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The theory of the ion cyclotron (IC) electrostatic parametric instabilitiesof plasma which are driven by the elliptically polarized fast wave (FW) of thefinite wavelength is developed. The growth rate of the IC quasimode decayinstability, which was considered as a potential source of the generation ofthe high energy ions in scrape-off layer (SOL) during FW injection in tokamaks,is derived analytically for arbitrary values of the FW electric field andwavelengths of the unstable IC perturbations. The comprehensive numericalanalysis of the dispersion equation for three wave system which contains the ICmode $\varphi_{i}\left(\mathbf{k}_{i}, \omega\right)$ and its harmonics$\varphi_{i}\left(\mathbf{k}_{i}, \omega-\omega_{0}\right)$, $\varphi_{i}\left(\mathbf{k}_{i}, \omega-2\omega_{0}\right)$, where $\omega_{0}$ is FWfrequency, is performed. It reveals that the parametric IC instability for thiswave system has the maximum growth rate for the IC waves with wavelengthcomparable with the thermal ion Larmor radius. It is found that the inverseelectron Landau damping plays essential role in the development of thisinstability. The possible mechanism of the saturation of this instability isthe scattering of ions by the ensemble of the IC waves with random phases,which limits the development of the instability on the high level. Theanomalous heating rates of ions resulted from the interactions of ions withparametric IC turbulence is determined employing the developed quasilineartheory for the IC quasimode decay instability. The derived results reveals,that the experimentally observed anisotropic heating of cold SOL ions may becaused by the parametric IC turbulence in SOL. However, the IC parametricturbulence is unlikely to be responsible for the experimentally observed burstsof poorly confined suprathermal ions in the SOL of tokamak plasmas.

Interaction of the fast wave with a scrape-off layer plasma in tokamaks. The ion cyclotron parametric instabilities and the anomalous heating of ions