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Compulsator provides an excellent approach to achieve compact energy storage and pulsed power generation for several multi-MJ, multi-GW applications, including electromagnetic launchers, directed energy systems, and fusion reactors. There is a continuous research effort toward increasing the power capability and compactness of this machine since its invention. In general, specific machine designs aim to maximize the output current and power by minimizing the transient inductance of the armature winding. The field and the inductance of the armature winding are some of the most important parameters in the compulsator design. This article presents the development of a generic method to analyze the magnetic fields and inductances of the armature windings in compulsators based on fundamental principles. It derives analytical models for inductance calculation in various types of alternators as unified terms of simplified formulas. These are used for the design, analysis, and optimization of all air-core, iron-core, compensated, and uncompensated pulsed alternators (PAs). By comparing the distribution of armature reaction fields and the self-inductances in compulsators having different configurations, this article investigates the basic relationships between the topology of the alternator and the fields and inductances. This is not limited only to the study of PAs but it can also be used in both slotless and air-core conventional machines.