Debye Sheath - Description

Description

Sheaths were first described by American physicist Irving Langmuir. In 1923 he wrote:

Electrons are repelled from the negative electrode while positive ions are drawn towards it. Around each negative electrode there is thus a sheath of definite thickness containing only positive ions and neutral atoms. Electrons are reflected from the outside surface of the sheath while all positive ions which reach the sheath are attracted to the electrode. it follows directly that no change occurs in the positive ion current reaching the electrode. The electrode is in fact perfectly screened from the discharge by the positive ion sheath, and its potential cannot influence the phenomena occurring in the arc, nor the current flowing to the electrode."

Langmuir and co-author Albert W. Hull further described a sheath formed in a thermionic valve:

"Figure 1 shows graphically the condition that exists in such a tube containing mercury vapor. The space between filament and plate is filled with a mixture of electrons and positive ions, in nearly equal numbers, to which has been given the name "plasma". A wire immersed in the plasma, at zero potential with respect to it, will absorb every ion and electron that strikes it. Since the electrons move about 600 times as fast as the ions, 600 times as many electrons will strike the wire as ions. If the wire is insulated it must assume such a negative potential that it receives equal numbers of electrons and ions, that is, such a potential that it repels all but 1 in 600 of the electrons headed for it.

"Suppose that this wire, which we may take to be part of a grid, is made still more negative with a view to controlling the current through the tube. It will now repel all the electrons headed for it, but will receive all the positive ions that fly toward it. There will thus be a region around the wire which contains positive ions and no electrons, as shown diagrammatically in Fig. 1. The ions are accelerated as they approach the negative wire, and there will exist a potential gradient in this sheath, as we may call it, of positive ions, such that the potential is less and less negative as we recede from the wire, and at a certain distance is equal to the potential of the plasma. This distance we define as the boundary of the sheath. Beyond this distance there is no effect due to the potential of the wire."