Approximants to the Tonks-Langmuir theory for a collisionless annular plasma

Maclaurin series approximant and Padé rational approximant are used to solve the Tonks-Langmuir theory for an annular plasma and investigate the radial transport behavior of charged particles. Coefficients of the well-known Maclaurin approximant are given in a novel form of recurrence relations which are convenient for computation and present a lower limit for the annular ratio of inner radius to outer radius (i.e., this approximant is not applicable to annular geometries with small inner radii). The newly introduced Padé approximant extrapolates the annular ratio limit determined by the Maclaurin approximant to a lower value and hence is applicable to most annular geometries. General radial profiles of the normalized plasma density and mean drift velocity of ions are given across the annulus and they are independent of the gas type and the Paschen number of the discharge. The annular modeling is applied to an argon plasma and obtains the electron temperature as a function of the Paschen number for different annular geometries.