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Results of experiments on the generation of picosecond runaway electron (RE) beams in air gaps with a strongly nonuniform electric field distribution are discussed. The mechanism and conditions for the field emission initiation of beams of this type and possible reasons for the limitation of the beam duration are considered. REs are supposed to be the dominant factor in the development of an ionization wave in the gap. Estimates of the mean velocity of propagation of the ionization wave are given.