The energy balance equation for the electrons, the electric field and current source are formulated for the Pierce diode stationary regime. The energy distribution is investigated by using the selfconsistent equations such as those of continuity, motion, Maxwell electric field and energy balance. The exact solutions of the nonlinear differential equations are presented for the dynamic variables. They determine the one-dimensional transport and stationary spatial oscillations. The field at the emitter as a function of the diode length is calculated.