Hall thrusters with internal cathodes achieve higher efficiency, smaller plume divergence angles, and improved plume symmetry compared with those with external cathodes. Electrons from the internal cathodes first encounter an axis magnetic field and are coupled with the plasma plume. However, few studies have focused on the influence of axis magnetic field on the operation of Hall thrusters with internally mounted cathodes. Two approaches-applying an additional inner coil and modifying the diameter of the central aperture-are proposed to change the axis magnetic field, and the discharge characteristics are tested. As the number of ampere turns of the additional coil current in-creased, the maximum magnetic-field strength increased by 11%, and the gradient at the exit of the internal cathode decreased by 83%, thus resulting in relative reductions of 0.81% and 1.75% in the thrust and efficiency, respectively, under the rated operating condition. As the diameter of the central aperture decreased, the maximum magnetic strength increased by 9.1% and the gradient at the exit of the cathode increased by 36.3%, thus resulting in relative reductions of 1.88% and 5.71% in the thrust and efficiency, respectively, under the rated condition. Although the performance tendencies are the same, quantitative differences are observed. An analysis of the mechanism indicates that an axis magnetic field with weak strength and a gradual gradient are conducive to electrons traversing down-stream and crossing the magnetic field to couple with the plasma plume. Thus, the differences between the discharge characteristic variations under the two approaches can be explained qualitatively, and guidance is provided for op-timizing the axis magnetic field of Hall thrusters with internal cathodes.