Excitation of a cylindrical retarding system of finite length by a modulated flux of charge particles

Electrodynamic calculation of spirals contacting the cavity ends

“…As a result, with decreasing b 1 (with the relationship sin ψ 1 b 1 preserved), the quantity β (1) for the corresponding modes approaches certain finite numbers approximately equal to 1.737, 4.708, 7.882, . .…”

“…In what follows we present some results of calculations for spirals with a significant slowing-down (sin ψ 1 1 and sin ψ 2 1). The eigenvalues of the frequency κ depend on the conductance angles ψ 1 and ψ 2 and on the sizes r 1 , b 1 , r 2 , and L.…”

“…For the lower-order modes with respect to frequency, the quantity D (1) is approximately equal to 0.970, 0.228, 0.0661, . .…”

“…, and J s and H (1) s are, respectively, the Bessel and Hankel functions of the first kind of order s. Equation (1) yields the amplitude of the electric-field projection onto the direction e(ψ) at radial distance ρ in an infinite waveguide of unit radius with a current flowing on a cylinder of radius r and having the direction e(ψ 0 ) specified by a constant angle ψ 0 of spiral conductance. The periodic field and currents in the structure obtained from a cavity of length L with spirals by successive specular reflection with respect to the cavity ends can be expanded over a Fourier series:…”

“…The objective of this paper is electrodynamic calculation of an axisymmetric structure, namely, a cylindrical cavity containing cylinders with anisotropic conductance which contact one or both of its ends. The calculation is performed with the use of a method similar to that in paper [1], whose authors find the transient radiation field excited by a modulated beam moving along the spiral axis in free space. However, we construct the system of linear equations for the coefficients of expansion of the spiral current over Chebyshev polynomials, rather than for the Fourier-transformed current components.…”