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An electron beam (e-beam) controlled switch makes use of the low-energy secondary electrons in a diffuse e-beam sustained discharge as the conducting medium which carries the switched current. The conductivity of the gas in the switch is negligible before the e-beam is turned on because the circuit parameters are chosen so that the open circuit voltage which appears across the switch electrodes is well below the static breakdown voltage of the gas in the switch gap. The e-beam switch can interrupt direct current because the density of the electrons in the switch decays by recombination and attachment when the e-beam is turned off and the switch conductivity decreases. In typical circuits, this decay in conductivity causes the switch voltage to rise and the switch current to fall, i.e., the switch "turns off." This paper presents the results of a series of theoretical calculations which were performed in order to: 1) identify the electron transport and other gas properties which optimize the performance of e-beam switches, 2) evaluate the performance of several real gases for use in e-beam switches, and 3) determine the laws which predict the scaling properties of e-beam switches. Results are presented for N2, Ar, a N2:Ar = 1:9 mixture, and CH4. These results show that CH4 provides the best e-beam switch performance. Comparison of experimental results and theoretical predictions for CH4 supports both the theory and the predicted good e-beam switch performance for CH4.