Kinetic Model of Tonks-Dattner Resonances in Plasma Columns

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Abstract
The linearized Vlasov equation is used to describe the coupling to plasma waves in bounded plasmas of externally driven quasistatic electric fields of frequency ω, treating as an example a cylindrically symmetric equilibrium. The coupling takes place at the plasma resonance, where ω equals the local plasma frequency. It is described by an asymptotic theory based upon the small parameter νT/ωL < < 1, whereνT, where is the electron thermal velocity and L the equilibrium scale length. A previously suggested mechanism based on a WKB solution of the Vlasov equation is then developed to provide trapping of the plasma waves between the plasma resonance and the wall sheath, including the effects of Landau damping. The effect of these internal resonances on the external admittance of the plasma is shown, and a numerical example containing typical experimental parameters is given. A comparision is made with previous theories which utilized a fluid model of the plasma.