A Field-Limited Theory of Cascade Development

Recently reported model experiments of Knapp [1] on electroded cascade development provide an excellent set. of data for testing presumptive development models since so many of the experimental parameters are available. A development model is presented that is based on the assumption that in the dynamic process of cascade development the instantaneous force binding a toner to a carrier is proportional to q, the charge on the toner, rather than to q
2
. This is in contrast to the q
2
force dependence observed in equilibrated mixtures. The mechanism of toner detachment is impact-assisted electric-field stripping. Statistical distributions for toner radius, surface charge density, and impact velocity are introduced. The results are compared with Knapp's experiments and with a recent theoretical model of Maitra, Scher, and Knapp (MSK). In contrast to MSK, although the specific form of the distributions is important for the conclusions, the particular parameters of the distributions have little effect. The statistics do not smear the physics.