In the article, results of numerical simulation of the gun with the cusp of magnetic field are presented. Short pulse version of the gun with explosion emission is investigated. Some preliminary analytical estimation of the beam and gun parameters are performed. Then, numerical optimization of the electrodes shape as well as magnetic field distribution is carried out. For preliminary separation of electrons and formation of the rectilinear beam, anode diaphragm is installed. After then, additional selection of electrons for decreasing the ripple is performed. For this purpose, channel walls are used for interception of some part of the electron beam. Reverse of the magnetic field in the diode part of the gun is formed. So, the formation of the rectilinear beam is combined with the region, where electrons obtain initial gyration energy. To prevent the disperse action of the own beam space charge forces, the system with big gradient of magnetic field (about 0.5-1 kGs/mm) is needed. According to results of the simulation, helical electron beam can be performed even at total compression ratio about 1000 and current density more than 50 kA/cm2. The designed electron gun provides acceptable performance for the large orbit gyrotron, such as operating current close to 300 A, the pitch-factor value about 1.5-1.7, deviation of the guiding centers from the axis (the ripple) λ/10 and λ/6 for operation on 3-rd and 5-th cyclotron harmonic correspondingly (wavelength λ=0.5 and 0.3 mm) and velocity spread within the range 10-15%.
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