Theory of a thick dynamic positive-ion sheath

The nature of the dynamic positive ion sheath formed in front of the negatively going anode of a gas discharge valve is considered. Approximations valid for thick sheaths at the high voltages appropriate to mercury valves are discussed, and a transient analysis of an idealized model performed. Expressions relating anode—cathode voltage and current to sheath thickness are derived. Approximate forms of these expressions are obtained, and numerical comparison is presented in one situation.