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

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