Guide to Mitigating Spacecraft Charging Effects

Appendix G

Simple Approximations: Spacecraft Surface Charging Equations

Whereas Appendix D addresses internal charging analyses, in this section we focus on surface charging. The simple approximations discussed in this section are of a worst-case nature. If this analysis indicates differential potentials between noncircuit surface materials of less than 400 V, there should be no spacecraft discharge problems. If potentials predicted on materials exceed 400 V, the Nascap-2k code (Section C.3.3) is to be used.

Although the physics behind the spacecraft charging process is quite complex, the formulation at geosynchronous orbit can be expressed in very simple terms if a Maxwell–Boltzmann distribution is assumed. The fundamental physical process for all spacecraft charging is that of current balance; at equilibrium, all currents sum to zero. The potential at which equilibrium is achieved is the potential difference between the spacecraft and the space plasma ground. In terms of the current (1), the basic equation expressing this current balance for a given surface in an equilibrium situation is

G.1

where

V = spacecraft potential

I_E = incident electron current on spacecraft surface

I_I = incident ion current on spacecraft surface

I_SE = secondary electron current due to I_E

I_SI = secondary electron current due to I_I

I_BSE = backscattered electrons due to I_E

I_PH = photoelectron current

I