Inhomogeneous Nonmagnetized Collisional Plasma Parameter Estimation From Reflected Phase Response

Abstract

The theoretical approach developed here uses the phase difference as a function of time between a reference signal and the reflected plasma signal in order to estimate the plasma parameters for a nonlinear bi-Gaussian electron density distribution using a single propagation frequency. A developed multilayer bi-Gaussian model is used to determine the reflected phase response as a function of time. A derivation from this information is used to estimate the real variable of the complex index of refraction across the plasma layers. This is used along with the time difference in order to estimate the plasma thickness. The approach assumes that the individual layer reflection coefficients are not known only the range of values. The reflection coefficient as a function of the complex index of refraction is used to define the imaginary variable of the complex index of refraction. It is defined in two ways. The first way is as a function of the real variable of the complex index of refraction and the real component of the reflection coefficient. With the estimate of the real variable of the complex index of refraction, the solution space for a layer is determined by the range of the real variable of the reflection coefficient. The second way is as a function of the real variable of the complex index of refraction and the imaginary component of the reflection coefficient. With the estimate of the real component of the reflection coefficient, the solution space for a layer is determined by the range of the imaginary variable of the reflection coefficient. The radial propagation frequency along with the solution space for the estimated complex index of refraction terms are used to estimate the plasma frequency and electron neutral momentum transfer collision frequency.