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It is found that the breathing mode oscillation of the discharge current is suppressed notably in a Hall thruster operating with the electromagnets driven in series by the discharge current. In order to study the physical mechanism of this suppression, the ionization distribution is measured experimentally and the spatiotemporal features of the ionization front motion are studied numerically with a one-dimensional quasineutrality hydrodynamic model. Results show that the ionization front motion is restricted in a small range due to the closed-loop feedback control of the magnetic field. The steady-state ionization distribution is narrow and condensed when the electromagnetic coils connect in series with the discharge circuit. The different magnetic field excitation accompanied by different ionization characteristics is the main reason for the suppression of the discharge-current low-frequency breathing mode oscillation.