The NOVAC11 LINAC [18], shown in Figure 1, provides an electron beam with four nominal energies: 4 MeV, 6 MeV, 8 MeV, and 10 MeV, allowing treating targets with a thickness of up to 2.6 cm within the 90% isodose or up to 3.0 cm within the 80% isodose.

The radiofrequency section of the accelerator provides a train of electron current pulses, each with approximately square shape in time and an approximate duration of 2.5 μs. The pulse repetition frequency has a range of 5–30 Hz.

This system does not use a scattering foil for beam broadening, but the electron beam crosses only the thin titanium window (60 μm thick) that seals the LINAC vacuum chamber and four steel plates (20 μm thick) which are the monitor ionization chamber electrodes. These elements also produce the beam scattering needed to spread the very narrow beam exiting from the RF section of the LINAC. At the same time, these materials modify the electron energy spectrum at the end of the accelerating structure and are the main source of emission of Bremsstrahlung photons.

The beam collimation system is purely passive and consists of a set of 5 mm-thick PMMA cylindrical applicators of different diameters ranging from 3 cm to 12 cm and of different lengths.

Each applicator consists of two parts: the upper part and the terminal section. The upper part, also called the applicator holder, is directly mounted to the radiant head, while the terminal part, also named the terminal applicator, is connected to the upper section via a ring nut. Both flat and beveled applicators are available, with possible inclination angles with respect to the surgical bed surface of 0°, 15°, 22.5°, 30°, and 45° offering both circular and elliptical fields. The source-to-surface distance (SSD) is 80 cm for the reference applicator (10 cm diameter) and 65 cm for the others.

Despite the relatively simple architecture of the cylindrical applicator, several collimation configurations (SSD, angle, etc.) can be obtained, with different outputs in terms of dose per pulse performance. It must be stressed that the dose per pulse outcome is a particularly relevant figure for an IOeRT system since it is directly proportional to the average dose rate D _R delivered, as reported by Eq. 1: D R = P R F ⋅ D p , (1) where PRF is the pulse repetition frequency. Another important parameter of the system, the instantaneous dose rate (IDR), or dose rate within pulse, can be obtained by dividing the dose per pulse D _p by the pulse length (Δt). Taking into account that for the NOVAC11, the pulse length is about 2.5 μs, the IDR can be easily calculated as Eq. 2: I D R ≃ 4 ⋅ 1 0 5 D p , (2) where the IDR is expressed in Gy/s when D _p is given in Gy. In the NOVAC11 system, despite a dose per pulse of up to 100 mGy, the average dose rate is quite limited, from 4 up to 30 Gy/min, due to the relatively low PRF (5 Hz in the clinical mode, up to 30 Hz in the service mode).

In this section, we describe the dosimetric characterization of the nominal 10 MeV electron beam of the NOVAC11 accelerator.

The beam current, pulse length, and delivered charge were measured by means of a Faraday cup, coupled with an oscilloscope and positioned after the titanium window. The Faraday cup employed for quantifying the NOVAC11 beam charge consists of a basic copper cup electrode linked to a Tektronix MDO4000C mixed domain oscilloscope [19]. Additionally, the Faraday cup features a suppressor plate set at a polarization of −80 V, serving to restrict the escape of induction electrons and maintain the integrity of charge collection. The utilization of the oscilloscope proves beneficial not only for charge measurement through waveform integration but also for assessing pulse length, thereby providing supplementary insights into the beam pulse characteristics.

The experimental setup for relative dosimetry, i.e., PDD and off-axis profiles, measurements consisted of a 3D motorized water phantom (MP3-XS, PTW, Freiburg, Germany [20]) equipped with an unshielded diode (Diode E, type 60017, PTW [21]) as the field detector and an ionization chamber (Semiflex Ionization Chamber, type 31010, PTW [22]) as the reference detector. The two detectors were connected to the dual-channel electrometer (UNIDOS E, PTW) [23].

The experimental measurements were performed using the reference applicator, which has a diameter of 10 cm, positioned to the water surface (no air gap) with a spatial resolution of 1.0 mm. The percentage depth dose was acquired along the beam axis perpendicular to the water phantom surface, while the transversal profiles were measured at the depths of maximum (R100), 80% (R80), and 50% (R50) of the PDD.

For absolute dosimetry measurements, the Advanced Markus ionization chamber (type 34045, PTW [24]) was used. This detector is a waterproof parallel plate chamber for the measurements of high-energy electron radiation. The small cylindrical sensitive volume of 0.02 cm³ with a diameter of 2.5 mm makes the chamber ideal for dose distribution measurements in a water phantom (the chamber has a protective acrylic cover of 0.87 mm for use in water), giving a good spatial resolution.

The absolute dose reference dosimetry was performed by positioning the ionization chamber at z _max, i.e., the depth of maximum dose value along the beam axes, according to the Italian National Health Institute [25].

In addition, to evaluate the output factor of the NOVAC11, the same absolute dosimetry measurements performed with the reference applicator were assessed for a smaller applicator with a diameter of 40 mm.

We evaluated the dosimetric quantities to be compared with experimental measurements by means of FLUKA [26, 27] Monte Carlo software (2020.0.10 version), which is widely used in medical applications and known to describe electromagnetic interactions with very high precision [28], and FRED, a GPU-accelerated MC-based dose engine [29–31].

As described in the previous section, the electron beam generated by the NOVAC11 with different nominal energies (4 MeV, 6 MeV, 8 MeV, and 10 MeV) is collimated on the surgical bed by a cylindrical applicator which can have different lengths and diameters.

In order to achieve the best possible agreement between the measurements and the simulation, we described the applicator geometry in great detail. In particular, the manufacturers provided all the information about the applicator structure and materials crossed by the beam.

For both MC simulations, the two applicators were modeled as a series of PMMA hollow cylinders of different dimensions and shapes centered on the beam axis (z-axis). The upper sections of the two applicators were both simulated as two sequential cylinders with diameters of 20 or 30 mm, a wall thickness of 5 mm, and lengths of 3.2 or 4.0 cm, respectively.

The terminal sections of the reference applicator were modeled using other three sequential cylinders with diameter equal to 27.5, 45, and 100 mm, wall thickness ranging from 5 to 15 mm, and lengths 2.2, 3.8, and 66.8 cm, respectively. The total applicator length, i.e., the SSD, was, thus, 80 cm. The terminal section of the 40 mm applicator was modeled as two PMMA cylinders with diameters of 30 and 40 mm with a wall thickness of 5–15 mm and a length of 3.6 and 54.2 cm, respectively. In this case, the SSD was equal to 65 cm.

In the upper section, the electron beam exits from the LINAC, passes through a 60 μm-thick titanium window that seals the LINAC vacuum chamber, and, after 16 mm, goes through four 20 μm-thick steel plates, which are the monitor ionization chamber electrodes. In the simulation, these elements were modeled as circular planes, inserted inside the applicator, with the same dimensions and material as those supplied by the manufacturer. In both simulations at the end of the applicator geometry, according to the setup used for the experimental data acquisition, a water phantom of 40 × 40 × 20 cm³ was placed. Figure 2 shows the FLUKA MC geometries for the 100 mm and 40 mm applicators in the plane containing the beam axis.

For the input of the Monte Carlo calculation, a model of the electron beam impinging in the LINAC titanium window was provided by the manufacturer. The spatial beam profile was assumed to have Gaussian shape with an FWHM of 1.3 mm. The angular spread of the accelerated electrons was considered negligible. The 10 MeV electron energy spectrum used in the simulation is shown in Figure 3 and was obtained from the PARMELA code [32].

The energy cutoffs for the transport and production of both electrons and photons were set to EMFCUT = 10 keV (kinetic energy). Particles with energy below this threshold are not transported anymore, and their energy is locally deposited.

The dose deposited in the water phantom at the applicator exit was calculated for each primary electron crossing the titanium window. In order to score the energy deposition, the phantom was divided into 201 × 201 × 200 voxels of size 2 × 2 × 1 mm³ in the x × y × z direction for both MC simulations. The FLUKA 2D dose distributions for the reference applicator are shown in Figure 5. To reduce the statistical MC fluctuation, the FRED and FLUKA simulations were performed using 10⁹ histories (or primary electrons). The experimental measurements and simulated curves of the relative dosimetry, i.e., PDD along the beam axis and dose profiles at the depth of 15 ± 1 mm (R ₁₀₀), 28 ± 1 mm (R ₈₀), and 36 ± 1 mm (R ₅₀), are reported in Figures 6, 7 for the reference applicator.

In the simulations, the dose in water was evaluated in volumes with a transverse area of 2 × 2 mm², corresponding to the sensitive area of the diode used in the measurements.

To test the agreement between the simulated and measured distributions, we performed a gamma index [33] analysis comparing FRED and FLUKA with the experimental data separately. Such test is widely used in medical physics to assess the agreement between planned and measured dose distributions, by evaluating both spatial and dosimetric differences, comparing corresponding points in the two maps. The test was conducted employing distance-to-agreement (DTA) and dose difference acceptance criteria of 3 mm/3% (standard criteria) and 2 mm/2% (more stringent criteria). Figures 6, 7 display the gamma index curve for 3 mm/3%.

As observed in both MC simulations, the γ index curves for the PDD and the R ₁₀₀ and R ₈₀ transverse profiles show that the majority of points fall below 1. This indicates that for 100% or 99.45% of the points in the distribution, the difference between the measured and simulated curves is less than 3 mm/3% for FLUKA and slightly greater than 3 mm/3 for FRED. However, for the R ₅₀ transverse profile, only 98.8% for FLUKA and 98.30% for FRED of the points meet this criterion.

As can be observed for both MC simulations, the γ index curves for the PDD and the R ₁₀₀ and R ₈₀ transverse profiles show that the majority of points fall below 1. This indicates that for 100%, for FLUKA, and 99.45%, for FRED, of the points in the distribution, the difference between the measured and simulated curves is less than 3 mm/3% for FLUKA and slightly greater than 3 mm/3% for FRED. However, for the R ₅₀ transverse profile, only 98.8% for FLUKA and 98.30% for FRED of the points meet this criterion. Table 1 summarizes the results obtained from the gamma index analysis with 3%/3 mm and 2%/2 mm acceptance criteria for both MC simulations.

For absolute dosimetry, the experimental measurements with the Advanced Markus at the peak values of the depth dose curves for both applicators were compared to the MC dose released in an ∼ 4.4 × 4.4 × 1 mm³ cubic voxel at the same position corresponding to the sensitive volume of the detector. From the two FLUKA simulations, we obtained a D ^max value equal to (1.285 ± 0.002) × 10^–12 Gy/electron and (2.847 ± 0.004)× 10^–12 Gy/electron for the applicator with 100 mm and 40 mm diameter, respectively. From the FRED one was instead obtained (1.269 ± 0.002) × 10^–12 Gy/electron for the 100 mm applicator and (2.918 ± 0.004)× 10^–12 Gy/electron for the 40 mm one. With these values, it is possible to compute the dose per pulse. To relate the dose in water to the current measurement at the NOVAC11 exit, the D^max values per LINAC electron were rescaled in order to match the equivalent charge of Q = 3.88 ± 0.32 nC (corresponding to (2.422 ± 0.775) ⋅ 10¹⁰ electrons per pulse) as measured by the Faraday cup. Table 2 shows the estimated and measured dose per pulse values for the applicator with 100 and 40 mm diameter. It is worthwhile noticing that the uncertainty on the (MC/data) ratio is mainly due to the uncertainty of the charge measurement.

To further test the agreement between the experimental data and the simulations, we compared the relative NOVAC11 output factor defined as O F d = D d , z max D d ref , z max , (3) where D(d, z_max ) is the absorbed dose at depth z_max in water for the beam collimated by an applicator with diameter d and D(d _ref , z_max ) is the absorbed dose in water evaluated for the reference applicator at depth z_max [34]. In the present case, we considered the reference field as the 100 mm-diameter applicator and the field of interest as the 40 mm-diameter applicator. According to Eq. 3 and using the D^max values reported in Table 2, the output factor evaluated from the simulation data is equal to 2.22 ± 0.01 and 2.22 ± 0.01 for FLUKA and FRED, respectively. This value was compared to the measured one, which is equal to 2.26 ± 0.06.