**The most outstanding results achieved in these areas are listed below.**

In course of further development a clinotron prototype was produced, in which the inhomogeneous distribution of the focusing magnetic field was taken into account, and clinotron’s position in the working gap of the focusing system was adjustable; this prototype served as a basis for developing a continuous wave magnetron designed to operate within a wide frequency range of 340-410 GHz with the maximum output power of 50 mW [1, 2].

In an effort to enhance the efficiency of the electron-wave interaction, we developed a clinotron with a three-stage comb for the frequency range from 79 to 106 GHz. The output power of this device was above 2 W, being highly stable within the smooth electron tuning range from 95.3 to 97.9 GHz [3, 4].

Performance curve and appearance of a 400 GHz continuous wave clinotron

Some new results were obtained while analyzing the cyclotron resonance maser (CRM) performance. It was revealed that there exists an “optional” mechanism of electron bunching within a weakly inhomogeneous magnetic field in low-voltage CRM. This mechanism was employed to enhance the efficiency of interaction between a helical electron beam and modes of a resonator of a conventional geometry at a record-low accelerating voltage of 2.2 kW, as well as to excite the modes TE_{11q} for a longitudinal index *q* being 1 through 7, which in its turn allowed to tune the frequency of the generated oscillations within the range of 8.0 – 9.3 GHz [5, 6].

Numerical modelling techniques were used to demonstrate the possibility of generating oscillations efficiently in gyrotrons with a double-mirror, confocal and planar resonator. Computations were performed for gyrotrons at the main gyroresonance within the range of 75 GHz, with the magnetic field density in the resonator area reaching 3 T. In a gyrotron with a planar resonator consisting of two plane mirrors the efficiency of a single-frequency generation was 15%; the ribbon helical electron beam (HEB) was formed by a planar magnetron-injection gun having the accelerating voltage of 12 kV and the current of 1 A [7]. The efficiency of the single-frequency generation for a gyrotron with a confocal resonator made of two cylindrical mirrors reached 14% at the accelerating voltage of 5 kV and the current of the ribbon HEB of 300 mA. In the both cases the pitch-factor values belonged to the range 1 – 1.35 [8].

A photograph of a low-voltage CRM and the results of the trajectory analysis of a ribbon HEB with a planar magnetron-injection gun

The above results were obtained by the team of scientists headed by Dr. B.P. Yefimov, and A.N. Kuleshov, PhD.

Under the guidance of Dr. B.P. Yefimov during the last decade a series of research was conducted to explore long-lived plasma formations excited by electric discharges in weak electrolytes. From 2008 to 2011 this research was carried out in the framework of two regular projects under the authority of STCU sponsored by the Government of Canada. The key scientific results in this area are:

- Electric modes of excitation of long-lived plasmoids with the lifetime in the air of 0.4 s were experimentally studied, and the high-speed shooting, radar and spectral analysis were applied to estimate the particle concentration in the plasmoid, its existence dynamics and spectral content of the radiation [9];
- A Doppler radar technique was developed that utilizes a three-channel radar to analyze the behavior of a long-lived plasmoid; the technique was implemented in an experimental set-up and tested on a stratified positive glow gap [10];
- An experimental set-up was developed and implemented for plasma ignition at the end of a uniconductor line, which essentially simplified the optimization of methods for long-lived plasma research; the operation modes of a uniconductor line for electromagnetic energy transmission were investigated in the millimeter and submillimeter wave ranges [11, 12];
- A model was suggested describing the dynamics of a long-lived plasmoid produced by exciting complex electromagnetic waves in layered periodical media, which was proven by an experimental research of water density waves under electric discharge and plasmoid nucleation [13].

Since 2007, the department is actively developing a relativistic 8-mm pulsed magnetron. This is the first attempt to produce such type of device in the millimeter wave range, being performed jointly with the scientists of the Institute of Plasma Electronics and Novel Acceleration Methods of National Scientific Center “KhPTI”, by using their high-voltage equipment.

The scientists of our Department calculated the optimal parameters of the resonance system and the interaction space of the magnetron, allowing to take the maximum advantage of the interaction with the spatial harmonics. S.N. Teryokhin, a Research Scientist of the Department, suggested a technique and manufactured a tool to measure the magnetron’s radiated wavelength.

The experiments conceptually confirmed the adequacy of the chosen solutions. The modernization of the experimental set-up goes on, we are searching the way to optimize the magnetron’s electromagnetic system and increase the efficiency, as well as to reach the highest possible radiation power (up to 1 MW) [14].

This device has strong chances to find its practical application in the electromagnetic compatibility research since it is able to remotely form an electric field of a given strength. The aim of such research is to determine the resistance threshold of radio electronic devices (and other objects) toward electromagnetic radiation in various parts of a spectrum of both artificial and natural origin (e.g. lightning discharges). Though in the long-wave ranges such research has been performed long ago, it cannot be done so easily in the short-wave range due to the lack of appropriate oscillators.

The theoretical research of the charged beam dynamics and the interaction between the beams and electromagnetic waves in the up-to-date powerful moderately relativistic microwave devices was the responsibility of the researcher team led by Dr. K.W. Illienko, PhD.

The electron dynamics in the pump field of a hybrid free-electron laser/maser (FEL/FEM) for the first time ever has been given an *analytical* description, that is true for all possible values of the guiding magnetic field and, on its basis, for the first time an *analytic* chaotization criterion of the dynamics of beam particles in hybrid FEL/FEM has been found [15]. The mode of an “optimal” excess of an exact magnetic resonance has been suggested allowing to achieve a high efficiency of a planar hybrid FEL/FEM amplifier with a regular waveguide at moderate values of the amplitude of the transverse alternating magnetostatic field of an undulator. A steady-state 3D non-linear theory of an FEL/FEM amplifier has been developed that consequently takes into account both the vortex part of the quasi-electrostatic field and the quasi-magnetostatic field of a space charge (non-propagating, overcritial component of an EM field excited by a charged beam). It was revealed that the vortex component of the space charge field reduces the defocusing effect of the potential component on the bunching in a beam [16]. It was shown how the evolutionary optimization can be applied to triple the efficiency of waveguide moderate relativistic FEL/FEM amplifiers [17]. A procedure has been suggested to solve the Maxwell equations in the Darwinian approximation for a (circular) cylindrical perfectly conducting drift chamber. The eigen quasi-static electric (allowing for the vortex) and magnetic fields have been found that are induced by random discharge and current densities satisfying the continuity equation. The issues of convergence of the obtained field expressions have been considered through the example of a potential component of the quasi-electrostatic field, and a generalization has been suggested for the case of a longitudinally limited drift chamber [18]. Analytical estimations have been obtained for a critical current of a magnetized circular charged particle beam in a longitudinally unlimited coaxial drift chamber in the presence of a dielectric insert of a finite thickness immediately adjacent to the outer coaxial conductor, as well as analytical estimations for the difference in the potentials between the internal and outer coaxial conductors [19]. A new approach was suggested to describe the static component of a potential electric field of a space charge of a charged particle beam propagating in a longitudinally unlimited regular simply connected waveguide, which is close to the Kisunko-Weinstein approach [20].

The scientists of our Department were the first who provided, in terms of physics, a theoretical explanation of the processes occurring in a magnetron of the “Kharkover” operation mode (under the guidance of Dr. V.D. Yeryomka, PhD). It was proven in theory and experiment that electron-wave interaction at the drift-orbital resonances makes the main contribution to the efficient energy exchange between electrons and electromagnetic waves in the static electric-magnetic crossed fields in a terahertz magnetron with the “Kharkover” operation mode [21, 22]. A new analytical model being tested through 3D numerical simulations essentially simplifies the parameter calculation and designing of terahertz pulsed magnetrons, namely it was applied to prove the feasibility of achieving the output power of several hundreds of watts in a submillimeter pulsed magnetron.

One of the most noticeable recent achievements of the researchers and engineers of our Department is the submillimeter clinotron installation providing an electromagnetic radiation of a high stability and the output power of 40 mW and above. Our team has also designed and manufactured a low-voltage cyclotron resonance maser utilizing an innovative concept of electron bunching and a microwave plasma igniter.

Another unique invention of us is a submillimeter frequency multiplier on the basis of a two-stage clinotron. At the first stage a 3-mm signal is generated, at the second stage the frequency is multiplied in three. In course of experiments the multiplier demonstrated relatively low-voltage operation modes with the magnetic field strength two or three times lower than that of conventional submillimeter clinotrons. At the wavelength of 0.93 mm, the output power of the multiplier was as high as 10 mW, with the electron frequency being tunable within the 365 MGz band. The suggested design of the frequency multiplier in combination with the “clinotron effect” promises great opportunities in the development of terahertz range. This design has no analogues among devices of this class (the design was developed by Dr. M.B. Milcho, PhD).

The following invented in our Department terahertz electromagnetic radiation sources with spatially developed electron flow have been covered with patents of Ukraine: cold-cathode pulsed magnetrons with drift-orbital resonance, clinotrons, giroclinotrons, clino-orotrons, orbictrons, clino-orbictrons, klystrons of distributed interaction, nanoklystrons. An original technique of stabilizing the output signal oscillation frequency in terahertz clinotrons, orbictrons and klystrons of distributed interaction, nanoklystrons and magnetrons has been suggested, implemented and patented [23-25] (authors: V.D. Yeryomka et al).