Analysis of electromagnetic scattering off a two dimensional periodic plasma structure by the quasiparticle method

It was previously shown experimentally, that a single plasma column can effectively attenuate and scatter an incident electromagnetic wave. The attenuation, greater than 30 dBs directly behind the plasma column, is due to collisional absorption and the scattering of the incident wave. The experimental results further show that the attenuation can in fact be much greater than that obtained if the diffracted signal going around the column can be eliminated. One way to minimize the diffraction without further increasing the ratio of the plasma column size to the wavelength is to utilize the picket fence concept which uses an array of plasma columns to enhance the absorption and scattering. In this work, the authors study how a periodic plasma structure, e.g. an array of hollow cathode discharge plasma, can enhance these effects. The analysis of this problem is based on a quasiparticle approach. A Wigner distribution function for the wave intensity in the (k,r) space is introduced and its governing equation is derived with an effective collision term giving rise to the attenuation and scattering of the wave. This kinetic equation leads to a hierarchy of moment equations in r space. They truncate this system of equations to the second moment which is equivalent to assuming zero quasiparticle pressure. They have then a closed set of equations for describing the aforementioned problem. These three coupled partial differential equations (one is from the continuity equation and two are from the momentum equation) are solved for a range of plasma parameters and wave frequencies. The results of the study will be reported