Based on the working mechanism of electron cyclotron devices, high-power gyrotron tubes are the source of millimeter-wave and terahertz-wave radiation ^[1]. The advantage of the cyclotron relative to the Cherenkov device is that it provides a higher average power. In addition, the cyclotron can utilize an electron beam with lower energy of 10~100 keV ^[2]. Therefore, gyrotron is known as one of the most promising high-power sources ^{[3,4,5,6,7,8,9]} and its applications for spectrum, communication, high-resolution RADAR, biomedical and terahertz band technologies have great potential for development.

Due to the needs of the application, the gyrotron needs to work at higher frequencies, higher power and higher efficiency. At the same time, with the increase of output power, the high-frequency structure of the gyrotron increases continuously, and it often works in the high-order mode, which brings difficulties to the transmission and mode conversion of electromagnetic waves. For example, for a gyrotron with an output power of 1 MW and a conversion efficiency of 50%, increasing the conversion efficiency by 1% means that the lost power will be reduced by 0.005 MW ^[10]. In view of the above reasons, we decided to use a quasi-optical mode converter to transmit electromagnetic waves at the output. The quasi-optical mode converter consists of a launcher and a mirror system. prebunching launchers are widely used in modern high power gyrotron tubes, such as periodic helical perturbation launchers ^[11,12], mirror-line launchers ^[13], and hybrid-type launchers ^[14]. Here, we adapt the periodic perturbation launcher because of an uptaper which can effectively reduce the reflected waves formed by the waveguide wall disturbance.

In recent years, the biological effects of millimeter wave radiation have attracted much attention. Because of its short wavelength and poor penetration, millimeter wave radiation is easily absorbed by tissues with more water content. Therefore, the local effects of millimeter wave radiation are mainly skin and eye damage effects. This study combines the rabbit behavior and skin damage effects in 94 GHz high power millimeter wave radiation, aiming to provide experimental basis for exploring the skin damage effects and mechanisms of high-power millimeter wave radiation.

The rest of this paper is organized as follows. In Sect. 1, this part starts with characteristics of mode selection. Then, one continues with the cold cavity design, followed by the hot cavity analysis. Subsequently, the magnetron injection gun is presented. The part concludes with the quasi-optical mode converter with high power efficiency and loss diffraction. The measured results of the gyrotron are shown in Sect. 2. Finally, one makes a summary in Sect. 4.

In order to achieve greater output power, the operating mode should select a high-order mode of 94 GHz. The traditional low-order waveguide mode does not work well, but Higher-order modes cause mode competition. Therefore, it is necessary to study the relationship between working mode and cavity further. In order to suppress the parasitic mode near the working mode, a gradual cavity is used ^[15].

According to the result of numerical calculation, the diffraction quality factor of the main mode TE_6.2 is 1 150, and the resonance frequency is 94.19 GHz. The cross section of the optimized cavity with the radius Rc =5.96 mm, input port R_in =5.25 mm and output port R_out =7 mm are shown in Fig. 1 together with the normalized cold-cavity electric field distribution of the operating mode TE_6.2.

After the design of the cold cavity is completed, the appropriate beam radius should be carefully selected to achieve the purpose of suppressing the competition mode and obtaining a good beam-wave interaction between the main mode and the electron beam. According to the beam-wave coupling equation of Ref.1, Fig. 2 shows the normalized coupling coefficient of the operating mode and the competitive mode as a function of beam radius. One can obtain the TE_+6.2 mode （co-rotating mode） produces strong coupling with the electron beam at a radius of 3.3 mm, and the TE_-6.2 mode （counter-rotating mode） produces a strong coupling at a radius of 4.3 mm. By comparing the radius of the two modes, the beam radius of the 4.3 mm beam in the TE_-6.2 mode is close to the cavity radius of 5.96 mm, so that electrons will more easily enter the inner wall of the cavity. Based on the above analysis, we chose a co-rotation mode with a beam radius of 3.3 mm.

By analyzing Fig. 2, when the beam radius is 3.3 mm, the modes TE_-4.3, TE_0.3, TE_-3.3, TE_-2.3 and TE_2.3 become the main competition modes. Therefore, we further study the starting current of the competition modes to solve the mode competition. According to the starting current theory of Ref. 14, Fig. 3 shows the starting current of the operating mode and the competitive mode as a function of the external magnetic field, where the beam voltage of 40 kV, beam radius of 3.3 mm and transverse-to-axial velocity ratio of 1.3 were selected in the calculation.

As shown, the TE_+6.2 mode can be started separately in the appropriate magnetic field range. By changing the external magnetic field, the purpose of suppressing the competition mode can be achieved. In summary, we can think of the TE_+6,2 mode as the desired gyrotron normal mode of operation.

After the design of cold-cavity and the studies of linear analysis, one need to the beam-wave interaction. Multi-mode simulation of a 94 GHz single-cavity gyrotron using the in-house developed non-linear time-dependent code ^[16]. We ignore the propagation velocity and space charge effect of electron beams^[17]. It is assumed that all electrons in the loop bundle have the same center radius. In the selection of competing modes in the simulation, the modes that the resonator frequency is between 90 GHz and 100 GHz and the beam-wave coupling of relative to the main mode is greater than 70% were selected. The startup simulation is shown in the Fig.4. As it shows that the main mode TE_+6.2 can reach at stable steady with the output power of 62 kW under the conditions of beam voltage of 40 kV, beam current of 4 A, transverse-to-axial velocity ratio of 1.3, beam radius of 3.3 mm.

According to the requirements of output power and efficiency, the best parameters of electron beam are given by the simulation results of the interaction cavity. The optimum value of the electron beam parameters is also given. Based on the theory of electron guns, the goal of MIG design is to emit electron beams at specific radial positions. Meanwhile, the electron beam has minimum velocity spread and the best velocity ratio. In view of these objectives, the optimized parameters include: cathode and anode geometry, the gap between them, the tilt length of the cathode, the cathode tilt angle, the cathode magnetic field distribution, and the anode voltage. In order to meet the parameters of the gyrotron, we developed a numerical code for designing the MIG and calculated the lateral velocity and longitudinal velocity distribution to be 2.7% and 4.0%. The trajectories and structure are shown in Fig. 5. The specific parameters of optimized beam are presented in Table 1.

One has developed a high power gyrotron operating at a frequency of 94 GHz TE_6,2 mode. Due to the high output power, when the electromagnetic field is output longitudinally, a heat distribution pattern is formed on the output window in the form of TE_6,2, which is unevenly distributed and is prone to stress and causes the output window to rupture. At the same time, the TE_6,2 mode electromagnetic waves directly output from the circular waveguide are distributed in a conical distribution in free space and cannot be directly utilized. Therefore, this paper uses a Denisov type launcher and four prebunching mirrors to improve the utility of the gyrotron and convert TE_6,2 into a fundamental Gaussian mode.

A harmonically deformed launcher is used in the system ^[18]. Disturbance of the waveguide wall changes the boundary conditions of the inner wall of the waveguide. The eigen modes in a circular waveguide will couple with other modes. The mutual coupling and superposition of modes will form a new field distribution. Table 2 shows the relative power of the 9 modes that form the Gaussian distribution ^[19].

Optimizing the perturbation of the waveguide wall enables a specific Gaussian field distribution to be obtained. Therefore, the design of the specific structural parameters of the launcher is very important. The radius of the launcher is different at each position （ϕ, z）. The change in radius can be expressed by the following formula

∆R=δ1cos∆β1z-l1φ+δ2cos∆β2z-l2φ

where φ is the azimuthal angle, is the longitudinal disturbance amplitude, and is the azimuth disturbance amplitude. is half of the longitudinal wavenumber difference between the longitudinal coupling modes, z is the longitudinal position and is half of the longitudinal wavenumber difference between the azimuthal coupling modes. and are the azimuth disturbance periods of the longitudinal disturbance term and the azimuth disturbance term, respectively.

R=R0+αz+∆R

where R₀ is the initial radius of the circular waveguide, R₀ =7.07 mm, t is the slope of wall radius taper of the launcher, = 0.003.

The wave beam is radiated from the launcher and propagates through a reflection system consisting of a four-sided mirror to the output window. The first mirror is an elliptical mirror, the second mirror is a parabolic mirror, and the other two mirrors are phase correcting mirrors. Both correction mirrors satisfy the Katsenelenbaum-Semenov algorithm. The mirror system adjusts the shape, convergence, and direction of the Gaussian beam to achieve enough energy for non-fatal biological effects.

After the analysis of the basic theory, we create a model in the FEKO （Electromagnetic simulation software）. It is shown in Fig. 6. The electromagnetic wave is transmitted by following our prescribed route and one can obtain good Gaussian mode in the position of output window in Fig. 7.

According to the above theoretical analysis and numerical simulation, the Gaussian content of the outgoing wave beam to the target function at the output window is about 93%, and the conversion efficiency of the entire mode converter is about 98.54%.

The corresponding W-band gyrotron is designed and manufactured using the above simulation results. The gyrotron has a single-anode magnetron injection gun, single cavity and single stage recessed collector.

In Table 3, we list the parameter data for the experimental test. Combining the analytical results with the test results, we know that there is a 4.45% error between the two. The reason for the error formation is mainly that the calculation results are obtained under ideal conditions. For example, in the simulation calculation, the velocity spread, the deviation of the guiding center radius, and the space charge effect are ignored. In summary, since the simulation calculation is only 4.45% deviation from the actual experiment, we believe that the simulation reasonably describes the experimental results. The calculation results based on the nonlinear coupled equation can be used to study the nonlinear interaction in the gyrotron.

The gyrotron with quasi-optical mode converter is shown in Fig. 8. The white paper was placed at 0.6 m from the output window for 3 seconds. The output beam of the gyrotron is radiated to white paper, and it began to burn, forming a coin-sized spot which the field mode is shown in Fig. 9. Obviously, observing the burnt white paper, the center of the spot appears white, which is consistent with the amplitude profile of the Gaussian beam.

As we can see in Fig. 10, the rabbit's neck was fixed on a wooden board and placed at a vertical position with a power density of 6.0 W/cm² below the gyrotron output port. We use the 94 GHz high-power millimeter wave source developed above, and the radiation duration is 30 s. After 20 seconds of radiation, the rabbit facial expression was painful and intermittent screams. As the radiation time prolonged, there were continuous behaviors such as body tremors, sharp head rotations, and limb struggles.

This paper designs a 94 GHz gyrotron for non-fatal biological effects. The experiment achieved a 50.9 kW operation with a Gaussian beam output. Based on the steady nonlinear self- consistent field theory, 34.3% of the interaction efficiency can be obtained by using TE6,2 as the working mode. To get good output power, we use a system consisting of a transmitter and four mirrors to focus the beam while adjusting the wave front phase to avoid divergence and side lobes in the output beam. The energy of the launcher is transmitted to the output window through the mirror system, achieving a power transmission efficiency of 98.54% or more.

The experimental results show that a high efficiency gyrotron can be obtained in practical applications if certain conditions are met. For this non-fatal biological effect test, we can draw conclusions that the overall scheme can 6 W/cm2 of 94 GHz high-power millimeter-wave radiation causes rabbit skin recoverable damage. The degree of damage increases with increasing radiation dose, which provides an experimental basis for further research.