and magnetic field components in the tape helix SWS are attained. The numerical computation of the proposed model yields definitive analytical results for the electron exit velocity, induced surface current density, power gain, conversion efficiency, and optimum interaction length.

Propagation of electromagnetic waves guided by perfectly conducting model of a tape helix supported by dielectric rods

The homogeneous boundary value problem existing in the electromagnetic wave propagation in a dielectric-loaded perfectly conducting tape helix with infinitesimal tape thickness is investigated in this study. The ill-posed boundary value problem is regularised using the mollification method. The homogeneous boundary value problem is solved for the dielectric loaded perfectly conducting tape helix taking into account the exact boundary conditions for the perfectly conducting dielectric loaded tape helix. The solved approximate dispersion equation takes the form of the solvability condition for an infinite system of linear homogeneous equations namely, the determinant of the infinite order coefficient matrix is zero. For the numerical computation of the dispersion equation, all the entries of the symmetrically truncated version of the coefficient matrix are estimated by summing an adequate number of the rapidly converging series for them. The tape-current distribution is estimated from the null-space vector of the truncated coefficient matrix corresponding to a specified root of the dispersion equation. The numerical results suggest that the propagation characteristic computed by the anisotropically conducting model (that neglects the component of the tape-current density perpendicular to the winding direction) is only an abstinent approximation to consider for moderately wide tapes.

Dielectric-Loaded Plasma Filled Helix Traveling Wave Tube Analysis Based on the Linearized Field Theory

A linear relativistic field theory of a plasma-loaded helix traveling wave tube is presented. The configuration consist of a solid electron beam propagating through a tape helix enclosed within a loss-free wall in which the gap between the helix and the outer wall is filled with a dielectric. The dispersion relation is derived for azimuthally symmetric modes. The effects of dielectric constant, plasma density, axial guide field, and electron beam density on the phase velocity and growth rate were considered numerically. Numerical results indicate that the phase velocity and growth rate increase in the presence of the plasma. Further the growth rate and frequency are maximum at the special value of the dielectric constant. The growth rate increases with axial guide field and remains relatively constant at strong magnetic field, however the growth rate increases considerably by incrementing the electron beam density.

Two Ways to Increase the Pulse Duration of the Solid Pulse-Forming Line Based on Dispersion Analysis

Solid dielectrics have been widely investigated as potential attractive candidates in compact portable pulsed-power systems. Slow-wave structure with good dispersion characteristics and broad transmission band can be used to increase the pulse duration while the size of pulse-forming line (PFL) decreases. In this paper, we present two different slow-wave structures, the tape helix for coaxial-line and the meander-line structure for the planar line, to increase the pulse duration of solid PFLs based on dispersion analysis. At first, the characteristic impedances, electric length, and dispersion curve of the PFL with the slow-wave structure are calculated by the electromagnetic dispersion theory. Based on the theoretical calculations, the PFLs are designed and simulated by the electromagnetic field tool. Finally, some test results on the PFLs are introduced. Currently, both the Al2O3 ( $\varepsilon _{r}= 9.3$ ) helical PFL and the glass–ceramic ( $\varepsilon _{r} = 225$ ) meander-line PFL can deliver a pulsewith 50-ns width, of which the dimension is $\phi ~67~{\mathrm{ mm}} \times 305$ mm and $95~{\mathrm{ mm}} \times 95~{\mathrm{ mm}}\times 4$ mm, respectively.

Dispersion analysis of the solid helical pulse-forming line

AbstractIn this paper, a solid helical pulse-forming line (HPFL) is described. The electromagnetic (EM) dispersion theory is used to calculate the important parameters of the HPFL based on tape helix model. Dispersion effects on the important EM parameters of HPFL, such as electric length and characteristic impedances, are analyzed. When Al2O3 ceramic is applied to be the dielectric in the HPFL, the pulse width of the HPFL is calculated nearly 50 ns only with the length of 305 mm. EM field simulation can draw the dispersion curve of the HPFL directly, which can describe the dispersion effect on the electric length of HPFL. Furthermore, the EM field simulation and experiments are carried out to verify the theoretical calculations of the pulse wide and characteristic impedances. Both simulation and experimental results can prove the EM analyses and calculations in this paper.

Dispersion Equations of a Rectangular Tape Helix Slow-Wave Structure

A rectangular tape helix slow-wave structure with infinitesimal thickness and finite width in free space is investigated. With the expansion of surface currents in the helix and the applications of the modified Marcatili's method, as well as average power flow matching method at the boundaries, the dispersion properties and the interaction impedance for transverse antisymmetric modes in a rectangular tape helix immersed in free space are obtained. It is shown that, compared with the results of the simplified sheath model by previous researchers, higher accuracy has been obtained between the calculation results of the present theory and the data obtained from HFSS, and the validity of the present theory is further demonstrated by comparison with experiments. The improved characteristic equations hold scientific and practical significance in the design and performance evaluation of such plane slow-wave structure in the application of compact traveling-wave tubes. The distribution characteristics on the cross section of the longitudinal electric field fundamental component are also discussed based on this theory.

Conducting tape helix loaded radially anisotropic liquid crystal clad optical fiber

The paper reports investigation of a rather new type of optical fiber composed of three layers with the outermost region being radially anisotropic liquid crystal material, and the inner two regions as linear, homogeneous, and isotropic dielectrics. As such, the anisotropy remains in the outermost section of fiber. The core–clad interface of the inner dielectric regions is assumed to be loaded with conducting tape helix structure. It has been found that the width of the tape as well as the helix pitch angle are the effective parameters to govern the dispersion characteristics. Taking into account the zero-order guided modes, the effects on confinements due to the amalgamation of birefringence (optical property of liquid crystal) and tape helix pitch (geometrical/structural property of perfect conductor) are reported. The obtained results are compared with the case of a conducting sheath helix loaded liquid crystal fiber structure, and it has been found that the conducting tape helix loadings would be more useful than the sheath helix loaded fibers.

Eigenmodes of a tape helix

A quasi-static method for solution of the electromagnetic problem of waves in a uniform helix made of an infinitely thin perfectly conducting tape that can be used for the analysis of the helix eigenmodes in a broad range of the structure parameters is proposed. The electromagnetic problem is reduced to a system of integral equations for longitudinal components of electric and magnetic currents. The system of integral equations is solved in the static approximation by the method of Schwinger transforms. Explicit forms of functions describing electric and magnetic currents are found. A variational solution to the electromagnetic problem is obtained. The results of the numerical analysis of the eigenmodes of a tape helix are presented.

Linear Analysis of Helix Traveling-Wave Tubes With Nonnegligible Space Charge Using the Improved Helical-Harmonics Approximation

Linear dispersion relation of helix traveling-wave tubes (TWTs) is obtained and numerically solved using the improved helical-harmonics approximation (HHA), which has been recently presented for modeling helix thickness. The presented technique allows simultaneous examination of effects of various parameters, such as helix tape thickness, nonuniform beam current density profile, potential depression across the beam, finite axial magnetic field, and rod shape, on the tube's small-signal characteristics. It is shown that while the results obtained from the 1-D Pierce theory agree well with those obtained from the field theory in the low-space-charge regime, they show major deviation in the nonresonant and high-space-charge regime. It is also shown that the small-signal gain and phase results obtained by means of the improved HHA agree well with those obtained from the tape-helix model and also the conventional HHA whenever the relevant cold dispersion characteristics are in a reasonable agreement.

Plasma Thermal Effect on the Growth Rate of the Helix Traveling Wave Tube

Field theory is applied to analyze the behavior of the thermal plasma-loaded tape helix traveling-wave tube in the presence of a solid electron beam present inside the plasma. The plasma temperature effect on the phase velocity and the growth rate of the system are investigated. It is shown that, if plasma temperature increases in the system, its working frequency and growth rate will increase. The results indicate that the axial electric field and growth rate increase with plasma density.

The effect of beam and plasma parameters on the four modes of plasma-loaded traveling-wave tube with tape helix

Field theory is applied to analyze the behavior of the electromagnetic wave in the presence of a solid electron beam and magnetized plasma-loaded tape helix traveling-wave tube. The obtained dispersion relation implicitly includes azimuthal variations and all spatial harmonics of the tape helix. Results indicate that the frequency and the phase velocity of (X bp − X p ) and (O bp − X p ) modes increase with cyclotron frequency and for (O bp − O p ) and (X bp − O p ) modes decrease. In the strong magnetic field limit, the maximum growth rate and frequency of all modes are constant at different values of cyclotron frequency and beam energy. If the plasma density increases, the frequency and phase velocity of four modes will increase. The maximum growth rates of the four modes in the lower plasma density are equal and for higher values of plasma density the (O bp − X p ) mode has greatest value. The phase velocity and the frequency of (X bp − X p ) with (X bp − O p ) modes and (O bp − O p ) with (O bp − X p ) modes are coinciding with each other and for first case increase with beam density, but for latter decrease. The maximum growth rate of (O bp − O p ) mode and the maximum frequency of (X bp − X p ) mode have highest values as a function of the electron beam density.

Plasma effect in tape helix traveling-wave tube

A linearized relativistic field theory of a plasma-loaded helix traveling-wave tube is presented for a configuration where a solid electron beam propagate through a sheath helix enclosed within a loss-free wall in which the gap between the helix and the outer wall is filled with a dielectric. Numerical study of the effect of plasma density on the phase velocity and growth rate has been done. Numerical results show that the plasma have different behaviors in different density limits.

Analysis of Helical Slow-Wave Structures for Modeling Helix Thickness Using an Improved Helical-Harmonics Approximation—Part I: Theory

In this two-part paper, an improved helical-harmonics approximation (HHA) is presented, and subsequently validated by applying it to the analysis of cold (beam-absent) helix slow-wave structures (SWSs) with smoothed rods. The first part presents the theory and relevant formulations. By starting from Maxwell's equations, we obtain an improved form of supporting equations for field components in the so-called helical coordinate system with the help of which the effect of helix pitch angle on the validity of HHA is revealed. By evaluating the error in solutions caused by small changes in the pitch angle across the tape thickness, we show that HHA holds to be valid in a region whose radial thickness is a fraction of actual helix tape thickness. Furthermore, field components of a helix SWS and its dispersion relation are determined using this modified approximation. Moreover, all helical armonics that are necessary for the convergence of the results are incorporated in our analysis. The present improved HHA-based analysis of helical SWS yields a more accurate modeling of the tape thickness than the analysis based on the conventional HHA as well as that by the tape-helix model.

A novel slotted helix slow-wave structure for high power Ka-band traveling-wave tubes

A novel slotted helix slow-wave structure (SWS) is proposed to develop a high power, wide-bandwidth, and high reliability millimeter-wave traveling-wave tube (TWT). This novel structure, which has higher heat capacity than a conventional helix SWS, evolves from conventional helix SWS with three parallel rows of rectangular slots made in the outside of the helix tape. In this paper, the electromagnetic characteristics and the beam-wave interaction of this novel structure operating in the Ka-band are investigated. From our calculations, when the designed beam voltage and beam current are set to be 18.45 kV and 0.2 A, respectively, this novel circuit can produce over 700-W average output power in a frequency range from 27.5 GHz to 32.5 GHz, and the corresponding conversion efficiency values vary from 19% to 21.3%, and the maximum output power is 787 W at 30 GHz.