IAP has been studying microwave heating and diagnostics of plasma in fusion devices for over thirty years. Already in the first large-scale experiments on the electron-cyclotron (EC) plasma heating in tokamaks, a very simple and convenient heating scheme was proposed. It employed an ordinary wave injected from the outside of the toroid (A. G. Litvak, E. V. Suvorov, A. A. Fraiman). An adequate natural geometric-optical calculation method using ray trajectories was introduced into practice for calculations of profiles of energy contribution during EC heating. The proposed heating scheme is still one of the main heating methods used in modern large-scale toroidal devices. Modification and further advancing of geometric-optical methods for calculation of energy contribution profiles and generation of induction-free currents have become the foundation for creation of many codes (frequently, name codes), the results of which are subjected to mutual cross-checks and are used in planning and interpretation of any large-scale experiment.
The most important research line in this field is EC heating and diagnostics of dense over-critical plasma, where the problem of delivering the "heating" radiation to the central fractions of the plasma column arises. The reasons underlying the interest for this problem are the achievement of the regimes with advanced confinement in large-scale tokamaks, development of alternative systems, for example, spherical tokamaks and optimized stellarators, and the advance in the development of systems for EC plasma heating, which are based on high-power millimeter-wave gyrotrons. IAP is working out new fundamental electrodynamic approaches to the development and optimization of such heating schemes. The following results have been achieved:

• the analytical theory of linear transformation of ordinary and extraordinary EC-range waves in the 3D inhomogeneous plasma of tokamaks and stellarators has been developed, which allows for the effects of magnetic-field torsion and the curvature of magnetic surfaces;
• the practice-relevant question about recalculation of wave fields separated by the zone of linear interaction, which allows one to restore, in the toroidal geometry, the amplitude-phase field distributions in the transmitted and reflected quasioptical beams ba-sing on the field distribution in the incident beam;
• the method for analytical and numerical solution of the problems of propagation of guided electromagnetic waves in anisotropic and gyrotropic media with spatial dispersion has been developed, which is based on the formalism of Riccati's operator equation.
  

Example of the theoretically found efficiency of the linear transformation of the Gaussian beam as a function of its width, as the beam traverses the surface of critical plasma density in the three-dimensionally inhomogeneous tokamak plasma (the dashed line is the result of the one-dimensional theory)

The theoretical developments are used successfully to study new possibilities of microwave heating and diagnostics of over-critical plasma in tokamaks and stellarators using a linear transformation of the electromagnetic EC range in T-10, FTU, TEXTOR, ASDEX-U, WEGA, and other devices (A. G. Shalashov, E. D. Gospodchikov).

Currently, the EC heating systems in modern tokamaks are used widely to optimize the plasma profile and stabilize MHD instabilities of the plasma column. Solving of these problems requires fine tuning of the conditions of radiation injection into plasma, aiming at achieving the minimum possible size of the energy deposition area at a strictly specified point. This imposes rigid requirements on the accuracy of simulation of wave beam propagation through inhomogeneous magnetoplasma. IAP has developed an original formulation of the theory of quasioptical beams. In the framework of this theory, the vector wave field is restored by solving the scalar quasioptical equation (A. A. Balakin, A. I. Smirnov, G. V. Permitin). The universal numerical software code developed on the basis of this theory is used to calculate quasioptical wave beams. The code allows for spatial dispersion, resonance absorption, and aberrations of hot magnetoplasma.
The importance of allowance for these effects, when one simulates energy deposition profiles during EC heating and current generation in the ITER-scale devices to solve the problems of plasma column stabilization, has been demonstrated for the first time.

IAP is developing experimental methods for diagnostics of fusion plasma, which employ scattering of high-power millimeter waves. Registration of the collective-scattering spectra of high-power millimeter waves on plasma density fluctuations allows one to obtain information about ion velocity distribution with good spatial and temporal resolution. IAP researchers were the first to demonstrate the possibility of reliable measurements of thermal-ion temperature in pioneer works on implementation of this method on the large-scale stellarator Wendelstein 7-AS in Germany (E. V. Suvorov, L. V. Lubyako, et al.). The collective scattering method was used at the same device successfully to study micro-instabilities, which are formed as a result of injection of high-power neutral beams into toroidal plasma, and implicit diagnostics of distributions of energetic ions (E. V. Suvorov, A. G. Shalashov). The results of the latter studies include the explanation proposed for the nature of the abnormal spectra of collective scattering of gyrotron radiation. Such spectra are registered regularly on a tokamak with a strong magnetic field, Frascati Tokamak Upgrade (FTU, Italy), and are connected with modification of the gyrotron radiation spectra at the wings of the generation line. It was shown that such an effect could arise in the system of diagnostics of fusion alpha particles by the collective scattering method in the ITER tokamak, and the methods of eliminating this undesirable effect were proposed (L. V. Lubyako, E. V. Suvorov, A. G. Shalashov, jointly with the researchers of Istituto di Fisica del Plasma — CNR Milano and the Institute of Alternative Energies in Frascati).

Receiver of the system, which was developed at IAP for registration of collective scattering spectra of the 140 GHz radiation on the FTU tokamak (Frascati, Italy)