# The Gyrotrons as Promising Radiation Sources for THz Sensing and Imaging
## 2 Advantages of the Gyrotrons as Powerful Radiation Sources for Sensing and Imaging  
The gyrotrons are vacuum electron tubes that belong to the family of gyro-devices, of which other prominent members are the Gyro-Klystrons, Gyro-TWT (Traveling-Wave Tubes), Gyro-BWO (Backward-Wave Oscillators), and CARM (Cyclotron Autoresonance Masers). All of these utilize hollow electron beams in which the electrons follow helical orbits gyrating with a cyclotron frequency \(\Omega_{c}\) in a strong magnetic field \(B\)  
\[\Omega_{c}=\frac{e}{\gamma m_{0}}B, \tag{1}\]where \(e\) and \(m_{0}\) are the charge and the rest mass of an electron, respectively, and \(\gamma=\left(1-\beta^{2}\right)^{-1/2}\) is the relativistic Lorentz factor (\(\beta=v/c\) being the electrons' velocity normalized to the speed of light in vacuum \(c\)). The operation of the gyro-devices is based on a physical phenomenon known as electron cyclotron maser instability, which takes place due to the relativistic dependence of the cyclotron frequency on the energy of the gyrating electrons provided a proper synchronism between the electron beam and the electromagnetic wave excited in the resonant cavity (usually a part of a cylindrical waveguide) is established in accordance with the following relations  
\[\omega=n\Omega_{c}+v_{z}k_{z}, \tag{2}\]  
\[\omega^{2}=c^{2}\Big{(}{k_{\perp}}^{2}+{k_{z}}^{2}\Big{)}, \tag{3}\]  
where \(\omega\) is the circular frequency of the electromagnetic wave, \(n\) is the harmonic number of the cyclotron resonance, \(v_{z}\) is the axial component of the velocity of the electrons, and \(k_{\perp}\) and \(k_{z}\) are the transverse and the axial wave-numbers of the cavity mode, respectively. Therefore, the resonance condition (synchronization) can be conveniently presented graphically as an operation point at the intersection of the beam line (2) and the dispersion curve (3) of the corresponding cavity mode as shown on the Brillouine diagram in Figure 1.  
During the beam-wave interaction, some electrons lose energy while others gain. Accordingly, the electrons for which the relativistic factor \(\gamma\) has been decreased will gyrate at higher cyclotron frequency while the accelerated electrons (with an increased \(\gamma\)) will rotate at decreased frequency. As a result of this relativistic effect, azimuthal bunching of the beam electrons occurs. Moreover, when the above conditions are satisfied, the formed bunch slips toward the decelerating phase of the electromagnetic wave, where it can transfer its energy via bremsstrahlung. In the case of gyrotrons, the Doppler shift term \(v_{z}k_{z}\) is small, and practically, they operate at frequencies close to the cyclotron frequency or its harmonics, which means roughly 28 GHz per Tesla at the fundamental resonance (\(n=1\)). Therefore, there are two routes for raising the frequency of the generated radiation: namely increasing of either the magnetic field intensity (which is limited only by the available superconducting magnets) or the harmonic number of the cyclotron resonance. Although the latter approach is hindered by severe mode competition and significantly lower efficiency, there is remarkable progress in the development of gyrotrons operating at high harmonics. They include second-harmonic conventional gyrotrons (utilizing helical electron beams with off-axis orbits) [27; 28; 29; 30; 31; 32] as well as tubes based on advanced concepts such as LOG (large-orbit gyrotrons with axis-encircling aka uniaxial electron beams) [33; 34; 35] and double-beam gyrotron [36]. The highest frequencies achieved by the gyrotrons have already passed the symbolic threshold value of 1 THz. For example, the pulsed gyrotron developed at the Institute of Applied Physics (N. Novgorod, Russia) has demonstrated an operation  
Figure 1: Gyrotron interaction illustrated by the Brillouine diagram. at 1.3 THz (with output power of 1 kW in pulses of 20 \(\upmu\)s and energy of 30 mJ) exciting the TE24,4 mode (fundamental operation) at magnetic field intensity of 51.5 T [37].