Model of the Retrograde Motion of a Vacuum Arc: Comparison to Experiments

In the absence of an external magnetic field, a cathode spot (CS) of a vacuum arc experiences a Brownian random walk (jumps) along the surface. A magnetic field parallel to the surface causes spot drift in the anti-Amperian direction (retrograde motion). Three statements are suggested to explain the retrograde motion and its features: 1) each CS jump is associated with a voltage drop fluctuation Delta V; 2) the tangential electric field (the Hall field) is created by the additional positive surface charges at the retrograde side of the spot. This field results in an additional voltage drop at the retrograde side of the spot delta V; and 3) the probability of the spot jumping in the retrograde direction is proportional to delta V/Delta V. Calculations based on these statements allow one to achieve qualitative and, in many cases, quantitative agreement with experiments concerning retrograde velocity dependences on these external parameters: magnetic field, arc current, interelectrode gap, and cathode surface conditions. No adjustable parameters were used in these calculations.