Radioactive aerosol charging with spatially varying ion concentrations

The bipolar ion production rate from β- or α-decays from a radioactive aerosol is not expected to be uniform in space, but to be concentrated close to aerosol particles. A charging theory is constructed which allows for this spatial dependence and contains ion recombination, radial ion diffusion and the aerosol attachment coefficients of Gunn (J. Meteor. 11, 329 (1954)). The radial equations for the positive and negative ion concentrations are transformed into equations for the mean ion concentration and the net ionic charge which enables change conservation to be treated explicitly. In the steady-state, the radial equations for the concentrations and the electric field are numerically solved iteratively to obtain the mean charge j on a radioactive aerosol. Results for j are obtained for wide ranges of aerosol concentrations and decay rates, and show very good agreement with values obtained assuming spatially uniform ion concentrations. The agreement, which arises in spite of large spatial variations in ion production rates, is attributed to the combination of radial ion diffusion and the ion recombination process. (Author)