Modified Dispersion Equation for Planar Open Tape Helix Travelling Wave Tube
07 Mar 2019-pp 101-104
TL;DR: In this article, the dispersion equation for a planar traveling wave tube with anisotropic conducting open helix structure is derived and the exact solution of a homogenous boundary value problem for Maxwell's equations is derived.
Abstract: The dispersion equation for a planar traveling wave tube with anisotropically conducting open helix structure is derived. Using, the accurate boundary conditions along all the sides of the planar TWT and along the winding direction of the TWT using indicator function, the exact solution of a homogenous boundary value problem for Maxwell's equations is derived. A total number of six different complex constants are derived from a set of six boundary conditions for the proposed cold wave analysis. The presented theoretical analysis will be used in the design of the planar travelling wave tube amplifier (TWTA).
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25 Apr 2023
Abstract: A rectangular open tape helix is analysed for its dispersion characteristics by deriving the dispersion equations that restrict the fields within the tape helix region by incorporating a confinement function. The dispersion equations are derived by applying the accurate boundary conditions to one-quarter of the structure in axial and transverse directions owing to the symmetricity of the rectangular helical waveguide. The dispersion characteristics are numerically computed from an infinite number of simultaneous equations. The computed characteristics is compared with the theoretical model of sheath helix consisting of only the fundamental harmonics. Plotted dispersion characteristics reveals the potential usability of such devices as compact traveling wave tubes by miniaturization and can be printed.
25 Apr 2023
TL;DR: A rectangular open tape helix is analyzed in this article for its dispersion characteristics by deriving the dispersion equations that restrict the fields within the tape-helix region by incorporating a confinement function.
Abstract: A rectangular open tape helix is analysed for its dispersion characteristics by deriving the dispersion equations that restrict the fields within the tape helix region by incorporating a confinement function. The dispersion equations are derived by applying the accurate boundary conditions to one-quarter of the structure in axial and transverse directions owing to the symmetricity of the rectangular helical waveguide. The dispersion characteristics are numerically computed from an infinite number of simultaneous equations. The computed characteristics is compared with the theoretical model of sheath helix consisting of only the fundamental harmonics. Plotted dispersion characteristics reveals the potential usability of such devices as compact traveling wave tubes by miniaturization and can be printed.
References
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TL;DR: In this paper, the large-signal behavior of traveling wave tube amplifier for a linear beam dielectric loaded anisotropic conducting tape helix slow wave structure (SWS) was realized through a swift and reliab...
Abstract: 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 reliab...
13Â citations
"Modified Dispersion Equation for Pl..." refers methods in this paper
...The field equations are substituted in the six boundary conditions resulting in six complex constants given as and [3,5,6]....
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TL;DR: In this article, the homogeneous boundary value problem arising in the propagation of electromagnetic waves guided by an open tape helix modelled to be of infinitesimal tape thickness and infinite tape-material conductivity is shown to be inherently ill posed.
Abstract: The homogeneous boundary value problem arising in the propagation of electromagnetic waves guided by an open tape helix modelled to be of infinitesimal tape thickness and infinite tape-material conductivity is shown to be inherently ill posed. It is demonstrated how the ill posed problem may be regularised using the mollification method. The regularised boundary value problem is then solved to yield the approximate dispersion equation which takes the form of the solvability condition for an infinite system of linear homogeneous algebraic equations viz., the determinant of the infinite-order coefficient matrix is zero. For the numerical computation of the dispersion characteristic, all the entries of the symmetrically truncated version of the coefficient matrix are estimated by summing an adequate number of the rapidly converging (after regularisation) 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. A comparison of the numerical results with those for the anisotropically conducting model (that neglects the component of the tape-current density perpendicular to the winding direction) of the tape helix reveals that the propagation characteristic computed on the basis of the anisotropically conducting model could be substantially in error even for moderately wide tapes.
12Â citations
"Modified Dispersion Equation for Pl..." refers methods in this paper
...The field equations are substituted in the six boundary conditions resulting in six complex constants given as and [3,5,6]....
[...]
TL;DR: In this article, a dielectric-loaded tape helix enclosed in a coaxial perfectly conducting cylindrical shell was analyzed for guided electromagnetic wave propagation, and the dispersion equation was solved to yield the solvability condition for an infinite system of linear homogeneous algebraic equations.
Abstract: The practically important case of a dielectric-loaded tape helix enclosed in a coaxial perfectly conducting cylindrical shell is analysed in this paper. The dielectric-loaded tape helix for guided electromagnetic wave propagation considered here has infinitesimal tape thickness and infinite tape-material conductivity. The homogeneous boundary value problem is solved taking into account the exact boundary conditions similar to the case of anisotropically conducting open tape helix model [1, 2]. The boundary value problem is solved to yield the dispersion equation which takes the form of the solvability condition for an infinite system of linear homogeneous algebraic equations viz., the determinant of the infiniteorder coefficient matrix is zero. For the numerical computation of the approximate dispersion characteristic, 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.
11Â citations
"Modified Dispersion Equation for Pl..." refers background or methods in this paper
...Here, and are the indicator functions in the direction and direction planes respectively and are defined as [5]-...
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...The field equations are substituted in the six boundary conditions resulting in six complex constants given as and [3,5,6]....
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DOI•
01 Feb 1984TL;DR: In this paper, a planar helix, constituted of a pair of unidirectionally conducting screens conducting in different directions, is suggested as a slow-wave structure for application in a travelling-wave tube (TWT).
Abstract: A planar helix, constituted of a pair of unidirectionally conducting screens conducting in different directions, is suggested as a slow-wave structure for application in a travelling-wave tube (TWT). Circuit parameters, such as interaction impedance and space-charge parameter, are derived for the suggested planar-helix TWT. Computed results for the planar helix indicate a performance comparable with that of its circular helix counterpart. Also, the change in interaction impedance and the dispersion characteristics of the planar helix, are considered in the presence of dielectric substrates and a metal shield. Results are obtained for a few different possible configurations of the planar helix on dielectric substrates with or without a metal shield. The phase velocity and interaction impedance reduce, both as the substrate thickness increases and as the metal shields are brought closer to the planar helix. However, the resulting degradation in the characteristics of the structure with commonly used substrate materials, for example alumina and beryllia, is less severe than in the case of the circular helix.
10Â citations
TL;DR: In this article, the approximate distribution of the current density induced on the tape surface by guided electromagnetic waves supported by an inflnite open tape helix is estimated from an exact solution of a homogenous boundary value problem for Maxwell's equations.
Abstract: The approximate distribution of the current density induced on the tape surface by guided electromagnetic waves supported by an inflnite open tape helix is estimated from an exact solution of a homogenous boundary value problem for Maxwell's equations. It is shown that the magnitude of the surface current density component perpendicular to the winding direction is at least three orders of magnitude smaller than that of the surface current density component parallel to the winding direction everywhere on the tape surface. Also, the magnitude and phase distribution for the surface current density components parallel and perpendicular to the winding direction are seen to be nearly uniform at all frequencies corresponding to real values of the propagation constant.
9Â citations
"Modified Dispersion Equation for Pl..." refers background in this paper
...The discontinuity in magnetic field components between regions gives rise to the current density component, as can be seen in the following boundary condition equations given in equations (27) to (34) [9,12,13]....
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