C.3.6 Thin sheath – space-charge-limited model

If the sheath thickness is much less than the curvature radius of the spacecraft surface the sheath can be locally assumed to be planar and a space-charge-limited current assumption can be made. This model has also been called the Child-Langmuir (space-charge-limited) diode model.

The current in a planar thin sheath model can be estimated from:

and an expression for the sheath thickness, d, can be written

if the current density is defined by

K* is 1 for a monoenergetic beam.

Langmuir and Blodgett also developed a space-charge-limited theory for radial electron flow from spherical diodes in 1924 [1].