A general nonlinear multi-dimensional interaction theory is employed to analyze Brillouin focused beams in klystrons and traveling-wave amplifiers. Harmonic currents and beam spread are found for a number of different situations. Closed-form solutions are being sought for the nonlinear equations. Beam stability in the presence of r-f and velocity distribution effects on the start-oscillation conditions of BWO's are two specific problems where these solutions are to be applied. Experimental programs to check these analyses are described. An appropriate taper on a ring-and-bar circuit for obtaining phase-focused operation is presented. Progress on the magnetron injection gun computer program is described. The trajectory starting problem appears to be solved, while further work on establishing the proper current density from the cathode is indicated. Provisions in the relativistic electron beam computer program for self-induced effects are also described. The status of the UHF helix-magnetron injection gun device is summarized. Performance data of the gun in a beam analyzer is presented. (Author).