Radiophysics and Quantum Electronics, Vol.55, No. 7, December, 2012 (Russian Original Vol. 55, No. 7, July, 2012) ON LINEAR TRANSFORMATION OF WAVES IN A TWO-DIMENSIONAL INHOMOGENEOUS MAGNETIZED PLASMA WITH COLLISIONAL ABSORPTION E. D. Gospodchikov ∗ and A. G. Shalashov UDC 537.876 We consider the linear coupling of waves in the electron-cyclotron frequency range in a non- one-dimensional inhomogeneous magnetized plasma in the vicinity of the plasma cutoﬀ surface with allowance for their collisional dissipation. Model wave equations describing the normal wave interaction in the considered case are formulated and solved analytically. Eﬀects of the absorp- tion anisotropy typical of magnetized plasma on the linear mode coupling in two-dimensional inhomogeneous geometry are analyzed. 1. INTRODUCTION The problem of linear coupling of electromagnetic waves in the electron-cyclotron frequency range, which propagate in a smoothly inhomogeneous magnetized plasma, has a long history. A start was made in the works by V. L. Ginzburg in connection with the radio-signal tripling eﬀect in the ionosphere [1–3]. Under astrophysical conditions, the linear coupling of waves is signiﬁcant, e. g., for describing the mechanism of output of the radiation from a dense plasma, in particular, from the solar corona [4–6]. In recent years, there has been a notable increase in interest in this problem in connection with the problems of heating and diagnostics of a dense plasma in controlled fusion setups with magnetically conﬁned plasma, tokamaks and stellarators [7, 8]. Most of the theoretical results related to the linear wave coupling processes in the electron-cyclotron range were obtained within a one-dimensional plane-layer approximation, in which it was assumed that all parameters of the medium vary in one preferred direction [1, 9–11]. Recently, attention was paid to the fact that the one-dimensional approximation may appear insuﬃcient for description of the linear coupling process under conditions of a laboratory experiment [12–17]. In [13, 14], truncated standard wave equations were obtained and studied in detail to describe the wave-ﬁeld distribution in the ﬁeld of linear transformation of electromagnetic waves with allowance for the two-dimensional inhomogeneity of the magnetized plasma when the gradients of the plasma density and magnetic-ﬁeld magnitude are not co-directional. More recently, some three-dimensional eﬀects due to the inhomogeneous direction of the magnetic ﬁeld, which is typical of toroidal traps, were also explored in [18–20]. The inﬂuence of the collisional absorption in the magnetized plasma on the linear coupling of electro- magnetic waves was studied in the one-dimensional approximation, speciﬁcally, in [10]. It was shown in that paper that in the plane-layer approximation, the absorption eﬀect is limited by the exponential attenuation of the reﬂected and transmitted waves in accordance with the optical paths they have passed. In the present paper, we analyze the inﬂuence of the collisional absorption on the linear coupling of electromagnetic waves in a two-dimensional magnetized plasma. * eggos@mail.ru Institute of Applied Physics of the Russian Academy of Sciences, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radioﬁzika, Vol. 55, No. 7, pp. 510–520, July 2012. Original article submitted March 26, 2012; accepted July 28, 2012. 462 0033-8443/12/5507-0462 c  2012 Springer Science+Business Media New York