# Gyrotrons as High-Frequency Drivers for Undulators and High-Gradient Accelerators
## 3 Gyrotron-Powered Microwave Wigglers and Undulators
Another possibility, discussed in [14], is an electromagnetic wiggler utilizing a traveling wave generated by a gyrotron. In such a scheme the coupling problems are nonexistent but higher peak powers are required than in the case of a high-Q cavity. FELs with RF standing wave wigglers have been proposed also in [15]. This study includes a detailed analysis of such schemes with both circular and linear wiggler polarizations. The results reported in [15] provide a deep insight into the resonance conditions and the coupling strength associated with each resonance of this type of FEL. A striking feature revealed by this investigation for the first time is that the electromagnetic standing wave wiggler FEL, under certain circumstances, exhibits a rich harmonic content due to the presence of both the forward and backward wave components of the standing wave wiggler field. Different schemes for infrared FELs based on gyrotron-powered electromagnetic wigglers have been proposed by [PERSON] et al. in [16; 17], where a design of a 10.6 \(\upmu\)m electromagnetic wiggler FEL for a proof-of-principle experiment (performed using a 6 MeV electrostatic accelerator with beam currents 2 and 5 A) has been considered. One of the studied wigglers utilizes a waveguide and the other a quasi-optical resonator. The above-mentioned papers are mainly conceptual design studies and proposals. A convincing example of a successful experimental demonstration of a gyrotron-powered standing-wave electromagnetic wiggler is [37]. The cavity consists of two major sections. The first straight section is the gyrotron interaction region (in other words, the gyrotron cavity) which is tapered down at the electron gun side to the cutoff of the operating mode. On the other side, the cavity is tapered up to another straight section which is referred to as the FEL interaction region or the FEL cavity. To create a standing-wave field in the FEL region, another down-taper is used. The final up-taper provides a gradual transition between the cavity and the output waveguide. The gyrotron has been operated in a regime of high field intensity and short interaction length regime using the mode TE\({}_{13}\) at 129.5 GHz. The experimental results indicate that higher wiggler field strengths should be feasible with higher-power electron beams. Next, we discuss several short-period RF undulators. The first one is a traveling wave undulator for the SASE (self-amplified spontaneous emission) source [35] made of a low-loss resonant ring where an operating wave moves toward the electron beam in one of ring's arms. As possible radiation sources, a magnicon and a relativistic gyro-klystron have been considered. This 34 GHz room-temperature RF undulator exploits the superposition of the hybrid HE\({}_{11}\) and HE\({}_{12}\) modes in a corrugated waveguide to minimize the losses. The authors estimate that in order to obtain parameter \(K_{w}=0.4\) in the waveguide of L = 250 mm length, about 120 MW input power, 470 ns filling time (loaded Q-factor \(5.1\times 10^{4}\) at waveguide radius 26.5 mm) are necessary. It has been concluded that among the considered schemes the hybrid HE\({}_{11}\) mode resonant ring is distinguished by the simplest design, and low surface fields, but the feeding requires huge RF power. On the other side, the TE\({}_{01}\)/TE\({}_{02}\) resonator with short efficient mode converters and coaxial coupler requires moderate power, has low surface fields, and can be operated in a regime of long pulses albeit the heating temperature is rather high. Another proposed undulator uses near to cut-off TM\({}_{11}\) mode which has frequency up-shift two times less in comparison with other considered versions but provides many advantages. Among them are low input power, low surface fields, simple design, and the possibility to be operated in a regime of long bunches.