Static Theory of a Discharge Column at Intermediate Pressures

A steady-state theory of the discharge column is derived which is applicable in the pressure range where the ion mean free path is neither much greater than nor much less than the column radius, and which goes over in the low- and high-pressure limits to the free-fall and ambipolar diffusion theories, respectively. Solutions for planar and cylindrical geometry are given for the density and potential profiles. The plasma-sheath boundary is discussed and the sheath potential drop is estimated. The theory is shown to agree well with measurements in mercury discharges over the pressure range 1–20 μ Hg.