[en] The calculation of the electronic motion in the pre-oscillation phase of a smooth bore magnetron is the problem of calculating the electronic motion in the region between two concentric cylinders with an applied radial electric field and a constant axial B/sub z/ magnetic field. The inner cylinder represents the electron emitting cathode and the outer cylinder represents the anode. The emission is assumed to be space charge limited. This results in an electronic cloud surrounding the cathode. The radial velocity of the electrons is limited by the space charge and in addition the axial magnetic field tends to curve the path of the electrons so that they return to the cathode. Consequently, the electronic orbit extends to some distance r₀ from the cathode and for values of the radius r > r₀ exists a charge free region. The model assumes relativistic electronic motion with self-consistent magnetic fields. The magnetic flux is assumed to be conserved; i.e., conducting cylindrical walls