Gain-frequency response of a helix traveling-wave tube with T-shaped dielectric support rods in a metal envelope

Dispersion control of helical slow-wave structure by double-negative metamaterial loading

“…Interestingly, the dispersion relation expressed as (10) obtained by the present field analysis becomes identical with that obtained by the equivalent circuit analysis by Datta et al [16] In order to estimate the axial electric field at the structure available for interaction with an electron beam of a traveling-wave device, we can find the interaction impedance of the structure K from the following expression [19,20]:…”

“…[19]. The structure is treated in the sheath-helix model in which the actual helix is replaced with a cylindrical sheath of infinitesimal thickness having infinite and zero conductivities in directions parallel and perpendicular to the helix winding direction respectively.…”

“…here, a is the sheath-helix radius, being the mean radius of the actual helix, and b is the metal envelope radius ( Figure 1). The fields in the structure regions are given by the following expressions in cylindrical coordinates (r, θ, z) for azimuthally symmetric mode ( ∂ / ∂ θ = 0) in which RF time dependence exp (jωt) is understood [19][20][21][22]: where the subscripts p = 1, 2 refer to the regions 1 and 2, respectively. rp (p = 1) = r1 = 1 and rp (p = 2) = r2 = r , say, are, respectively, the relative permittivities of region 1, which is a free-space region inside the helix (0 ≤ r ≤ a), and region 2, which is the MMT region (a ≤ r ≤ b) ( Figure 1).…”

“…A p , B p , C p , D p (p = 1, 2) are the field constants it being implied, however the field constant B 1 = D 1 = 0 in order to prevent the fields from blowing up to infinity at the axis of the helix (r = 0). [19][20][21][22] The dispersion relation of the structure (Figure 1) can be derived with the help of the field expression (1) and the electromagnetic boundary conditions at the sheath helix r = a (interface between the regions 1 and 2) and the metal envelope r = b. The boundary conditions at the sheath-helix (r = a) are [21,22]:…”

Application of planar helix slow-wave structure in backward-wave oscillators

“…The circular helix with more practical considerations like vane-loading, T-shaped dielectric support, etc. have also been analysed using field theory-based analyses [93], [94]. The following sub-sections provide a brief introduction to the analysis of circular helix in free space based on sheath-helix and tapehelix approximations.…”