A discharge with plasma filling a flat-bottom cavity of depth δ in the cathode, partly closed by a dielectric plate with a hole (determining the aperture of the discharge between the cavity bottom and the anode), has been studied. In a discharge cell of type 1 with δ = 0.5 mm and a hole diameter of 22 mm, a pulsed electron beam was obtained with a duration of tEB = 700 ns and a beam current jEB approximately 10 times greater than that (jAD) of the equivalent anomalous discharge (at fixed discharge voltage U and gas pressure pHe = 3.5 Torr). An electric field with the direction opposite to the field of applied voltage appeared at the cathode that was related to a space charge formed at the cathode plasma boundary, which could not follow a rapid drop of voltage across the discharge gap. In a discharge cell of type 2 with δ = 0.5 mm and a narrow slit (S = 0.1 × 5 cm2) in the dielectric plate, a pulsed electron beam was obtained with a duration of tEB = 2 ns and a beam current of jEB = 0.7 kA/cm2 (jEB/jAD = 1.5) at U = 4.2 kV and pHe = 50 Torr.