The capacitively coupled plasma is investigated kinetically utilizing the particle- in-cell technique. The Argon (Ar) plasma is generated via two radio-frequencies. The plasma bulk density increases by increasing the voltage amplitude of the high frequency (≥ 13.56 MHz) which is much greater than the ion plasma frequency. The intermediate radio-frequencies ( ≈ 1 MHz) which are comparable to the ion plasma frequency causes a broadening of the ion energy distribution considerably, i.e., ions gain energies above and lower than the time-averaged energy. The good agreement between published experimental results and our theoretical calculations via the Ensemble- in-Spacetime model confirms the modulation of ions around time-averaged values. Intermediate frequencies allow ions to respond partially to the instantaneous electric field. The response of ions to the instantaneous electric field is investigated semi- analytically. The dispersion relation of the plasma sheath and bulk are derived. Stable ion acoustic modes are found. The ion-acoustic modes have two different velocities and carry energy from the sheath edge to the electrode. Also, intermediate frequencies excite solitons in the plasma sheath; the results may help to explain the ion density, flux, and energy modulation, and, consequently, the broadening of the ion energy distribution.

Radiofrequency capacitively coupled plasma is studied theoretically using a Particle-in-Cell code. For He discharge, the timeaveraged sheaths are in the range of few centimeters. The sheath potential, ion, and electron energy and angular distributions, discharge current, and dissipated power depend on the driven potentials and frequencies. Increasing the amplitude of the high radio frequencies increases the bulk density and the sheath potential and, consequently, increases the plasma processing rate. Increasing the intermediate radio frequency amplitude allows a wider sheath with a broad ion energy distribution and a narrower ion angular distribution. Changing the amplitude and the phase shift between driven frequencies provide different energies and angular distribution allowing performing various processes. The interplay between the sheath and bulk dynamics in the intermediate radiofrequency regime and the high-frequency regime may excite harmonics in the discharge current.