Stepwise Simulation on the Motion of a Single Cathode Spot of Vacuum Arc in External Transverse Magnetic Field

Abstract

In this paper, the relationship between the external transverse magnetic field (TMF) and the ignition probability of new cathode spot in different directions is developed assuming that the ignition probability of a new cathode spot is proportional to the magnetic pressure around the old one. Furthermore, a method is established to simulate the 2-D motion of a cathode spot step-by-step. With this approach, stepwise simulations of the 2-D retrograde motion of a single Cu cathode spot are carried out in a large range of flux density of TMF (B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">em</sub> ). Simulation results indicate that, if the self-generated magnetic field B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sm</sub> exceeds the applied magnetic field B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">em</sub> , i.e., B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">em</sub> ≤ B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sm</sub> , there is a linear relationship between the velocity of the retrograde motion and B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">em</sub> , in certain range of B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">em</sub> , after which the velocity of the retrograde motion increases slowly and nonlinearly with further increase of B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">em</sub> . This phenomenon agrees well with relevant experiment results. In the linear stage, the dependence of velocity constant on the spatial step and the temporal step of the motion of cathode spot is investigated as well. Moreover, when B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">em</sub> ' B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sm</sub> , the velocity of cathode spot decreases with the increase of B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">em</sub> , even the macroscopic motion is still in the retrograde direction. This effect might also contribute to the reversal of cathode spot motion from the retrograde direction to the Amperian direction at strong TMF besides the predominant effect of the deflection of arc column toward the Amperian direction.