Asymptotic theory of an electrostatic probe in a weakly ionized plasma with negative ions

The problem of a spherical electrostatic probe in a weakly ionized dense plasma with negative ions is solved by matching asymptotic expansions in powers of the small parameters δ=(rD/rp)2→0 and ω=(rs/rp)2→0, where rD is the Debye radius, rs is the recombination length, and rp is the probe radius. Account is taken of such kinetic processes in a plasma as volume ionization, ion-ion and ion-electron recombination, and electron attachment to electronegative plasma components. It is shown that the plasma perturbed by the probe can be divided into three regions: space-charge sheath near the probe, a quasineutral inhomogeneous plasma region, and a quasineutral homogeneous plasma region. The profiles of the charged-particle density and potential are found for each of these regions. The integration constants and the relationships between the boundary conditions at the probe surface and in an unperturbed plasma are found by asymptotically matching the solutions at interfaces between the plasma regions. The electron-energy relaxation length is assumed to be much shorter than the characteristic scale length on which macroscopic plasma parameters vary, so that the electron distribution function is determined by the local values of Ne and T