The effects of electron collisions on electric dipole radiation through a conical plasma sheath

The radiated power of an electric dipole antenna in a thin, dissipative, infinite conical plasma sheath is analyzed. The electromagnetic fields are represented by contour integrals, and the radiated power is calculated according to the method of Baños et al. The sheath is characterized by a single parameter, which is proportional to the integrated electron density and depends inversely on the electron collision frequency. The radiation pattern is distorted from the form of the free-space dipole pattern because of the interaction between the primary dipole fields and the fields induced on the surface of the plasma sheath. In most cases it is found that for small electron densities, electron collisions attenuate the induced surface fields so that the patterns approach their free-space form. For larger electron densities, the pattern has a characteristic heart shape for zero collision frequency. The pattern increases in magnitude, while retaining the same form, as the collision frequency increases from zero. As the collision frequency is further increased, the pattern approaches the free-space pattern in magnitude and form.