Appendix D

Internal Charging Analyses

See Appendix G for surface charging analyses.

As stated earlier, the computations involved in estimating dielectric charging resemble surface charging calculations with the inclusion of space charge. That is, the basic problem is the calculation of the electric field and charge density in a self-consistent fashion over the volume of interest. In other words, Poisson's equation is solved subject to the continuity equation. The relevant formulas are Poisson's equation (in one dimension):

D.1

the continuity equation (in one dimension):

D.2

and Ohm's law (for electrons):

D.3

These can be combined to give

D.4

where

E = electric field at *x* for time *t*

ρ = charge density at *x* for time *t*

σ = conductivity in (Ω · cm)^{−1} = σ_{0} + σ_{r}

σ_{0} = dark conductivity

σ_{r} = radiation-induced conductivity

ε = ε _{0} ε _{r}

ε _{0} = free-space permittivity = 8.8542 × 10^{−12} F/m

ε _{r} = relative dielectric constant

J_{R} = incident particle flux (current density) where - ∂*J*_{R}/∂*x* = charge deposition rate at *x*

J_{c} = particle flux (current density) due to ...

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