[en] The use of the field emission as means of filling the electron traps is proposed. Because of the electron tunneling at the cathode tip, the energy of the emitted electrons is lower than the electrostatic potential of the tip surface by the work function of the tip material. Consequently the electrons are trapped by the electrostatic well without requiring the dynamic trapping. The Brillouin density will be reached readily because the injection on the axis of the cylindrical symmetry dictates that the canonical angular momentum of the electrons vanishes. Furthermore the evaporative cooling due to the electrons escaping from the trap over the potential barrier may be able to cool the trapped electrons to cryogenic temperatures. The interesting regimes of the strongly correlated plasma and the quantum mechanical plasma may be obtained. (author)