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A new method for increasing the efficiency of runaway electronbeamgeneration in atmospheric pressure gas media has been suggested and theoretically proved. The method consists of creating a hot region (e.g., a spark channel or a laser plume) with a decreased numerical density of gas molecules (N) near the cathode. In this method, the ratio E/N (E-electric fieldstrength) is increased by decreasing N instead of increasing E, as has been done in the past. The numerical model that is used allows the simultaneous calculation of the formation of a subnanosecond gas discharge and the generation of runaway electrons in gas media. The calculations have demonstrated the possibility of obtaining current pulses of runaway electronswith amplitudes of hundred of amperes and durations of more than 100 ps. The influence of the hot channel geometry on the parameters of the generatedbeam has been investigated.