Coherent terahertz high-harmonic radiation has been obtained in a gyrotron with an axis-encircling electron beam. An electron-optical system with a cusp gun and a following drift section of adiabatic magnetic compression with an area factor of 3000 provides the formation of an $80\mathrm{\text{−}}\mathrm{keV}/0.7\mathrm{\text{−}}\mathrm{A}$ beam of gyrating electrons in a wide range of voltages and magnetic fields. Stable single-mode generation with a power of 0.3–1.8 kW in microsecond pulses is detected at four frequencies in the range 0.55–1.00 THz at resonant magnetic fields 10.5–14 T.

First bandwidth measurements of a novel gyrotron amplifier are presented. The coupling between the second harmonic cyclotron mode of a gyrating electron beam and the radiation field occurred in the region of near infinite phase velocity over a broad bandwidth by using a cylindrical waveguide with a helical corrugation on its internal surface. With a beam energy of 185 keV, the amplifier achieved a maximum output power of 1.1 MW, saturated gain of 37 dB, linear gain of 47 dB, saturated bandwidth of 8.4 to 10.4 GHz ( $21\%$ relative bandwidth), and an efficiency of $29\%$, in good agreement with theory.

A new microwave system in the form of a cylindrical waveguide with a helical corrugation of the inner surface is proposed for a gyrotron traveling wave tube (gyro-TWT). The corrugation radically changes the wave dispersion in the region of small axial wave numbers. This allows significant reduction in the sensitivity of the amplifier to the electron velocity spread and an increase in its frequency bandwidth. An $X-\mathrm{band}$ gyro-TWT operating at the second cyclotron harmonic with a 200-keV, 25-A electron beam produced an output power of 1 MW, corresponding to a gain of 23 dB and an efficiency of 20%.

A helical corrugation of the inner surface of an oversized cylindrical waveguide provides, for certain parameters, an almost constant value of group velocity and close to zero longitudinal wavenumber of an eigenwave for a very broad frequency band. The use of such a helical waveguide as an operating section of a gyrotron traveling wave tube (gyro-TWT) allows significant widening of its bandwidth and an increase in the efficiency at very large particle velocity spreads. In this paper, the new concept is confirmed by theoretical analysis and "cold" measurements of the helical waveguide dispersion. Results of a linear and nonlinear theory of the helical gyro-TWT as well as two designs for subrelativistic (80 keV, 20 A) and relativistic (300 keV, 80 A) electron beams are also presented. For both designs, parameters providing a very broad frequency band (about 20%) and high efficiency (above 30%) have been found, When the transverse velocity spread is increased from zero up to a very high value of 40 %, simulations showed only a 20%-30% narrowing in the frequency band and a 20% decrease in electron efficiency. The theoretical analysis demonstrates important advantages of the helical gyro-TWT over the "smooth" one in frequency bandwidth, sensitivity to electron velocity spread, and stability to parasitic self-excitation

The maximal frequency of radiation higher than 1 THz has been recently obtained in pulse gyrotrons both at IAP (Nizhny Novgorod, Russia) and FIR (Fukui, Japan). CW generation at a 2.2-kW power level is radiated from a 300-GHz gyrotron and used for technological applications. New gyrotrons demonstrate single-mode operation at the second cyclotron harmonic with a frequency of 395 GHz in the CW regime with a power of 100 W and at the third harmonic with frequencies of 371-414 GHz in 10-mus pulses with power of 10-20 kW. Methods of selective excitation of higher cyclotron harmonics, frequency multiplication, and smooth frequency tuning in terahertz gyrotrons are also discussed in the review.