In the theory proposed recently,1 ,2) the effect of small orbit gyration of electron beam before the magnetic cusp was investigated analyhcally and numerically. The small orbit gyration comes from the crossing of the electron beam and the magnetic flux line and it affects all characteristics of the electron beam such as the velocity ratio, the Lannor r d u s , the guiding center r d u s and the velocity spread. The physical model used in the analysis is shown in Fig. 1. In the drift region defined as [z1+z2] in Fig. 1, the electron beam is assumed to be in a small orbit gyro-motion that is caused by the crossing of the electron beam and the magnetic flux line in the diode region. The diode region is defined as the extent from the cathode to z, in Fig.1. Here, as shown in Fig.1, an ideal magnetic cusp is used for analyhcal calculation The radial position of the electron at the position of the mayetic cusp is given as Eq. (1).