Theory of gyrotron helical electron beams (HEB) formed by magnetron-injection guns (MIG) may be considered as complete under conditions of ideal axial symmetry of electrodes and magnetic field and neglecting electron reflections from magnetic mirror. However this theory doesn't allow for the explanation of a number of observable effects. Besides there arises an interest to the forming systems different from traditional MIG. Some of these problems are briefly considered below.
A. N. Kuftin,
"Theory of helical electron beams in gyrotrons", Proc. SPIE 1929, 17th International Conference on Infrared and Millimeter Waves, 192975 (7 December 2017); doi: 10.1117/12.2298374; https://doi.org/10.1117/12.2298374