The laminar electron flows in triode electron guns with field emission

3D simulation of triode electron gun is performed with regards its structure of multiple-tip field emission cathode. The table of geometrical parameters of electron gun is defined (d_g-a/D_a=1.5-4.0; d_g-a/d_g-c=10^-4-10^-2) as well as the optimal potentials of grid with large scale holes where the electrical field is uniform. Thus the effect of electron lens of grid comes to a minimum and laminar electron flow is formed. The computer modeling of 19- beam electron gun with field emission glassy carbon cathode in magnetic field (N=10⁶cm^-2) and planar single-beam electron gun with CNT cathode (N=4·10⁸cm^-2) are carried out.