A New Property of the Complex Kummer Function and Its Application to Waveguide Propagation

It is proved numerically that if, k -> -infinity the products vertical bar k vertical bar zeta((c))(k,n) and vertical bar a vertical bar zeta((c))(k,n), where zeta((c))(k,n) is the nth positive purely imaginary zero of the complex Kummer confluent hypergeometric function Phi (a, c; x) in x(n = 1, 2, 3, ... ), with a = c/2 - jk-complex (k-real), c = 2Rea-restricted positive integer and x = jz-positive purely imaginary (z-real, positive), tend to the finite positive real number L(c, n), though the zeros themselves in this case become infinitesimal. Applying this fact to the investigation of the azimuthally magnetized circular ferrite waveguide for normal T E-01 mode, an envelope curve at which the phase characteristics for negative magnetization terminate is found and the condition for phaser operation of the structure is obtained. It shows that the latter exhibits phase shifting properties only in a bounded frequency band whose limits depend on its material and geometry parameters and the number L(c, n).