Further Note on the Quasi‐Static Theory of a Cylindrical Impedance Probe for Magnetoplasma

Abstract

In a previous paper (Wait, 1966), an expression was derived for the fields of two parallel line charges in an anisotropic medium. A quasi‐static theory was used, and to facilitate the analysis, the line sources were encased in a cylindrical dielectric rod. An important conclusion was that the resonant frequencies of the driving point impedance did not depend on the geometry of the device; at least, this was true to within a first order. This is in contrast to many other plasma diagnostic devices (Heald and Wharton,. 1965).It is the purpose of the present note to generalize the above‐mentioned derivation to include the effect of a sheath at the boundary of the plasma next to the probe. The influence of a cylindrical glass container for the dielectric rod is also considered. The situation is illustrated in figure 1 where the common z axis of the Cartesian (x, y, z) and the cylindrical coordinate system is normal to the paper. Two infinitesimally thin parallel wires are located at (ρ0, φ0) and (ρ0, φ0 + π), as indicated. For purposes of the quasi‐static analysis, these are assumed to have charges of q and −q coulombs per unit length, respectively. The thin wires are encased in a cylindrical rod of dielectric constant ε1 and radius c. The dielectric rod is enclosed by a cylindrical glass container of dieiectric constant ε2 and outer radius b. The sheath separating the plasma from the device is then regarded to be a cylindrical layer of vacuum of dielectric constant ε0 which has an outer radius a. The external medium is a homogeneous electron plasma and it is characterized by a (angular) plasma frequency ω0, collision frequency v, and (angular) cyclotron frequency ωc. If the d‐c magnetic field lies in the (x, z) plane and subtends an angle θ with the z axis, the relevant components of the dielectric tensor of the plasma are (Ratcliffe, 1959)