Calculating the effective trapped charges on the dielectric sample surface

In the present work, it has been presented a theoretical study to explore the effect of the polarization charge on the number of trapped ions within the aspect of the phenomenon of an ion mirror effect. A mathematical equation was derived, representing the surface potential by the effect of the polarization charge. The surface potential equation was modified to include the effect of the polarization charge by two ways, the first way is adopting a point charge distribution model and the second way is adopting a hemispheroid distribution model. The results showed that the polarization charge has a significant effect on the number of trapped charges. This effect appeared as a changing in the amount of surface potential as well as in the amount of the reflection point of the incoming ions.