A general theoretical expression is derived for an electron trajectory in an oscillating electric field. This result is extended to an electron stream, and the current and velocity are found exactly, in the absence of space charge, for any plane within the region of the oscillating field. The limits on the validity of the analysis are established, and application is made to the parallel‐plane diode or klystron gridded gap. Within the restriction that the normalized gap voltage be less than the normalized gap lenth, exact results for current and velocity are obtained.