Particle balance in a steady state plasma in a dipole magnetic field

Abstract

Detailed experiments and modeling are performed to investigate spatial (r and θ) dependence of particle production (Z), loss (Lp) and retention (Z − Lp) rates in a steady state plasma in a dipole magnetic field. A mathematical model is developed that solves the particle balance equation, considering generation through ionization, losses through diffusion and recombination, and by taking into account the measured values of plasma parameters and dipole fields in space. Depending upon the pressure p and angle θ, Z is found to peak ∼r = (3 – 6) × 10−2 m from the center of the magnet and decreases downstream, whereas Lp steadily increases toward the chamber wall. Particle balance (Z = Lp) is realized either at a single point in space or over a wider region, and can be tuned by varying p, whereas Z − Lp is found to be a maximum at an optimum pressure (∼1.0 mTorr). Results indicate that while the diffusion is primarily classical (∼1/B2), the recombination coefficient scales as ∼1/B0.5, as a result of its implicit dependence on the magnetic field through the electron temperature. The ionization coefficient is rather high and approximately uniform until ∼0.02 Tesla, and thereafter decreases linearly at lower fields.