The method we used to characterize the detectors under a proton or alpha beam of ∼70 MeV (total energy) is presented in Figure 3. These experiments took place at CAL-Nice and at ARRONAX-Saint-Herblain. Both accelerators are cyclotrons, and ARRONAX is equipped with a pulsation at injection, allowing the generation of a pulsed beam similar to that of a synchrocyclotron, with adjustable pulse and inter-pulse durations.

The detectors used in these experiments are scintillators coupled to photomultiplier tubes. Various scintillation crystals were employed to determine optimal characteristics based on their luminosity and scintillation constants.

A PMMA target serves as a phantom to stop the proton beam and generate secondary radiation. In the following, we will focus mainly on the results obtained at ARRONAX with pulsed beams, whereas experiments at CAL were used to study the behaviour of various detectors with continuous beams. The target was irradiated with a beam whose intensity could be adjusted up to 20 µA during pulses at ARRONAX. The measurement of the beam intensity was carried out by an ionization chamber located upstream from the exit window of the accelerator beamline in vacuum. Detectors are positioned around the target to detect the secondary radiation or particles produced during irradiation. The signals from the detectors are recorded using a LeCroy DSO oscilloscope, allowing automatic recording of approximately 100 waveforms of the characterized detector signals with 20 GHz sampling period. Recording is triggered by the beam pulse signal. Figure 4 provides an example of waveforms obtained on a PbWO₄ detector at ARRONAX, illustrating the correlation between the signal of the incident alpha beam pulse from a fast beam monitor (single diamond used as a solid-state ionization chamber) and the generated secondary particles.

The recorded waveforms are then analyzed by a Python script, which initially corrects slight fluctuations in the detectors’ baseline (average value subtraction, calculated from the start of the waveform that corresponds to 50 ns without signal). Subsequently, the script performs the integration of the detector signal over the duration of the beam pulse. Various parameters will be explored, such as the evolution of the integral with respect to the incident beam intensity, PMT bias (detector gain), and the distance from the impact point on the target (15 or 25 cm). Moreover, this Python script is able to detect each individual signal within the pulse (Figure 5) to enable correlation between the amplitudes of these signals and their integrals. The detection of individual signals occurs with the following conditions: a threshold value corresponding to 6 times the standard deviation of the points used for determining the baseline value, a time duration of 2.5 ns above this threshold, and a minimal time separation of 2.5 ns between two consecutive signals. The integral of an individual signal is calculated over a duration of 32.5 ns, 7.5 ns before the local maximum, and the subsequent 25 ns.

The first experiments at CAL and ARRONAX demonstrated a rapid saturation of detectors with high luminosity (NaI and BaF₂), when count rates are no longer small compared to the accelerator frequency, as illustrated in Figure 6. In order to avoid detector saturation, a reduction of the PMT bias is necessary to reduce signal amplitudes so that a lower number of PG is expected–with a loss of information–after data analysis based on individual signal detection.

Subsequently, the results will pertain to a scintillator crystal, PbWO₄, with a surface area of 4 cm² and a thickness of 3 cm, coupled with a PMT Photonis-XP2020. PbWO₄ was chosen due to its low luminosity (100–300 photons/MeV compared to approximately 38,000 for NaI(Tl)) and rapid scintillation decay constant (6 ns compared to 250 ns for NaI(Tl)), making it an ideal candidate for such applications. Indeed its fast decay time allows it, in principle, to return to its baseline between two consecutive proton pulses separated by 30 ns. However, this low luminosity induces a degraded energy resolution.

The simulations allowed for the determination of the evolution of deposited energy based on longitudinal displacements (with 8 detectors in operation) and lateral displacements (with 16 detectors) of the PMMA target. Figure 7 illustrates the obtained results. In each case, a correlation between the target displacement and the energy deposited per incident particle can be observed. In the longitudinal case, two groups of detectors are noticeable—those located upstream from the target (backward) and those located downstream (forward). Within one group, each detector exhibits the same behavior as the others, due to the geometry and symmetry of the setup. Forward detectors (numbered from 0 to 3) experience an increase in deposited energy as the target approaches them, due to the increase of their solid angle relative to the PG emission points. The situation is reversed for backward detectors.

Similarly, the observed variation during lateral displacement is attributed to the variation in the solid angle of the detectors relative to the emission points. However, other effects contribute to this variation, including the thickness in materials that secondary particles must traverse to reach the detectors. Additionally, the target displacement leads to a modification of the beam entry point and thus the depth of the Bragg peak, resulting in a parabolic evolution of the detected energy in forward detectors for large target displacements. Similar to the longitudinal displacement, symmetries are also clearly seen, explaining the similar evolution of detector pairs, for example, [0,4] [1, 3], and [5, 7] for forward detectors.

The relatively large number of simulated incident ions (10⁹) allows for the modeling of a certain number of beam pulses containing a specific quantity of protons. One may add the responses of backward detectors on one hand, and those located forward on the other hand, to detect longitudinal displacement. This increases the perceived statistics as well as precision by a factor N , with N being the number of detectors in the group. Figure 8 illustrates the evolution of the total number of detected particles (left) and the total energy deposition (right) in all detectors of each group for one given pulse of 1.5 × 10⁷ incident protons.

A quasi-linear behaviour is observed (mainly due to the observation angle). The sensitivity of each method is obtained by the ratio between the standard deviation of the simulated statistics and the slope of the linear adjustment function. In this way, the sensitivity to displacement along the beam axis using the PGPI method was calculated to be 1.3 mm at 1σ, while that of the PGEI is 3 mm at 1σ.

The experiments carried out at ARRONAX allowed us to obtain the evolution of the response of a PbWO₄ scintillator coupled with a PMT XP2020 (from Photonis) as a function of the incident beam intensity and the PMT bias, for two distances between the entry point of the target and the detector: 15 and 25 cm (Figure 9). First, these experiments show that for each bias value, the integral evolves linearly with the beam intensity until reaching a saturation value (close to 5 × 10⁷ pV⋅s), at which loss of linearity is seen; the loading charge of the PMT becomes too high. Lowering the bias voltage, and thus reducing the PMT gain, helps to overcome this saturation. Second, as expected, increasing the distance between the detector and the source reduces the detector counting rate, and thus increases the useable range of beam intensity. This is due to the decrease of the detector solid angle: we could check that the count rate ratios are approximately equal to (15/25)² (the square of the ratio of “target center-detectors” distances) for a given bias in the linear response regime.

These results can also be compared to the documentation from the manufacturer of the PMT XP2020, which provides the characteristic evolution of gain as a function of the bias voltage. By plotting the evolution of the integral of signals against the applied bias, as shown in Figure 10, lines with the same slopes as those in the literature are obtained. The saturation configurations of the detector also appear in these figures; indeed, there is a noticeable inflection in all curves beyond an integral value of approximately 2 × 10⁷ pV⋅s.

An example of correlating the amplitudes of individual signals with their integrals is illustrated with density maps shown in Figure 11. These results correspond to a PMT bias of 2000 V for a distance of 25 cm between the target and the detector and a beam intensity of 380 nA (left) and 3,200 nA (right). These results reveal a clear correlation between the signal amplitudes and their integrals. At 380 nA (left figure), saturation is observed for signals above 1.6 V, which is due to the oscilloscope’s acquisition window and pertains to only a small number of signals. Moreover, although the two acquisitions presented in Figure 11 correspond to beam intensities different by almost one order of magnitude, there is no indication for detector saturation, as the correlation is maintained. Furthermore, it can be observed that the increase in intensity leads to both an increase in the amplitude of each signal and its integral. In this experimental configuration, the duration of pulses are about 3–4 ns, and they are separated by 33 ns (HF period). Therefore, photons detected from the same pulse do lead to both added amplitudes and added signal integrals.

These results are confirmed by the histograms of the integrals of each of these individual signals, which are presented in Figure 12. The spread of the spectrum of integrals at high intensity can be seen in comparison with the lowest intensity.

The conducted simulations demonstrated that each of the PGPI and PGEI methods is sensitive to the displacement of a target along either the incident beam direction or a transverse axis. Furthermore, it has been shown that the sensitivity obtained from both methods is of the order of a few millimeters with 1.5 × 10⁷ incident protons, positioning these techniques competitively compared to other PG detection methods in the context of online monitoring in hadron therapy [9]. The degradation observed between these two methods arises from two factors. First, the absence of any filter for the PGEI method leads to the necessity of accounting for the contribution induced by neutrons and all other secondaries during irradiation, which carries less precise information about the ion path. Second, even if one considers only prompt-gamma rays, the PGEI method undergoes degradation compared to the PGPI method due to the wide energy spectrum of prompt-gamma rays, ranging from 1 to 10 MeV with an average located at 2 MeV. This leads to a broad dispersion of the averaged sums when multiple photons are detected during a beam pulse (total energies are of the order of 10⁵ MeV in Figure 8). Additionally, the sensitivity of each of these two methods increases with the expansion of the detection zones or the number of detectors around the target.

This experiment demonstrated that the PbWO₄ crystal used, with a surface area of 4 cm² and a thickness of 3 cm, coupled with an XP2020 PMT, is capable, in certain configurations, to withstand a significant deposited energy flux without saturating the readout system. Thanks to the system performance, we were able to use the same peak intensities as those employed in clinical settings with pulsed beams from clinical synchro-cyclotron accelerators, or even much higher intensities, making the use of the PGEI method feasible for online monitoring in hadron therapy. The crystal used in these characterizations has an equivalent depth but a much smaller surface area than those used in the simulations. In the best case, this detector represents a solid angle about 10 times smaller than that of a detector used in simulations. However, this detector keeps a linear response at high beam intensities, well above the maximum intensity of the considered synchro-cyclotron. It may therefore be possible to increase its solid angle, with a limit of detector saturation at 1 µA. This increase could be accompanied by an expansion of the solid angle by increasing the detection surface. Nevertheless, it is worth noting that a technological constraint on the size of PbWO₄ crystals may arise, requiring an increase in the number of detectors in the device to enhance its solid angle.

Furthermore, the development of this method will make use of a dedicated electronic system capable of integrating the signal from each detector. In practice, these signals will be compared to predictions by simulations associated to treatment plans to deduce any potential discrepancies.

The simulations were performed with large-sized detectors (cylindrical with a radius of 5 cm). These surface areas are exaggerated but can partly be compensated by increasing the depth of the crystals, which has been set here at 2.5 cm. Indeed, this depth corresponds to a 35% probability of absorption of a 4 MeV photon for LaBr₃. Increasing this depth could be a way to compensate for the reduction in surface area. Finally, the application context of these techniques, particularly the PGEI, with pulsed and high-intensity beams offered by synchro-cyclotrons, leads to large loading charge to each detection channel. Therefore, the choice of the scintillation crystal is of crucial importance. The sensitivity of the technique must be studied with realistic simulation of patient treatments. Since MC simulations are not able to thoroughly model all background sources, an additional background level based on experimental measurements can be a posteriori added as proposed in [40, 41]. These realistic simulations will allow us to estimate false negatives due to a compensation of different variations (e.g., combined variation in tissue composition and in beam energy) and false positives due to wrong or outdated calibrations (geometry, radiation damage).

The proposed PGEI method has some pros and cons with respect to other range verification methods envisaged for pulsed-particle beam therapy. The detection setup should be compact, like for iono-acoustic [35, 36], electric-field [32] and magnetic field [33, 34] detection. The short-lived beta + emission detection [6] is less compact, but corresponds to a more mature technology. Iono-acoustic detection is an integral method, restricted to soft tissues (without bone barrier). Electric field measurement is an integral method that faces the issue of very low signal, and its feasibility has not been demonstrated yet. Magnetic field measurements are also an integral method, the expected signals are very low and may be perturbed by the environment (beam HF, magnets). The short-lived beta + annihilation detection faces the issue of low statistics at the spot scale for real time verification, and, relative to in-beam PET, the long positron range of beta + emitters like ¹²N blurs the signal.

Last, the present feasibility study has been intentionally performed using a phantom target with simple geometry, and homogeneous chemical composition. The next step will consist of more realistic studies using several real-size detectors and more complex (anthropomorphic) phantoms irradiated under clinical conditions, in order to compare PGEI measurements with corresponding Monte Carlo simulations. Ideally, a clinical-routine system should be compliant with the (possibly rotating) nozzle and the patient positioning couch. Therefore, a flexible design should be envisaged, depending on the treatment type.