C.5.6 Conductivity and resistivity

Charges can move from or to surfaces via conduction processes in the bulk of the material or on the surface. The surface and bulk conductivity can vary considerably from one material to another. The use of low conductivity material (e.g. Teflon) can favour the occurrence of differential charging especially between sunlit and non-sunlit surfaces. The resistivity is by definition the inverse of the conductivity.

A floating metallic part of area A exposed to space connected to the spacecraft ground through a resistance R can have a potential with respect to the ground equal to

where J is the current density through A.

An upper bound of the current density J can be set at 10 nA cm-2 for current collection from the natural environment. Requirements on the maximum value of the potential sets requirements on AR.

For partially conductive materials of resistivity r, thickness t and surface A, laid on top of a more conductive material the resistance to the ground is

and the potential difference between the ground and the structure can be written

Therefore requirements on the maximum potential on the dielectric set a requirement on rt.

For a partially conductive patch materials of thickness w, laid on top of a less conductive material e.g. an insulator, and grounded at the edges the conduction can occur through its whole thickness. The corresponding resistance is

where

• d is the distance to the nearest ground, and

• w is the width perpendicular to the direction of the nearest ground.

The potential difference can then be assumed to be

Therefore requirements on the maximum potential over the dielectric set a requirement on rd²/t.

Conduction can takes place at the surface within a thin layer of usually unknown thickness d. The resistance of a rectangular patch grounded at 2 opposite edge separated by length d and with a perpendicular dimension w is then:

where R_S is so-called the surface resistance and is expressed in Ohm per square.

Therefore requirements on the maximum potential over the dielectric surface set a requirement on R_S.

It is important to note that the conductivity varies with the dose due to radiation, the temperature and the charging level (cf section on deep-dielectric charging). The surface conductivity also varies with the amount of contamination.