Certain configurations of anode, grid sections, and uniformly emitting cathode produce rectilinear motion of the electrons, both with and without velocity modulation. These systems are (a) plane parallel electrodes and grid sections of unlimited extent, (b) coaxial circular electrodes and grid sections of infinite length along the axis, and (c) concentric spherical electrodes and grid sections. The uni‐dimensional character of the motion permits a complete evaluation of the effect of space charge on the bunching process in the range of drift space where overtaking (crossing of orbits) does not occur.