This article presents the results of a design study of an electron-optic system (EOS) for a sheet-beam ${G}$ -band traveling-wave tube. An electron gun providing a 0.1-A, 20-kV sheet beam emitted by a 0.8 mm $\times0.8$ mm curved cylindrical cathode is designed. The beam dimensions at waist position are 0.05 mm $\times0.8$ mm with a compression ratio of 16 in the vertical direction. A magnetic system providing 1.1 T magnetic field, which is nearly seven times higher than the Brillouin field, is designed, and beam transmission in the 0.1 mm $\times0.85$ mm beam tunnel is studied by 3-D particle-in-cell (PIC) simulation. It is demonstrated that the beam has a complex structure of particle distribution, i.e., a high-density central part (core) and a peripheral low-density part (halo). The effect of assembly tolerance on beam transmission is studied. The prototype gun is fabricated, which compresses the beam to 0.1 mm by electrostatic field only. The 135-mA current with 95% transmission through the 0.2-mm anode aperture is measured.