Microwave Conductivity of an Ionized Decaying Plasma at Low Pressures

Margenau's analysis for the microwave conductivity of an infinite decaying plasma in a uniform field is extended to the case of a bounded plasma in a slightly nonuniform field. It is shown that, if we assume a power expansion for the electron-collision frequency as a function of energy, the conductivity at low pressures can be computed as a function of time and position when the spatial and time variations of the density and energy moments of the electron-distribution function are known. An approximate method, based on a convenient integration of Boltzmann equation is given to compute these quantities, when inelastic collisions can be neglected. The steady-state conductivity in the late afterglow of a diffusion-controlled decaying plasma is thus explicitly determined for two experimental conditions: a plasma filling a cubic quartz bottle centered in a parallelepiped microwave cavity and a plasma filling a quartz tube·{}of square cross section in a wave guide. The limit for the validity of the theory set by the appearance of inelastic collisions at high electric fields is investigated.