# 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).

##### Citations

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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.

##### References

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TL;DR: In this article, a special type of helical slow-wave structure encompassing a rectangular geometry is investigated, and the slowwave characteristics are studied taking into account the anisotropic conducting helix.

Abstract: A special type of helical slow-wave structure encompassing a rectangular geometry is investigated in this paper, and the slow-wave characteristics are studied taking into account the anisotropically conducting helix. By using the electromagnetic integral equations at the boundaries, the dispersion equation and the interaction impedance of transverse antisymmetric modes in this structure are derived. Moreover, the obtained complex dispersion equation is numerically calculated. The calculation results by our theory agree well with the results obtained by the 3-D EM simulation software HFSS. The numerical results reveal that the phase velocity decreases and interaction impedance increases at higher frequencies by flattening (increasing the aspect ratio of) the rectangular helix structure. In addition, a comparison of slow-wave characteristics of this structure with a conventional round helix is made.

37Â citations

### "Modified Dispersion Equation for Pl..." refers methods in this paper

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TL;DR: In this paper, a planar structure comprising a pair of parallel arrays of periodically spaced conducting strips which conduct in different directions in the two arrays is considered, and the guiding properties of this plan-ar structure are found to be similar, in one case, to those of circular tape helices.

Abstract: Considered here is a planar structure comprising a pair of parallel arrays of periodically spaced conducting strips which conduct in different directions in the two arrays. The guiding properties of this planar structure are found to be similar, in one case, to those of circular tape helices. While in general, different dielectric media are assumed in the sandwiched and outer regions, the special cases studied are 1) the case in which air constitutes both the media, 2) the normal-helix case in which the inner medium is a solid dielectric and the outer medium is air, and 3) the "inverted-helix" case with the two media interchanged.

30Â citations

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TL;DR: In this paper, a planar helix is proposed as a slow-wave structure for application in a traveling-wave tube (TWT) and field theory is applied to analyze the behavior of the planar structure in the presence of a flat electron beans present between the two screens.

Abstract: A pair of unidirectionally conducting screens, conducting in different directions, constitute a planar helix. The planar helix is proposed as a slow-wave structure for application in a traveling-wave tube (TWT). Field theory is applied to analyze the behavior of the planar helix in the presence of a flat electron beans present between the two screens. Results indicate the presence of three modes, with one mode having a negative attenuation constant, as in the case of the usual helix-type TWT. Curves are shown for a typical proposed planar TWT. Also, the effect of beam current is indicated.

16Â citations

### "Modified Dispersion Equation for Pl..." refers methods in this paper

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TL;DR: The dispersion equation for electromagnetic waves guided by an open tape helix for the standard model of an inflitesimally thin and perfectly conducting tape is derived from an exact solution of a homogeneous boundary value problem for Maxwell's equations as mentioned in this paper.

Abstract: The dispersion equation for electromagnetic waves guided by an open tape helix for the standard model of an inflnitesimally thin and perfectly conducting tape is derived from an exact solution of a homogeneous boundary value problem for Maxwell's equations. A numerical analysis of the dispersion equation reveals that the tape current density component perpendicular to the winding direction does not afiect the dispersion characteristic to any signiflcant extent. In fact, there is a signiflcant deviation from the dominant-mode sheath- helix dispersion curve only in the third allowed region and towards the end of the second allowed region. It may be concluded that the anisotropically conducting model of the tape helix that neglects the above transverse-current contribution is a good approximation to the isotropically conducting model that takes into account this contribution except at high frequencies even for wide tapes.

14Â citations

### "Modified Dispersion Equation for Pl..." refers background in this paper

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TL;DR: In this article, the homogeneous boundary value problem in the electromagnetic wave propagation in a dielectric-loaded perfectly conducting tape helix with infinitesimal tape thickness is investigated.

Abstract: 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.

10Â citations

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