Review scientific adviser in the graduate qualification work of the SPbSU student Efimov Maxim Ruslanovich The field cathodes periodic system in the rectangular lattice modeling    The image forms relatively wide electron beams in the field emission systems, so a method is needed to calculate the exact value of the potential near the cathode surface and in the wide near-cathode region. In this graduate qualification work a periodic system of field cathodes is modeled in a rectangular lattice. Each emitter is located in the center of the cell of a periodic rectangular lattice. To solve the problem, one cell of the system was selected, which is a diode system - a field cathode in the form of a emitter on a flat substrate, the voltage at which is zero, and the anode in the form of a plane parallel to the substrate with a given constant voltage. The effect of the field cathode on the potential distribution was replaced by the influence of a system of point charges located on the cell axis. The distribution of the electrostatic potential is found analytically in the entire region of the multi-emitter system. To perform numerical calculations of the potential and the equipotentials curvature radius of the system Efimov M.R. wrote a C ++ program in the Microsoft Visual Studio. In accordance with the obtained calculation results it was found that with a decrease of the cell-size period, the curvature radius of the emitter top increases, which corresponds to the known experimental shielding phenomenon of the periodic system of field cathodes.   The graduate qualification work of Efimov M.R. shows a high degree of preparation of the author and deserves an "excellent".   Scientific adviser, D.Sc., Electromech. Comp. Syst. Model., Professor                  Vinogradova E.M.