Absbact -In work the theory ofGyroton with a wide electron beam is constructed. Optimum regime of Gyroton with a wide electron beam are investigated. Frequency characteristics of Gyrotons, goffer and magnitostatic distributions are received. Dependence of gyroton efficiency on width of an electron beam is determined I. Introduction The Gyroton is new type ofthe electron device [I-41. The principle of its action cardinally differs from processes in girotron and consists that the rectilinear electron beam cooperates with rotating slowed down electromagnetic wave E,, of type. The electron beam deviates an axis of the device under action of a cross component of a magnetic HF field and then gives the longitudinal energy to a longitudinal component of HF electric field. Thus any longitudinal or cross bunching of an electron beam does not occur. Synchronism of interaction of an electron beam with the slowed down rotating wave is set by the wave E l l and supported by longitudinal magnitostatic field. It is obvious. that the slowed down wave such as E , , cannot be distributed in a waveguide not being transformed in H I , . It's waves are interconnected. Therefore calculations of a Gyroton can be carried out only at the account of both types of waves.Results of calculations. The some characteristics of Gyrotons have been given in [ 5 ] . There it has been shown, that the Gyroton with a thin electron beam and a regular goffered waveguide can have efficiency coming nearer to 100 %. The basic role in work of the device belong to wave Ell, however in this process not last role to wave H,,. Without taking into account a wave HI, the gyroton efficiency achieves the same level. but at other parameters of waveguide and magnitostatic field. At increase a width of electron beam the Gyroton efficiency decreases, but it is not so essential. Fig.1 shows, that with increase in radius of electron beam fiom dr=2nAr/h=O up to dr=0.9 the efficiency decrease from 97 % up to 40 %. Calculations were cai-ried out on five layer models of electron beam. For reduction of influence by efficiency of width of electron beam the optimization of a structure of a goffered waveguide and distribution of Here ifp, iep -an initial and final index of parameters specifying the goffer period, ifv and iev -an initial and final index of parameters specifylng goffer depth. Optimization of Gyroton was carried out for an 1 2 0,s 0.6 'D 0,4 0 Regular I = ?$ 0,2 0 0,2 0,4 0,6 0,s 1 dr Fig.