The development of compact amplifiers with an average power of the frequency range 0.2–0.3 THz is related to the design of electron‐optical systems using converging sheet beams that allow obtaining sufficiently high current densities with a lower current load on the cathode and with a lower value of the magnetic field. Based on the theory of synthesis the numerical simulation results for electron‐optical systems for the formation of a converging sheet electron beam are presented. Reduction of the current load on the cathode allows the principle of transformation of a cylindrical electron beam into a sheet by employing electrostatic compression of the beam in one plane. A sheet beam electron‐optical system with a field emission cathode with convergence of 10, and with the beam of 0.1 × 1.1 mm2 and current density of 45 A/cm2 has been performed. The electron gun employing the cathode–gate structure with diameter of 1 mm has an emitting current up to 10 mA in experiment. The modulation coefficient of the cathode current for a gun with a sheet electron beam has 0.3% of the anode potential.