In order to improve the arc quenching ability of the multigap system, it is important to know the principle of arc quenching and how the chamber structure affects the arc development process in the multigap system. In this study, the two-dimensional geometric model of the multigap system is established based on the magnetohydrodynamics theory in COMSOL multiphysics simulation platform. The principle of arc quenching in the multigap system is explained in detail by analysing the physical characteristics of the arc in the multigap system. The simulation result shows that the arc is compressed at large scales in the semi-closed chambers of the multigap system, which results in an instantaneous temperature rise of the arc, thus, forming the self-expanding airflow. The strong self-expanding airflow cuts off the arc channel and blocks the energy supply of the arc. The influence of the chamber structure on arc quenching in the multigap system is manifested in the fact that proper improvement of the width and depth of the chamber subserves arc cooling, the reduction of the deflection angle and the increment of the number of the chambers are conductive to arc extinction.