Model of the anode region in a uniform multi-cathode-spot vacuum arc

Abstract

A model is developed for the anode region of a uniform multi-cathode-spot vacuum arc. A first-order approach is used, in which the plasma up until the anode sheath is assumed to be produced solely by a multitude of cathode spots and is described by a zero-order plasma model previously developed, and the influence of the anodic emissions on this plasma is assumed initially to be negligible. Calculations of the electron mean-free-path and the Debye length indicate that the anode sheath may be modelled as collisionless. The anode potential is calculated by imposing the requirement of current continuity, and it is found that the overabundant supply of random electron current forces the anode to assume a negative potential with respect to the adjacent neutral plasma with a magnitude of approximately (1/3)(kTe/e)(vT/vd), where Te is the electron temperature, vd is the electron drift velocity, and the thermal velocity vT is defined by (kTe/2πme)1/2. The magnitude of the electric field at the anode surface is also calculated, and it is found that under certain circumstances, its value may approach the value of 107 V/m known to produce cathode spots. The possibility of ‘‘cathode spot’’ formation on the negatively charged anode is discussed. The energy flux incident on the anode surface is analyzed and is found to contain both a component originating from the electron flux, and a component originating from the ion flux. The two components are of the same order of magnitude, with the ion flux dominant at lower values of Te, and the electron flux dominant at higher values of Te. The overall energy flux is given by JφE, where J is the current density and φE is an effective anode drop whose value in a Cu arc ranges from 13 V for Te=1 eV to 33 V for Te=9 eV. Neutral atom emission from the anode surface by evaporation and by sputtering is analyzed. Evaporation will be significant after a sufficient heating time has elapsed, on the order of 64 ms for a 3 eV, 107 A/m2 Cu arc, for example. Sputtering, in the case of a Cu arc, may produce a local neutral density equal to 37% of the ambient ion density. All of the neutrals emitted from the anode surface are eventually ionized by electron impact. Extension of the model to cover arcs where macroparticle-produced plasma is significant, and where nonuniformities are produced by the electrode geometry or magnetic constriction, is discussed qualitatively.