Determination and optimization of the mathematic model using the non-linear least square and iteration methods

Abstract

The mathematic model of ring-shaped electrostatic sensor is often represented by its spatial sensitivity, which is defined as the ratio between the induced charge on the electrode to the charge carried by a particle at a different location in the sensing zone. The first step of this study was carried out to investigate the response of the electrode to a charged particle moving axially and radially [1] through simulation, and the second step was to optimize the mathematic model using the non-linear least square and iteration methods. Based on the response to single charge particles, the spatial response of the electrode to a flow stream at different radial position was derived. The purpose of modelling was to establish an accurate analytical expression of the sensor response to single charged particles and flow streams for further study of spatial sensitivity compensation.