# Gyrotrons as High-Frequency Drivers for Undulators and High-Gradient Accelerators
## 4 Gyrotron-Driven Ultra-Compact Particle Accelerators  
Accelerators of charged particles are powerful tools in fundamental research (e.g., nuclear and high-energy physics), medicine, material treatment, security, and many other advanced technologies. They, however, are bulky and large (of the order of several meters or even tens of meters) expensive, and require sophisticated infrastructure. All these characteristics make it difficult to embed them in both the laboratory and industrial environments, where they are used. The progress in the development of the high-power RF sources allows transition to higher frequencies and peak field amplitudes which results in more compact accelerating structures. Generally, there are two ways to miniaturization namely traveling wave and standing wave structures. Besides the traditional RF sources (e.g., klystrons) [43; 44], it has been proposed a long time ago to use gyrotron-driven accelerating cavities [45; 46; 47; 48] including such based on gyro-klystrons [49; 50; 51]. Their important advantages are: (1) high accelerating gradients up to above 200 MV/m; (2) mm-size dimensions of the structure produce more efficient RF cavities; (3) increased frequency results in  
Figure 4: Classification of RF wigglers/undulators. significantly shorter fill times, thus the energy needed to power the accelerator decreases dramatically, enabling higher repetition rates; (4) the gyrotron radiation can be transported, switched and compressed with quasi-optical elements. The role of frequency increase is clear from the following scaling relations (derived for typical disk-loaded traveling wave structures) [43]  
\[P\left[\frac{\mathrm{MW}}{\mathrm{m}}\right]\approx 6.6\times 10^{-2}\frac{E_{a}^{ 2}\left[\frac{\mathrm{MW}}{\mathrm{m}}\right]}{v^{2}\left[\mathrm{GHz}\right]}\, \tag{8}\]  
\[t_{f}\left[\mathrm{ns}\right]\approx\frac{3.8\times 10^{3}}{v^{2}\left[\mathrm{GHz }\right]}\, \tag{9}\]  
\[u\left[\frac{\mathrm{J}}{\mathrm{m}}\right]\equiv Pt_{f}\approx 0.25\frac{E_{a}^{ 2}\left[\frac{\mathrm{MW}}{\mathrm{m}}\right]}{v^{2}\left[\mathrm{GHz}\right]}. \tag{10}\]  
Here \(P\) is the microwave power per unit length that is required to achieve a gradient \(E_{a}\) with RF power of frequency \(\
u\), \(t_{f}\) is the fill time of the accelerating structure, and \(u\) is the necessary microwave energy per unit length. From these scaling relations, it is obvious that for a particular design that is characterized by a gradient \(E_{a}\) less RF average power is required at higher frequencies. To illustrate the current progress in the development of gyro-klystrons for high-gradient accelerators two examples will be given. The 36 GHz RF system presented in [51] utilizes a 30 cm long slow-wave structure (SWS) and delivers more than 12 MV of linearising voltage at a 1 kHz repetition rate, and operating at a gradient of 42.5 MV/m. The developed RF sources are capable of delivering up to 3 MW, 1 us pulses at a 1 kHz repetition rate using moderate modulator voltages. The second example is the MW-level 48 GHz gyro-klystron amplifier [52]. The design of the gyro-klystron is expected to deliver an output power of up to 2.3 MW with a gain of 36 dB and an efficiency of 44% at 48 GHz, when driven by an electron beam of voltage 140 kV and current 37 A. The remarkable history of the University of Maryland's program that has been focused on the investigations of gyro-amplifiers as potential sources for linear colliders is presented in detail in the review paper [53] which includes essential references to the early work on this topic. It has been estimated that using one megawatt of RF power from the gyrotron may allow reaching a peak accelerating gradient of 400 MeV/m [54, 55, 56]. In order to test the developed mm-wave standing-wave single-cell accelerating structure, a pulsed gyrotron operating at 110 GHz has been used. RF breakdown (both direct and multipactoring) is one of the major phenomena that limit the achievable gradient in accelerating structures.