Transverse magnetic field (TMF) contacts and applying external TMF are often adopted for reducing the ablation of the contact surface, but TMF will also affect the breaking performance of the vacuum interrupters. In this paper, we investigated the influence of weak TMF on the expansion of the plasma in the post-arc phase with one dimension implicit Particle-in-cell/Monte Carlo collision model. And we added an external circuit to the model to ensure the correctness of the calculation results. We simulated multiple magnetic field strengths(<30mT), compared the plasma expansion process when TMF with the strength of 0mT and 10mT, and discussed the influence of metal vapor density on the insulation performance recovery of the vacuum interrupter. From the results, applying TMF with strength below 5mT has little effect on the expansion of the plasma, and when the magnetic field above 10mT can increase the plasma density to improve flow capacity, which is because the particles become more difficult to leave the discharge area under the force of the magnetic field. In general, We find that weak external TMF may adversely affect the breaking performance of the vacuum circuit breakers.
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