A number of important aspects of the production of annular electron beams by foilless diodes are examined, both theoretically and experimentally. The theories of Ott, Antonsen, and Lovelace (OAL) and Chen and Lovelace (CL) are compared, and the CL theory is extended to include the effect of an axial gap in an approximate fashion. For the case of finite magnetic field strengths, Larmor orbits are examined and radial oscillations of the beam profile are predicted from a beam envelope analysis. Experimental results obtained with both low‐ and high‐impedance sources have been compared with the theory, and based on such studies, the design and construction of an intense hollow beam generator are described. Experimental results obtained with the new diode compare favorably with both the analytic theory and the results of numerical simulations. The device currently produces 2‐MeV electrons at beam currents of 65–70 kA.