C.3.7 Thick sheath – orbit motion limited (OML) model

If the sheath thickness is much greater than the central spacecraft dimension, the ability of particle to reach the surface is more limited by particle orbit considerations than by the size of the sheath.

If the spacecraft can be considered as a sphere of radius R, it can be shown that for an attracted particle with mass m, speed, v_o and charge q ,to reach the spacecraft, a condition is that its impact parameter R_i is below a critical value as follows:

The total current of this attracted species striking the satellite surface for a monoenergetic beam can be written as:

If the attracted species have a Maxwellian distribution their current on the spacecraft is

By comparing the ratio

with respect to unity, it can be estimated, in principle, whether the orbit motion limiting theory (x<<1) or the sheath limiting theory (x>>1) applies. When this ratio is around 1, none of these theories is a priori suitable and more complex models (cf below) are used. In practice it seems that the applicability of the OML approximation is much wider than x>>1.