Saturation of the two-plasmon parametric decay instability in experiments on the electron cyclotron plasma heating due t
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TICAL, NONLINEAR, AND SOFT MATTER PHYSICS
Saturation of the Two-Plasmon Parametric Decay Instability in Experiments on the Electron Cyclotron Plasma Heating due to the Extraordinary Pump Wave Depletion E. Z. Gusakov* and A. Yu. Popov** Ioffe Physicotechnical Institute, Russian Academy of Sciences, St. Petersburg, 194021 Russia *e-mail: [email protected] **e-mail: [email protected] Received April 22, 2017
Abstract—The saturation level of the low-threshold parametric two-plasmon instability of the extraordinary pump wave decay to two upper hybrid plasmons is analyzed under conditions when the only efficient saturation mechanism is the pump depletion. A closed system of differential equations describing both the instability excitation and saturation is derived. The system is solved numerically and an analytic expression is obtained for the anomalous absorption coefficient of the pump wave caused by the development of this instability. The saturation level of the two-plasmon decay instability and the related anomalous absorption efficiency are estimated from data obtained in experiments on the electron cyclotron resonance heating of the plasma by an extraordinary wave in the TEXTOR tokamak. DOI: 10.1134/S1063776117090047
1. INTRODUCTION Currently anomalous phenomena accompanying the propagation of high-power microwave beams in plasmas of toroidal devices have been extensively studied. Among them is the anomalous reflection of a pump wave accompanied by its frequency down-shift [1–6] and the generation of accelerated ions and formation of a tail of the ion distribution function in regimes excluding any possibility of the linear interaction of microwaves with plasma ions [7, 8]. These anomalous phenomena can be caused by low-threshold parametric decays of the pump wave [9–11] leading to excitation of secondary waves capable of interacting with ions and generating radiation at frequencies below the pump-wave frequency. A considerable decrease in the excitation thresholds of these nonlinear phenomena compared to the values predicted in earlier works [12, 13] can be explained by the threedimensional localization of one or several secondary waves in the presence of a nonmonotonic plasma density profile and a finite-width pump beam [9–11]. In particular, the scenario of a low-threshold two-plasmon parametric decay instability (PDI) of an extraordinary wave [11] exciting two secondary three-dimensionally localized upper hybrid (UH) waves during its development predicts the extremely low excitation threshold of the instability (tens of kilowatts). This threshold can be easily exceeded in present-day experiments on electron cyclotron resonance heating (ECRH). Analysis of the nonlinear regime of this PDI
[14–16] reproduces with good accuracy the experimental spectrum of anomalously reflected waves and their radiative temperature [2]. The agreement between conclusions of the theoretical model and experimental data gives grounds to believe that the theoretical prediction of rather strong anomalous absorption (25%
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