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The recent introduction of high‐energy storage rings with very long straight sections for dedicated synchrotron radiation research has significantly expanded the parameter space accessible to insertion devices as well. In particular, when the generation of soft x rays on a storage ring such as the Stanford Positron Electron Project (PEP) is considered, its straight sections, which exceed 100 m, may be shown to be naturally amenable to low‐to‐medium K undulators with a large number of relatively long periods. This in turn allows for the establishment of relatively weak on‐axis fields in such devices. In this paper it is shown that these conditions permit the use of electrostatic fields, as well as the concomitant development of fixed‐gap, variable‐period undulators. Such devices are shown to be superior in many respects to the variable‐gap magnetostatic undulators currently in vogue. Two novel variable‐period undulator designs, one for a transverse electrostatic undulator and the other for a helical device (HEU) are described. The performances of both devices are calculated, and the numerous advantages of the HEU configuration in producing either soft or hard x rays of arbitrary polarization on high‐energy rings such as PEP are pointed out.