The eddy current distribution in the shield of an air-core passively compensated pulsed alternator (compulsator) is discussed. The action of the shield reduces the inductance of the armature winding considerably, thus enabling it to deliver high-power pulse to low-impedance loads. By virtue of its function, the shield is stressed mechanically as well as thermally. An analytical solution of the 2-D diffusion and convective diffusion equations is obtained. The solution is obtained by the extraction of the poles and corresponding residues of the transformed equations. The theory was developed specifically for the shield of an air-core compulsator, which is a single-phase alternator. By using superposition, the results can also be applied to determine the transient eddy current distribution in the shield of superconducting synchronous generators.