The evolution of the mathematical and technical aspects of heavy ion beam probe plasma diagnostics

The paper analyzes the way of development of thermonuclear plasma diagnostics - Heavy Ion Beam Probing in application to the toroidal devices with magnetic plasma confinement. The mathematical foundations of the diagnostic method of plasma probing by a beam of heavy ions and inverse problems of processing the results of experiments, originated whith inspiring participation of Professor Yuri Nikolaevich Dnestrovsky, are considered. Diagnostic systems for probing plasma of tokamaks TM-4, TJ-I, TUMAN-3 and T-10, stellarators WEGA, TJ-II and Uragan-2M created with the support of the Yu. N. Dnestrovsky, are presented. Also given the promising results of the project work on the use of HIBP to various existing modern installations, such as TCV, TCABR, MAST, COMPASS, GLOBUS-M and W7-X and the International thermonuclear experimental tokamak-reactor ITER, currently on construction. The paper presents results of the experimental study of plasma electric potential in toroidal systems with magnetic confinement. The study is based on the data of unique diagnostics to study the potential in the core plasmas - Heavy Ion Beam Probing (HIBP), as well as other diagnostics. Paper describes HIBP diagnostic systems for probing the plasmas of the T-10 tokamak and the TJ-II stellarator and of geodesic acoustic modes of plasma oscillations and Alfvén Eigenmodes excited by fast particles of Neutral Beam Injection heating are described. A wide range of the operational modes of tokamak and stellarator with different magnetic configurations and methods of plasma heating was investigated. General regularities in the behavior of the electric potential and turbulence in a magnetized plasma were revealed.