Non-linear central charge potential in dusty plasma

Summary form only given, as follows. Spherical central charge potentials in dusty plasmas are usually approximated by a Debye type potential. However this linear approximation is not appropriated in dusty plasmas because the coupling parameter F (F = electrostatic energy/thermal energy) is not small. Here an approximated non-linear potential is presented using a two-point quasi-rational approximation procedure, which was previously applied to obtain a non-linear Debye potential for point charges in plasmas Two kinds of approximations are presented. The simplest approximation is correction to the usual Debye potential for spherical charges of radius Ro, which produces better results, and as we will also show, the surface electric field obtained is now the right one. All the parameters of this approximation are function of the central charge radius Ro. The second algebraic approximation is obtained using a combination of rational and exponential functions. The accuracy is now much better, but the computation is a little longer. For large values of the coupling parameter (F>5) the Poisson-Boltzmann model seems not suitable, however the accuracy of this last approximation is good until values about ten times that value. Several other parameters as the non-linear effective screening length and the number of particles in the non-linear Debye sphere have been also computed.