The ion transit effects on the sheath dynamics inthe intermediate radiofrequency regime: excitationsof ion-acoustic waves and solitons

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.