Propagation of Ion Acoustic Waves from and to a Spherical or Cylindrical Conductor

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Abstract
Analytic expressions for the spatial variation of the phase velocity and amplitude of ion acoustic waves propagating radially through the plasma boundary layer at a conducting sphere or cylinder are derived using the two-fluid model. The Debye length is assumed to be small compared with any relevant dimension of the problem and the wavelength small compared with the radius of the conductor. The limits of ion mean free paths small and large compared with the radius of the sphere are considered. In the cylindrical case only the collisionless limit has a self-consistent solution. It is found that both the converging and the diverging waves are damped and that the phase velocity of the wave is approximately equal to the sum of the ion acoustic velocity in a homogeneous plasma and the ion drift velocity. The contribution of Landau damping to the total damping is estimated.

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