The compensated pulsed alternators (CPAs) have good applications in high-energy lasers, electromagnetic rail guns, and other electromagnetic launch devices. Among various electrical machine topologies, homopolar inductor alternators (HIAs) have attracted interest as CPAs due to their merits of simple and reliable structure, brushless excitation, and high-speed operation. However, the length of the conventional HIA is difficult to expand because it is limited by the rotor diameter, and the rotor diameter is restricted by the maximum speed of rotor tip, which results in low-energy storage capacity of a single machine. Besides, HIA suffers from the relatively low-power density due to its unipolar air-gap flux density (UAFD). To solve these problems, two novel HIAs with multistage stator cores (HIA-MSCs) are proposed in this paper. One is HIA with UAFD (HIA-UAFD) and the other is HIA with unipolar and bipolar air-gap flux density (HIA-UBAFD). First, the structure and operation principle of HIA-MSCs are illustrated. Then, the key parameters of HIA-MSCs are derived, and the corresponding models are built. Finally, the electromagnetic performances of HIA-MSCs are investigated by 3-D finite-element analysis method. Compared with HIA-UAFD, HIA-UBAFD has relatively higher discharge current and output power, which indicates that HIA-UBAFD is a better candidate for the pulsed alternator.