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The effect of changing the driving frequency on the plasma density and theelectron dynamics in a capacitive radio-frequency argon plasma operated at lowpressures of a few Pa is investigated by Particle in Cell/Monte CarloCollisions simulations and analytical modeling. In contrast to previousassumptions the plasma density does not follow a quadratic dependence on thedriving frequency in this non-local collisionless regime. Instead, a step-likeincrease at a distinct driving frequency is observed. Based on the analyticalpower balance model, in combination with a detailed analysis of the electronkinetics, the density jump is found to be caused by an electron heating modetransition from the classical $\alpha$-mode into a low density resonant heatingmode characterized by the generation of two energetic electron beams at eachelectrode per sheath expansion phase. These electron beams propagate throughthe bulk without collisions and interact with the opposing sheath. In the lowdensity mode, the second beam is found to hit the opposing sheath during itscollapse. Consequently, a high number of energetic electrons is lost at theelectrodes resulting in a poor confinement of beam electrons in contrast to theclassical $\alpha$-mode observed at higher driving frequencies. Based on theanalytical model this modulated confinement quality and the related modulationof the energy lost per electron lost at the electrodes is demonstrated to causethe step-like change of the plasma density. The effects of a variation of theelectrode gap, the neutral gas pressure, the electron sticking and secondaryelectron emission coefficients of the electrodes on this step-like increase ofthe plasma density are analyzed based on the simulation results.

The effect of the driving frequency on the confinement of beam electrons and plasma density in low pressure capacitive discharges