A mathematical model of electron-optical processes has been developed and studied. The results of this analysis show that the ion current to a microscopic point emitter can be significantly reduced in planar edge field emission (PEFE) structures. The mechanism of this decrease is related to a special configuration of the electric field in the cathode-gate-anode system, which features a slope of the equipotential lines in the near-cathode region. The advantage of PEFE structures over the traditional systems based on Spindt cathodes is characterized by a decrease in the ion-current-related thermal load by more than five orders of magnitude. This decrease ensures high durability of the PEFE structures, which has been confirmed in experiment.