Starting from the general momentum and energy balance equations for charged particle swarms in a gas, as furnished by momentum-transfer theory, we obtain expressions for mean velocity and mean energy of an electron swarm in an r.f. electric field under spatially uniform conditions, in the frequency range WTe > 1, where Te is the energy collisional relaxation time. If Te is a decreasing function of energy, it is shown that the cycle-averaged mean energy reaches a maximum at a certain frequency. Physical arguments are provided to support this result and the prediction is verified for a constant elastic cross section model by direct numerical solution of Boltzmann's equation.
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Robson et al. (1995) studied this question.