Theory of the expanding plasma of vacuum arcs

Publisher Website
Google Scholar
Abstract
Investigations of the diffuse plasma expanding from cathode arc spots into a vacuum have revealed some unexpected properties calling for physical explanation. A theoretical model of such plasmas which is based on one-dimensional time-dependent hydrodynamic two-fluid equations can be solved analytically in the form of asymptotic power series approximately describing the plasma parameters as functions of the variable s = (I/r)2/5 (current I, distance r). The main results give a quantitative decomposition of the force accelerating the ions into three partial forces caused by the electric field, by the ion pressure gradient and by the electron-ion friction, which are of comparable importance: they contribute, on average, roughly 30 +/- 10% (field), 15 +/- 10% (pressure gradient) and 55 +/- 10% (friction), respectively, to the high kinetic ion energies (in the case of Cu), still depending on the specific kind of model. Unlike the ions, the electrons are accelerated by the pressure gradient only, but are decelerated both by the field and by friction; all these forces cancel each other almost completely. The direction of the electric current is opposite to the direction of the field; therefore, the resistance of the plasma is negative. The diffusion current exceeds the (opposite) conduction current by approximately a factor of 3. The plasma temperature decreases with distance. Space charge is negligible, but a potential hump of about 5-10 V exists near the cathode. The limitations of the validity of the derived solution are discussed, as are possible extensions and simplifications of the model.

This publication has 21 references indexed in Scilit: