Transverse Forces and Motions at Cathode Spots in Vacuum Arcs

Consistent analyses are provided for the motion of cathode spot cells in the presence of magnetic fields parallel to the cathode surface (retrograde motion), for the spontaneous splitting of cells, and for the grouping of cathode spot cells in organized structures. The formulas for retrograde motion and cell splitting frequencies are evaluated for cells carrying 1-80 A on copper vacuum arc cathodes. The results for retrograde motion are shown to agree satisfactorily with published experimental data. It is concluded that retrograde motion can be explained simply, and that measurements of retrograde velocities can provide useful information concerning cell sizes in cathode spots. The close connection demonstrated between retrograde motion and cell splitting yields the conclusion that cell splitting should slow in the presence of an ambient gas, as does retrograde motion. Cathode spot sizes and energies of formation are evaluated for spots that are circular clusters containing up to twelve individual cells. It is concluded, in apparent agreement with experiment, that such clusters should not be stable under conditions of clean vacuum where the cells exhibit retrograde motion.