Theory of anomalous backscattering in second harmonic X-mode ECRH experiments

A quantitative model explaining generation of the anomalous backscattering signal in the second harmonic X-mode electron cyclotron resonance heating (ECRH) experiments at TEXTOR tokamak as a secondary nonlinear process which accompanies a primary low-threshold parametric decay instability (PDI) leading to excitation of two—upper hybrid (UH)—plasmons trapped in plasma is developed. The primary absolute PDI enhancing the UH wave fluctuations from the thermal noise level is supposed to be saturated due to a cascade of secondary low-threshold decays of the daughter UH wave leading to excitation of the secondary UH waves down-shifted in frequency and the ion Bernstein wave. A set of equations describing the cascade is derived and solved numerically. The results of numerical modelling are shown to be in agreement with the analytical estimations of the growth rate of the initial and secondary parametric decays and the saturation level. The generation of backscattering signal is explained by coupling of the daughter UH waves. The fine details of the frequency spectrum of the anomalously reflected extraordinary wave and the absolute value of the observed backscattering signal in the second harmonic X-mode ECRH experiments at TEXTOR are reproduced.