A C-band type electron LINAC that operates at a radio frequency (RF) of 5.712 GHz, installed in the DIRAMS research center, was used throughout this study. The LINAC was constructed for the research of radiotherapy machines, with the designed electron energy of 6 MeV at an RF power of 2.5 MW [1,2].

The electron energy depends on the RF power supplied from the magnetron and heater current of the electron gun. In our previous study, the energies of electron beams varied from 2.5–6.1 MeV, depending on the heater currents [9]. Additionally, the magnetron, which was operated with a 50 kV and 120 A pulse power, supplied the pulse modulator and generated a 2.5 MW RF power for a 2.5 µs pulse width. The designed maximum pulse frequency was 250 Hz. However, frequencies below 200 Hz were used for the stable operation of the LINAC.

Although the pulse width of the current system was fixed due to the pulse forming network type pulse modulator, DIRAMS developed a semiconductor-based pulse modulator to adjust the pulse width [10]. Continuous and pulsed modes were available during the LINAC operations to effectively control beam generation and interruption. In this study, the pulse mode was used to precisely measure the dose rate for a short period in a high dose-rate environment.

Fig. 1 shows the irradiation device designed for this study, where a ₁ is the diameter of the scattering foil. The collimated field size (a ₂) and device length (l) were considered to allow the placement of samples, with a diameter of approximately 15 cm, at various distances for multi-purpose experiments, including irradiations for pre-clinical studies. The collimator body and foil attachment ring were made of 15 and 10 mm aluminum plates, respectively. The foil attachment ring was used to maintain a 10 mm distance between the primary and secondary foils. The a ₁, a ₂, and l values, as shown in Fig. 1, were 7, 18, and 37 cm, respectively.

An interface slot, at the end of the collimator, was provided to connect an additional applicator at a later stage. A rail system was mounted in front of the irradiation device to move the sample, with 1 mm precision, in a straight line from SSD=40 cm to 100 cm. Here, the SSD is the distance from the source (scattering foil surface) to the sample’s surface.

The intensity of the electron beam, emitted from the exit window of the accelerating waveguide, depends on the operating parameters of the LINAC, such as the pulse frequency, pulse width, and heating current of the electron gun. Additionally, the dose rate is directly proportional to the average intensity of the electron beam but varies with the distance from the source. Moreover, the dose rate should be established as a function of LINAC parameters coupled with the SSD to develop multi-purpose irradiation systems. When the LINAC operates at a constant RF power and heater current of the electron gun, the dose rate (D) at an SSD can be expressed as,where D _ref is the dose rate (Gy/s) at a reference depth in water for the reference conditions of r=100 cm, f=100 Hz, and τ=2.5 µs. The reference depth is a point in the sample to which the dose is delivered and generally the depth of the maximum dose along the beam axis. s(r) is a distance-dependent function, where r is the SSD. Furthermore, p(f) and w(τ) are functions of the pulse frequency, f, and pulse width, τ, respectively. In case of an ideal LINAC, the beam intensity or dose rate is linearly proportional to the value of f and τ. However, our LINAC is not linear due to the combined characteristics of its components, such as the RF generator, high voltage devices, vacuum, and cooling system. Therefore, these functions should be determined experimentally. Various factors affect the dose rate in a LINAC based irradiator, making it difficult to evaluate the dose rate systematically. Fortunately, τ is fixed in the current system, as mentioned above; thus, here, w(τ)=1.

D _ref, s(r), and p(f) were determined to evaluate the irradiation system experimentally. If the modulator system changes, the w(τ) function can be recalculated to update the irradiation system.

In this study, a thin stainless steel sheet was used as the material for the scattering foil, because the steel is not easily oxidized and is easy to process. While the thick foil increases the uniformity of the dose distribution on the irradiation field, it causes a significant energy loss. Therefore, the optimum thickness produces a uniform dose distribution in the field with low energy loss. However, it is known that dual foil produces more uniform dose distributions while maintaining the same energy loss as compared to single foil.

Owing to experimental difficulties, Monte Carlo calculations were used to determine the optimal foil thickness. The Monte Carlo N-particle extended (MCNPX) code supporting flexible geometric configurations was used in this study [11]. In the calculations, the initial electron beam energy incident on the scattering foil should be determined. Here, we determined the initial electron energy delivering, R ₅₀, which coincided with the measured R ₅₀ on the percentage depth dose curve through the measurement of the LINAC beam, and the calculations for 4.0, 5.0, and 6.0 MeV initial electrons. Both the measurement and calculations were performed with a scattering foil of thickness 0.15 mm in the polymethyl methacrylate (PMMA) phantom, at SSD=100 cm. As shown in Fig. 2, the initial energy for Monte Carlo calculations was 4.7 MeV. The electron energy used in the calculation was mono-energy of value 4.7 MeV, which was significantly different from the actual beam energy distribution. However, the measured R ₅₀ was in a good agreement with the calculated R ₅₀, as the difference between them was less than 0.1 mm.

According to the IAEA dosimetry protocols, R ₅₀ is the quality index of electron beams, and the mean energy at the phantom surface is determined by E ₀=2.33R ₅₀ [12]. This method is suitable for initial energy determination, and has been applied to Monte Carlo studies by Ding et al. [13].

Fig. 3 shows the geometry used for Monte Carlo calculations. The energy loss variation and beam profile uniformity were investigated. Moreover, we determined that the optimal thickness of the scattering foil was 0.3 mm for a single foil using this geometry. The determined single foil was replaced with a dual foil by dividing it into two foils with half the thickness to improve the uniformity of the beam profile. The dual foil was then applied to the experiments of the irradiation system [14]. Furthermore, Monte Carlo calculations were performed to verify the improvement of the beam profile uniformity at SSD=40 and 100 cm. The calculated results for these processes are described in the Results section of this paper.

The +F6 tally was used in our calculations to output the absorbed dose to the detector in MeV/g, along with the statistical uncertainty in the MCNPX calculation [11]. The statistical uncertainties were within 0.01 (1%) for 10 to 100 million histories at SSDs=40 to 100 cm. The cutoff energies of 50 and 10 keV for electrons and photons, respectively, were also applied during transport calculations.

As mentioned above, D _ref, in equation (1), refers to the dose rate (Gy/s) under the reference conditions of SSD=100 cm, f=100 Hz, and τ=2.5 µs. Furthermore, the absorbed dose rate was measured using a calibrated ionization chamber (Advanced Markus, PTW Freiburg, Freiburg, Germany), positioned at a depth of 1 g/cm² in the water phantom (T41023; PTW Freiburg, Freiburg, Germany).

The absorbed dose to water was determined by employing the IAEA TRS-398 dosimetry protocol [12]. Additionally, the ionization chamber was irradiated with electron beams characterized by 100 pulses using the pulse mode of the LINAC control system. The absorbed dose was determined using the average value of 5 measurements, where the operating pulse frequency was set to 100 Hz. Consequently, the single measurement time for the reference dose rate determination was 1 s.

s(r) is the relative dose with SSD along the beams axis. For the electron beams, the inverse square rule can be approximately applied for two doses located at a close distance. However, it is difficult to apply the rule to doses at SSDs ranging from 40 to 100 cm, used in this study. Therefore, the dose rates were directly measured and evaluated using the film dosimetry technique. The radiochromic film (Gafchromic EBT3; Ashland, Wayne, NJ, USA) was positioned at SSDs of 40, 50, 60, 80, and 100 cm. The measured values on films were normalized to that of SSD=100 cm and fitted using a logarithmic scale. For this measurement, the film was calibrated to 6 MeV electron beams at a depth of maximum dose at SSD=100 cm in the water phantom using the medical LINAC (Infinity; Elekta, Crawley, UK). Furthermore, electron beams were irradiated the calibration films with doses ranging from 100 to 1,000 monitor units (MU) at the dose rate mode of 400 MU/min. The irradiated films were analyzed using a scanner (1000XL; Epson, Long Beach, CA, USA) and software (FilmQApro; Ashland, Bridgewater, NJ, USA).

The function, p(f), represents the relative dose rates as a function of the pulse frequency of the LINAC. The dose rates were measured for pulse frequencies of up to 200 Hz at a depth of 1 g/cm² in a water phantom using the ionization chamber, similar to that used for the dose rate measurement. p(f) was determined via two fitting functions using a normalized value for the pulse frequency of 100 Hz.

The Monte Carlo calculated percentage depth doses (PDDs) and beam profiles at SSD=40 cm, as functions of the scattering foil thickness, are shown in Fig. 4. In these calculations, the energy of the incident electron was assumed to be mono-energetic 4.7 MeV, as previously discussed. In the given figure, as the foil thickness increases, the PDDs move toward the surface and beam profiles become more uniform. These properties are attributed to the energy loss and increased scattering of the electrons passing through the foil.

For the quantitative evaluation of energy loss, the mean energies at the phantom surface were calculated using R ₅₀ depths, given in Fig. 4a, as E ₀=R ₅₀, the results of which can be found in Fig. 5a. The energy losses were approximately 0.1 MeV per 0.1 mm thickness within 0.3 mm foil thickness but increased to approximately 0.2 MeV for thicknesses greater than 0.3 mm.

In the beam profiles, the W ₉₀ and W ₉₅ values were used to analyze the dose uniformity, as shown in Fig 5b, where W ₉₀ and W ₉₅ are the field diameters of 90% and 95% doses, respectively, compared to the central dose of the field. Here, W ₉₀ and W ₉₅ are the values for the irradiation system used in this study. In case of experiments on small animals, W ₉₅ should be greater than 5 cm to deliver a uniform dose of 95% to 100%, relative to the central dose. This condition is satisfied for thicknesses greater than 0.3 mm, as shown in Fig. 5b, where W ₉₅ for a 0.3 mm foil is 7.4 cm. Additionally, the size of adult mice is typically about 7.5 to 10 cm, and W ₉₅ for a 0.3 mm thick foil is approximately close to that of the size of a small mouse for pre-clinical studies. W ₉₀ can be used for large samples requiring dose uniformity within 10%. The calculated results are obtained at SSD=40 cm, which is the minimum SSD for this irradiation system. Moreover, the field diameter increases with increasing SSDs. Through these empirical analyses using the Monte Carlo calculated results, the 0.3 mm thickness was determined as the optimal thickness of the scattering foil in this study.

In practice, the dual foil was used in the irradiation system, wherein the foil was created by dividing the optimal-thickness single foil. The beam profiles for single and dual foils at SSD=40 and 100 cm were calculated, as shown in Fig. 6. The results of the dual foils for two SSDs were approximately 14% greater than those of the single foils, as shown in Fig. 6., which demonstrates that dual foils are more effective in producing uniform irradiation fields [14]. In the future, studies regarding the optimization of the thickness, shape, and separation of the foils should be considered.

The measured results of D _ref, s(r), and p(f), used in equation (1), are described in this section. Fig. 7a shows the experimental setup for the reference dose-rate (D _ref) measurement using the ionization chamber. To apply the TRS-398 protocol, R ₅₀ was determined via the normalized depth dose curve using film dosimetry in a PMMA phantom, as shown in Fig. 8 [12]. In this figure, the depth axis is the water equivalent thickness in g/cm² using the scaling methods described in TRS-398 [12].

The measured results, using the ionization chamber, are summarized in Table 1. Additionally, the dose rate was 7.156 Gy/s at a depth of 1 g/cm² in water. In the irradiation system, in general, the reference depth in the sample is set to the depth of maximum dose in water. The value can be converted by using the measured percentage depth dose data, and the estimated dose rate at the maximum depth was 7.573 Gy/s, as described in Table 1. Furthermore, we set the value as D _ref in equation (1). The relative standard uncertainty (1σ) in this measurement was estimated to be approximately 1.4% from the statistical summation of the ionization chamber calibration factor (0.7%), charge measurement (0.6%), correction of charge (0.2%), quality factor (1.0%) and other variables (0.5%).

In Table 1, the pulse per dose refers to the dose for an electron beam pulse. If the dose per pulse is higher than approximately 0.1 Gy/s, ion-recombination corrections are required for the result of the ionization chamber [8]. Therefore, we employed film dosimetry for the measurement of various SSDs, and the dose rates between SSD=40 and 100 cm were derived from the results of the ionization chamber dosimetry at SSD=100 cm. In addition, an objective of this study was to evaluate the possibility of FLASH research using the proposed LINAC system. Therefore, the optimization of the scattering device was performed at SSD=40 cm.

Fig. 7b shows the experimental setup using radiochromic films. The films with an area of 14¡¿14 cm² were positioned at a depth of 1 cm in the PMMA phantom. The doses at the central and peripheral regions of the film were used to determine the relative dose rates and beam profiles at the SSDs. The measured relative doses and fitted values are shown in Fig. 9. The derived function of the SSD, s(r) is,where, u ₁=3.699 and u ₂=–1.849.

The relationship between the pulse frequency and dose rate is shown in Fig. 10. The measured values were obtained using the Markus ion-chamber positioned at 1 g/cm² in the water phantom at SSD=100 cm. The normalized doses for the dose at f=100 Hz were fitted using linear and polynomial functions over the frequency ranges as follows, where, g₁=–0.00964, g₂=0.0106 Hz^–1, g₃=–0.05982, g₄= 0.01358 Hz^–1 , and g₅=–3.060¡¿10^–5 Hz^–2. The dose rate was approxi¡©mately linear up to 100 Hz and slowly increased up to 200 Hz. As previously mentioned, the properties depend on the performance of the LINAC components, such as the pulse modulator and RF generator. When replacing the components, equation (3) should be updated via measurements in terms of quality assurance of the irradiation system.

From the determined values of D _ref, s(r), and p(f), the dose rates in Gy/s as a function of SSD and pulse frequency can be determined, as shown in Fig. 11. The values in this figure were recorded at a depth of maximum dose in water. Since the sample can be positioned at the extended SSD over 100 cm in the irradiation room, the dose rate evaluation was performed for up to 120 cm, as shown in Fig. 11. The result shows that the maximum dose rate for this irradiation system is 59.16 Gy/s at 200 Hz. If a low dose rate is required, the dose rate can be reduced to 0.0522 Gy/s (5.122 cGy/s) at an SSD=120 cm under 1 Hz operation.

The measured beam profiles, normalized at the central dose, are shown in Fig. 12a and those normalized at the central dose of SSD=100 cm can be found in Fig. 12b. When evaluating the beam profiles, the W ₉₅ value at SSD=40 cm was 8.8 cm, and the W ₉₅ values at other SSDs were greater than 12 cm. However, current devices pose a challenge in producing a uniform irradiation field for diameters above 15 cm. Thus, an additional applicator may be required. In the future, a study on suitable applicators to improve the irradiation system will be conducted.