## 2 Research Methodology
### Linear Accelerator for the Sterilization System  
Synchrotron Light Research Institute, Thailand has successfully installed and commissioned the LINAC 6 MeV sterilization application that is shown in Figure 9. The structure of the designed system is divided into several main sections. The electron gun is a diode thermionic gun, used to emit electrons with a peak current of 400 mA into the 6-MeV side-coupling LINAC. All emitted electrons are accelerated at an S-band resonant frequency of 2.9982 GHz by a longitudinal electric field generated from the 12-hole-slot magnetrons. At the LINAC exit, these electrons collide with a tungsten target, which emits photons in the form of X-rays; therefore, X-ray production is maintained at the desired dose for the entire irradiation process. All systems and sub-systems should work properly. For this LINAC, the electrons are accelerated up to 6 MeV with a resonant frequency of 2.9982 GHz at a temperature of 40 \({}^{\circ}\)C and a vacuum pressure of 1 \(\times\) 10\({}^{-9}\) torr. One of the most crucial components for the reliable performance of X-ray production is an automatic frequency control (AFC) system. The electrons successfully accelerate only RF pulses from the magnetron and must be coupled with the LINAC cells. This means that the RF pulse must display exactly the correct resonant frequency. The resonant frequency of the magnetron can be  
\begin{table}
\begin{tabular}{c c} \hline
**Descriptions** & **Values** \\ \hline Number of resonant cavities & 12 \\ Cathode radius (R\({}_{\rm C}\)) & 9.160 mm \\ Anode radius (R\({}_{\rm A}\)) & 17.023 mm \\ Cavity radius (R\({}_{\rm V}\)) & 3.195 mm \\ Voltage applied (VAPP) & 45,000 v \\ Permanent magnet (B\({}_{\rm APP}\)) & 0.152 t \\ Tuner slot distance (T\({}_{\rm SLOT}\)) & 3.22–8.22 mm \\ \hline \end{tabular}
\end{table}
Table 1: Specification of the cavity magnetron.  
adjusted to correct the mismatch in the LINAC frequency as the machine operates by using the automatic frequency control (AFC) algorithm. The design of the AFC system depends on the RF signal taken from a directional coupler connected with a waveguide. It gives output signals, one of which displays forward power, and the other is the output signal obtained from the forward power and is referred to as the reflect power [26]. Both signals are compared by calculating the different phases. The difference in these signals is used as the error and the magnetron frequency is tuned to the resonant frequency. To reduce undesirable signals, high frequency and noise from the AC power supply are eliminated by using a low-pass filter. The difference in signal is used to generate the amplitude of the signal pulses with a proportional phase ratio of the frequency input--this is the principle of the AFC system's modules for designing the tuning frequency of the magnetron to match the accelerator tube continuously. Thus, the module of the AFC system is the key component for controlling the AFC system's reliability and stability, and the processes of the AFC system are shown in Figure 10. In addition to the tuning of the resonant frequency, the system is designed via the technique of an online adaptive parameter, referring to the condition that occurs as the Takagi-Sugeno model.