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Devices as large as ring laser gyroscopes (RLGs) for fundamental physics and geophysics investigation are currently run by means of radio frequency (RF) power supply systems. This is not the standard method to supply a gas laser, which typically is powered by a DC system. In literature, RF power supply lasers were studied several years ago, and to correctly understand the behavior of devices such as RLGs, a more detailed study has been pursued. Detailed study of the radial distribution of the optical gain of a He-Ne discharge cell in function of gas pressure and radio frequency (RF) power supply will be illustrated, discussed, and compared with existing literature. The presented analysis demonstrates that it is possible to optimize ring laser gyroscope (RLG) operation with a proper choice of gas pressure and power level of the RF power supply. Accordingly, we have been able to establish transversal and longitudinal single-mode operation of our prototype GP2.