Abstract

The non-linear grain charge evolution is considered here assuming negatively charged grains with a collection of ions and electrons, where the OLM (Orbit Limit Motion) theory is valid. In previous treatments a non-linear first order equation was found by other authors, which is usually approximated by a first order perturbation scheme, leading to a characteristic charging time tau(c). In this work the non-linear solution is numerically calculated for different values of the dusty plasma parameters (T-e, T-i, r(d), and n(0)) and compared with the linear approximation already published. A better approximation has been found using higher powers of the perturbation analysis. Its accuracy is determined using the non-linear numerical solutions previously mentioned. A comparison of this non-linear and previous linear approximation has been performed. Several error curves changing the plasma parameters are also presented.