Electrostatic transfer process of four layers structure (photoreceptor, toner, paper, and transfer belt) which is specified by four R–C parallel circuits combined in series and expressed by a set of 3 differential equations, is investigated with coefficients of time constant and dielectric thickness instead of R and C. The analytic closed form solutions are obtained with a method of eigenvalue and eigenvectors. Initial conditions of solutions are determined by static voltage difference of each layer, which are given by electrostatic Poisson's equations, and then space dependence and time one of solutions are unified by this analysis. Time evolution of each voltage, transfer efficiency, and Paschen's discharge are discussed. It is shown that Paschen's discharge occurs in non-image white area, dominantly.
Yuji Furuya, "Space and Time Dependence of Electrostatic Transfer Process in Electrophotography" in Journal of Imaging Science and Technology, 2001, pp 542 - 546, https://doi.org/10.2352/J.ImagingSci.Technol.2001.45.6.art00007