Nonlinear processes in the inductively coupled plasma. The parametric instability driven by the ponderomotive current

The stability theory of the skin layer plasma of the inductive discharge is developed for the case when the electron quiver velocity in the RF wave is of the order of or is larger than the electron thermal velocity. This theory is grounded on the methodology of the electron oscillating modes of the perturbations of the electron density and of the electrostatic potential. These modes have a static structure of a plane wave $\sim \exp\left(i\mathbf{kr}_{e}-i\omega t\right)$ in the frame of references which moves with velocity of electron in the spatially inhomogeneous skin layer RF field with frequency $\omega_{0}$. In the laboratory frame, these electron oscillating modes are detected as the wave structures which involves infinite number of harmonics $\sim \exp\left(i\mathbf{kr}-i\left(\omega-n\omega_{0}\right) t\right)$, $n=0, \pm 1, \pm2,...$. We found the instability of the skin layer which develops due to the coupling of the plane wave mode $\sim \exp\left(i\mathbf{kr}-i\omega t\right)$ of the ion density and electrostatic potential, determined in the laboratory frame, with the harmonics of the electron oscillating mode of the electron density perturbation with Doppler shifted frequency resulted from the electron ponderomotive current. The instability exists in the finite interval of the ponderomotive current velocity and is absent in the uniform boundless plasma.