High-frequency scattering from a conducting cylinder with an inhomogeneous plasma sheath

The high-frequency backscattering characteristics of an infinite conducting cylinder enveloped in a radially inhomogeneous plasma sheath are studied in detail. When the permittivity of the sheath has a general power-law dependence,
\epsilon(\rho) = \epsilon(\rho_{0}) (\rho/\rho_{0})^{p}
, where
\rho_{0}
is the outer radius of the sheath and
p
is any real number
\neq -2
, the wave function in the plasma is expressible in terms of Bessel functions of a fractional order. The slowly convergent series form of the backscattering coefficient is first recast into an integral by means of the Watson transformation, which is then asymptotically evaluated by the method of stationary phase. The mathematical result is conveniently interpreted in terms of geometrical optics by identifying the contributions due to the central ray and the trapped "interrupted" and "uninterrupted" rays. In contrast to the rather unpredictable and violent backscattering coefficient variations with frequency when a conducting cylinder is clad in a homogeneous plasma sleeve, the change in the coefficient for the same cylinder enveloped in a plasma sheath with a power-law radial inhomogeneity is much more smooth and, in most cases, the approximate locations of the maximums and minimums can be predicted. Numerical results showing the dependence of the backscattering coefficient on the type of power-law inhomogeneity, sheath thickness, and permittivity level are presented in graphical form.