Characterization of LiF:Mg,Ti thermoluminescence detectors in low-LET proton beams at ultra-high dose rates

Objective. This work aims at characterizing LiF:Mg,Ti thermoluminescence detectors (TLDs) for dosimetry of a 250 MeV proton beam delivered at ultra-high dose rates (UHDR). Possible dose rate effects in LiF:Mg,Ti, as well as its usability for dosimetry of narrow proton beams are investigated. Approach. LiF:Mg,Ti (TLD-100TM Microcubes, 1 mm × 1 mm × 1 mm) was packaged in matrices of 5 × 5 detectors. The center of each matrix was irradiated with single-spot low-LET (energy >244 MeV) proton beam in the (1–4500) Gy s−1 average dose rates range. A beam reconstruction procedure was applied to the detectors irradiated at the highest dose rate (Gaussian beam sigma <2 mm) to correct for volumetric averaging effects. Reference dosimetry was carried out with a diamond detector and radiochromic films. The delivered number of protons was measured by a Faraday cup, which was employed to normalize the detector responses. Main results. The lateral beam spread obtained from the beam reconstruction agreed with the one derived from the radiochromic film measurements. No dose rates effects were observed in LiF:Mg,Ti for the investigated dose rates within 3% (k = 1). On average, the dose response of the TLDs agreed with the reference detectors within their uncertainties. The largest deviation (−5%) was measured at 4500 Gy s−1. Significance. The dose rate independence of LiF:Mg,Ti TLDs makes them suitable for dosimetry of UHDR proton beams. Additionally, the combination of a matrix of TLDs and the beam reconstruction can be applied to determine the beam profile of narrow proton beams.


Introduction
FLASH radiotherapy is a proposed approach for tumor treatment with radiation, characterized by delivering the treatment using ultra-high dose rates (UHDR, average dose rate >40 Gy s −1 , Favaudon et al (2014)). Compared to conventional radiotherapy, FLASH radiotherapy has the potential advantage of reducing the side effects to healthy tissues with the same tumour control . Such an effect has been observed in biological experiments conducted with electron and photon beams (Montay-Gruel et al 2018, Vozenin et al 2019). However, more experiments are required to verify possible protecting effects with proton beams (Beyreuther et al 2019, Colangelo and Azzam 2020, Hughes and Parsons 2020.
Technical challenges associated with the accelerator technology (e.g. beam current, energy, treatment time) limit the feasibility of the experiments with proton beams (Jolly et al 2020). Nonetheless, several studies have investigated possible strategies to overcome these challenges and retrofit facilities for biological experiments with UHDR protons (Patriarca et al 2018, Diffenderfer et al 2020, Lee et al 2022. Among these facilities, the Center for Proton Therapy (CPT) at the Paul Scherrer Institute (PSI, Switzerland) hosts a gantry recently commissioned to support pre-clinical FLASH studies with proton beams . Single pencil beams of 250 MeV can be delivered with average dose rates in the (1-9000) Gy s −1 range.
The narrow width of the pencil beam (Gaussian sigma <5 mm) is a challenge for the dosimetry of this beam, which adds to the requirements related to dose measurement at UHDR (Schüller et al 2020, Romano et al 2022. To address the challenges of dosimetry of such narrow proton beams, Togno et al (2022) have proposed to use a Faraday cup as a dose rate independent detector to monitor the delivered dose online. In that study, the Faraday cup was also employed to characterize the response of other detectors, such as a diamond detector and radiochromic films. While Kranzer et al (2022) demonstrated a dose rate dependence of the diamond detector in UHDR electron beams up to an instantaneous dose rate of 2.6 × 10 6 Gy s −1 , Togno et al (2022) showed a dose rate independence in the CPT UHDR proton beam up to an average dose rate of 2200 Gy s −1 . In the same study, the films were shown to be dose rate independent up to an average dose rate of 9000 Gy s −1 in the CPT UHDR proton beam.
Here one must be careful to distinguish between instantaneous dose rate and average dose rate, as most of the studies are performed with pulsed beams. At the CPT, for example, the instantaneous dose rate within a proton pulse is about 17 times higher than the average dose rate (see section 2.2.2).
Using the Faraday cup as a dose rate independent monitor, Christensen et al (2021) demonstrated the dose rate independence of Al 2 O 3 :C optically stimulated luminescence detectors (OSLDs) in proton beams and their applicability to narrow beams. The dose measurements with Al 2 O 3 :C OSLDs are highly reproducible (Yukihara et al 2008) and the OSLDs can be cut into sub-millimeter sizes to mimic the size of e.g. biological samples. However, since OSLDs are light sensitive, they need to be protected from light after irradiation.
Thermally stimulated luminescence detectors (TLDs) are an alternative to OSLDs for narrow proton beams dosimetry. TLDs have several advantages, amongst which are the widespread use in personal and medical dosimetry, wide dose linearity range, small size, low cost, high precision, and light insensitivity (Yukihara et al 2022).
Among the thermoluminescence materials, LiF:Mg,Ti remains widely used for clinical dosimetry. Its response has also been characterized in clinical proton beams (Sądel et al 2015, D'Avino et al 2020. Their small size makes them good candidates for dosimetry in narrow beams. LiF:Mg,Ti was shown to be dose rate independent up to 4 × 10 9 Gy s −1 in electron beams (Karsch et al 2012) and up to 6 × 10 5 Gy s −1 for photon beams (Zorloni et al 2020). In both studies, the reported dose rates are instantaneous dose rates. Nevertheless, to the best of our knowledge, there are no studies in the literature investigating the usability of LiF:Mg,Ti for dosimetry of proton beams delivered at UHDR. Compared to electron and photon irradiations, the response of the TLDs in proton beams is affected by the higher ionization density (Horowitz 1984, Olko et al 2004.
Therefore, this work aims at characterizing LiF:Mg,Ti TLDs in the UHDR proton beam delivered at the CPT. Specifically, we investigated possible dose rate effects in LiF:Mg,Ti, as well as the usability of this material for dosimetry of narrow proton beams.

Materials and methods
2.1. TLD-100 TM detectors LiF:Mg,Ti (TLD-100 TM ) was used in the form of Microcubes (1 mm × 1 mm × 1 mm, Harshaw Chemical Company, Cleveland, OH, USA). Before irradiation, the detectors were annealed at 400°C for one hour and 100°C for two hours in two separate muffle furnaces (models F48020-33-80 and FB1310M-33, Thermo Scientific Thermolyne) and afterwards cooled down at room temperature on a metal plate.
Matrices of 5 × 5 detectors were employed for all measurements. The matrices were packaged in 3D-printed cylindrical holders made of polylactic acid (PLA, polyester with a density of 1.24 g cm −1 ), specifically designed to fit the experimental setup and to minimize the sample motion (figure 1). A 0.5 mm thick PLA layer was used as a cover.
The detectors were read starting one day after the irradiation using a Lexsyg Smart automated reader (Freiberg Instruments GmbH, Freiberg, Germany) equipped with a UV-VIS PMT (model 9235QB, Electron Tubes Inc.), a 90 Sr/ 90 Y beta source (1.53 GBq activity on 6 February 2018, Eckert and Ziegler, Germany), and various optical filters. For readout, the samples were heated up to 400°C at a heating rate of 5°C s −1 . The 'IRSL/ TL-410 nm' filter combination (Schott BG39 + Semrock HC 414/46) was selected for the detection of the signal from the detectors irradiated at doses <5 Gy and the 'BSL, TL-365 nm' filter combination (Hoya U340 + Delta BP 365/50 EX) for higher doses. These filters were chosen to maximize the detection of the emitted photons (TL emission centered at 410 nm, McKeever et al 1995), without saturating the PMT.
For each sample, the readout protocol consisted of the sequence: 1. Thermal stimulation of the detector irradiated in the proton beam to obtain the signal S.
2. Reference irradiation of the detector with the built-in beta source in laboratory (1 s, ∼50 mGy).
3. Recording of the TL curve after the reference irradiation to obtain the signal S R .
For steps 1 and 3, the recorded TL curves were fitted with first-order TL peaks (Randall andWilkins 1945, Horowitz andYossian 1995), and the area under peaks 4 and 5 was chosen as the dosimetric signal (the peak numbering refers to figure 2). The ratio S/S R was hence calculated for each TLD. As reported in Yukihara et al (2005) for the case of Al 2 O 3 :C OSLDs, this protocol eliminates the dependency of the dosimetric signal on the dosimeter mass, dosimeter sensitivity, and reader sensitivity.

TLD-100 TM Microcube detectors calibration
The calibration of TLD-100 TM Microcube detectors was carried out with the Lexsyg Smart 90 Sr/ 90 Y beta source by irradiating the samples at different irradiation times and recording the signal S. Then, the samples were irradiated again for 1 s and subsequently read out to acquire the reference signal S R . Five annealed detectors were used per irradiation time. Given the wide range of delivered doses in the UHDR irradiation, two calibration curves were determined for the two different detection filter combinations. The irradiation time was varied in the (2-100) s and (20-500) s intervals for the low dose and high dose ranges, respectively.  To establish the calibration coefficient from irradiation time to proton absorbed dose to water, the TLDs were irradiated in a well-characterized clinical proton beam at CPT at different doses. The maximum achievable beam energy in this gantry is 230 MeV. Groups of five annealed detectors packaged into plastic bags were irradiated in a 10 cm × 10 cm proton beam of 230 MeV, together with an Advanced Markus chamber (PTW-Freiburg GmbH, Freiburg, Germany). The chamber was calibrated in absorbed dose to water with a 60 Co source at the Swiss Federal Institute of Metrology METAS. The delivered doses were 1 Gy for the low dose calibration curve and in the (1-20) Gy range for the high dose calibration curve.

Proton irradiation at ultra-high dose rate
The UHDR irradiations were performed at CPT with a single pencil beam delivered at 250 MeV, in a gantry devoted to pre-clinical studies for FLASH radiotherapy . The gantry was optimized to deliver the undegraded 250 MeV proton beam from the COMET accelerator and, therefore, to maximize the beam current and dose rate , Togno et al 2022. The COMET cyclotron generates 0.8 ns long proton pulses with a pulse repetition frequency of 72.85 MHz. Hence, a pulse is delivered every 14 ns. The dose rate reported in this work is an average value, calculated as the ratio of the total delivered dose measured by a diamond detector (microDiamond, PTW-Freiburg GmbH, Freiburg, Germany, with 1.1 mm radius) and the total delivery time (time between the first and the last pulse) measured by the control system. Given the pulse duration and frequency, the instantaneous dose rate within a pulse is about 17 times higher than the average dose rate.
The proton pencil beam is characterized by a double Gaussian lateral profile. In this work, we refer to the beam sigma (σ x , σ y ) to describe the beam lateral spread.
The experimental setup consisted of a 5 cm thick PMMA phantom placed 50.2 cm from the nozzle on the treatment table, as shown in figure 3. The phantom has 12 cylindrical holes to accommodate detectors or biological samples. The 3D-printed cylinders, containing the TLD matrices, were inserted in the phantom holes (figure 1), with the center of the matrix aligned with the beam axis. Additionally, a 2.2 cm PMMA slab was placed upstream of the phantom for build-up and 0.8 cm PMMA cylinders behind the TLD packages.
Each TLD matrix was irradiated with an average dose rate in the (1-4500) Gy s −1 range. Three beam configurations were used to obtain the dose rates delivered in this study. For dose rates lower than 1200 Gy s −1 , the beam was degraded by means of three polystyrene range shifters and the dose rate was varied by changing the beam current. With this setup, the beam spread at the detector position was σ x ≈ σ y ≈ 5.1 mm, where x and y denote the horizontal and vertical directions, respectively. For dose rates in the (1200-3300) Gy s −1 interval, the range shifters were removed and the experimental setup was moved 30 cm closer to the nozzle to obtain a narrower beam (σ x ≈ 3.1 mm, σ y ≈ 3.7 mm), which resulted in a higher dose rate. To further reduce the beam spread to σ x ≈ 1.4 mm and σ y ≈ 1.9 mm, in addition to the removal of the range shifters and the reduction of the distance from the nozzle, the magnet settings were varied and the highest dose rate (∼4500 Gy s −1 ) was achieved. Due to the chosen setups, the beam energy at the nozzle varied between 244.4 MeV (three range shifters inserted) and 250 MeV (no range shifters).
The microDiamond was inserted into the PMMA phantom by means of a dedicated holder and used as reference detector for the determination of the delivered dose and dose rate. The detector calibration and characterization in UHDR proton beam is described in Togno et al (2022). The microDiamond was also employed for the beam alignment, such that the beam axis corresponded to the detector axis. Additionally, Gafchromic® EBT3 films (Ashland ISP Advanced Materials, Kearny, NJ, USA) were placed behind the build-up slab, upstream of the TLDs, to measure the beam profile for certain dose rates. The EBT3 film evaluation is described in Togno et al (2022). A Faraday cup, placed downstream of the experimental setup (figure 3), was used as reference dose rate independent detector to measure the delivered number of protons (Lin et al 2009, Winterhalter et al 2021. The proton charge measured by the Faraday cup was used to normalize the detector responses at the different dose rates. While the TLDs were calibrated in a clinical proton beam with a maximum energy of 230 MeV, the irradiations at UHDR were carried out at higher energies with a maximum of 250 MeV, corresponding to the undegraded beam, to maximize the beam current and, therefore, the dose rate. However, both in the calibration and in the UHDR irradiations, the detectors were positioned at the entrance region, where the linear energy transfer (LET) variation across the detectors is negligible. For the investigated energies, no corrections for quenching are needed (Zullo et al 2010, Olko andBilski 2020). Therefore, the results reported in this work are valid only for the entrance region (low LET) of the proton beam. For measurement in the Bragg peak region, the variation of the detector efficiency needs to be accounted and distinguished from possible dose rate effects.
A 4 Gy dose was delivered in each irradiation except for the highest dose rate, where the dose was 18 Gy, as the shortest possible delivery time was limited to about 2 ms. In each irradiation session multiple dose rates were delivered. For each investigated dose rate, two to six independent irradiations were carried out, with one TLD package per irradiation.

Signal averaging evaluation
Given the beam spot size reduction at increasing dose rate, the effects of the beam averaging over the volume of the TLD-100 TM Microcube detector and of the reference microDiamond detector were investigated. At the highest dose rate, the beam spread (sigma) is comparable to the detectors size (1 mm side for TLD-100 TM and 1.1 mm radius for microDiamond), which results in a volumetric averaging of the signal and consequently a discrepancy between the measured dose and the beam central dose. To simplify the study, a uniform energy deposition in the detector depth was assumed and, therefore, the averaging effects were investigated over the detector surface.
To evaluate the averaging effects, the beam shape is approximated by a two dimensional Gaussian model (Togno et al 2022), with beam spread (σ x , σ y ), center (x 0 , y 0 ) and central dose (D center ), corresponding to the peak dose. The proton fluence Φ across the detectors can be described as , 1 x y x y The integral in equation (3) was calculated both for the TLD-100 TM Microcube and the microDiamond, and for the measured beam spread corresponding to the investigated dose rates. Since no EBT3 films were used in the irradiations at 100 Gy s −1 , a beam sigma of 5.1 mm was considered. For 1 Gy s −1 , the beam sigma measured by EBT3 films in another experiment was used. Two limiting cases were considered: the beam impinging on the detector center and at the detector edge, which give the smallest and largest volumetric averaging, respectively.

Beam shape estimation
At the highest dose rate, a beam reconstruction procedure was applied to the TLD matrices to determine the beam parameters introduced in section 2.3, beam central dose D center and spread (σ x and σ y ), based on the procedure developed by Christensen et al (2021). In this procedure, the response of each TLD was calculated from equation (3), where D center , (σ x , σ y ), and (x 0 , y 0 ) were free parameters to be fitted. The best estimate of the beam parameters was found by minimizing the sum of the squared differences between the measured and the calculated TLD doses. The obtained beam spread was then compared to the measurement with EBT3 films. Such procedure was not applied to the matrices irradiated at lower dose rates, because the matrix size is comparable to the beam sigma and therefore the 25 detectors are not sufficient to reconstruct the beam profile.

Detector response definition
To investigate the response of the TLDs, as well as the reference detectors, as a function of the dose rate, the measured beam central dose (D center ) was considered.
For the TLDs, the beam central dose corresponds to the maximum of the TLD matrix for the packages irradiated at dose rates <4000 Gy s −1 , and the fitted central dose at the maximum dose rate. For the microDiamond, the beam central dose is estimated based on the measured dose corrected for the averaging effects, as outlined in section 3.2. For EBT3 films, the measured beam central dose was considered, as determined by fitting a two dimensional Gaussian to the film dose matrix.
To compare the independent irradiations, the detector dose response was divided by the charge measured by the Faraday cup. Since the variation in the beam spot size with the dose rate affects the maximum particle fluence and hence the beam central dose by a factor ( · ) s sx y 1 (see equation (2)), the detector response η was defined as . 4 x y center,det FC The beam spread measured by the EBT3 films was used, while a value of σ x = σ y = 5.1 mm was assumed for the irradiation at 10 Gy s −1 . For repeated measurements at the same dose rate, the EBT3 films were employed only in one session, therefore only one beam spread data is available for each dose rate. The detector response η was then studied as a function of the dose rate. All the reported uncertainties were given for a coverage factor k = 1. For the TLDs and the EBT3 films, only type A uncertainties (standard deviation of the data) were considered. The microDiamond uncertainty (0.9%) included the reproducibility and the uncertainty on the calibration.

Calibration curve
The calibration curves are shown in figures 4(a) and (b) for the low dose and high dose intervals, respectively. In the figures, each point shows the average response of the five samples irradiated at the same irradiation time, while the error bars show the standard deviation of the data. A quadratic function was fitted to the data as shown in figures 4(a) and (b).
The use of the ratio S/S R eliminates the variations of the detector sensitivity, which are responsible for the larger standard deviation of the signal S (∼11%) compared to the signal S/S R (<5%). As the obtained residuals are within ±3%, the S/S R experimental data are well represented by the quadratic model.
The absorbed dose to water in figure 4 was obtained using a calibration coefficient, calculated as the average value of the ratio between the delivered dose measured by the Advanced Markus chamber and the built-in source irradiation time corresponding to the measured S/S R signal. The obtained calibration coefficients are (45.6 ± 1.5) mGy s −1 and (48.9 ± 1.2) mGy s −1 (coverage factor k = 1), for the low and high dose ranges, respectively. The difference in the obtained calibration coefficients is due to the different filters employed for the detector readout in the low dose and high dose ranges.

Signal averaging in TLD-100 TM Microcube detectors and microDiamond detector
The results of the signal averaging evaluation for the microDiamond and the TLD-100 TM Microcube are shown in figures 5(a) and (b), respectively. The points represent the calculated measurable signal, while the lines serve to guide the eye. The measurable signal, namely the ratio D D det center from equation (3), was derived from the beam spread measured by EBT3 films and for the beam impinging on the detector center or on the edge.
Given the beam spot asymmetry at dose rates higher than 2000 Gy s −1 , the integral at the microDiamond edge was calculated both for (x 0 , y 0 ) = (0, R) and (R, 0), where R denotes the detector radius. For the TLD, the edge case corresponds to the beam impinging on the detector corner.
For dose rates lower than 2000 Gy s −1 , corresponding to the largest beam size, the signal averaging causes an average discrepancy of ∼3% and ∼1% for the microDiamond and the TLD, respectively. At the highest dose rate, where the beam is narrower, the discrepancy can be as high as ∼30% (microDiamond) and ∼12% (TLD), when the beam hits the detector edge.
To account for the averaging effects in the microDiamond, the detector response at all dose rates was corrected by the factors calculated for (x 0 , y 0 ) = (0, 0) only, as the microDiamond was employed for the beam alignment. For the TLD, as the discrepancy between the measured dose and the beam central dose is <2% at all dose rates lower than 3000 Gy s −1 , no corrections were introduced. Therefore, for dose rates lower than 4000 Gy s −1 , the maximum dose of the TLD matrix was assumed to be the beam central dose. At the highest dose rate, the beam central dose was determined with the beam reconstruction procedure outlined below.

Beam reconstruction
The beam reconstruction procedure described in section 2.4 was applied to the three TLD matrices irradiated at 4500 Gy s −1 . The dose maps are plotted in figures 6(a)-(c) together with the residual maps in figures 6(d)-(f) (relative difference between the measured and the calculated dose of each TLD). In the figure, the TLD matrix is represented by the solid grid, while the red dot indicates the center of the beam profile, whose contour lines are shown by the black dashed lines. The maps show that, as expected from the EBT3 film measurements, the beam is not circular, but elongated in the vertical direction. The largest discrepancies between the calculated and the measured doses are observed at the corners, which correspond to the Gaussian tails.  Figure 10. The TLD response compared to that of the reference detectors (microDiamond and EBT3 films) as a function of the dose rate. The data are normalized to the average response of TLD-100 TM Microcubes. The dashed yellow line represents the average response of the microDiamond and the red dotted line the EBT3 films one. The order of the symbols follows the irradiation session numbering. The data relative to one dose rate in an irradiation session were offset (±10%) to help the reader distinguish the data and the uncertainties.
The beam spread (σ x , σ y ) obtained from the fit was compared to the measurements with the EBT3 films, irradiated simultaneously with the TLDs. The results are shown in figure 7 for the three irradiations at 4500 Gy s −1 . The beam sigma derived from the fit agrees with the measured one within 0.1 mm. The maximum deviation (4%) is observed for σ x measured in the irradiation 3. The agreement between the TLD and film derived spot sigmas shows how the TLD matrix and the Gaussian fitting procedure can be employed to determine the beam spread for narrow proton beams.
The fitted beam central dose (D center ) derived from the beam reconstruction was compared to the maximum dose of the TLD matrix (D max ), to verify the signal averaging effects induced by the narrow beam spread. The results are shown in figure 8, where the TLD dose is divided by the charge measured by the Faraday cup, to compare the three independent irradiations at the same dose rate. Due to signal averaging, the maximum dose is not constant in the three irradiations, and a maximum deviation of 9% form D center is observed in the irradiation 3. Indeed, as shown in figure 5, a variation in the relative position TLD-beam axis may induce an underestimation of the beam central dose as high as 12%. Due to the better estimation of the true beam central dose, the TLD signal at 4500 Gy s −1 was assumed to be D center , derived from the beam reconstruction, instead of D max as for the other dose rates.

Dose rate effects
To investigate possible dose rate effects in LiF:Mg,Ti, the detector response η was studied as a function of the dose rate. For each dose rate, the average and the standard deviation of the TLD signal η were calculated. A 4% uncertainty on the delivered dose rate was also included. Figure 9 shows the dose rate response of TLD-100 TM Microcubes, normalized to the average of all data points, and grouped by the irradiation session. In the figure, the blue band covers the k = 1 standard deviation of the data around the mean (dotted line). The data are scattered around the average value with a maximum deviation of +5% at 10 Gy s −1 and −5% at 4500 Gy s −1 .
Given the uncertainties in the data, no dose rate effects are observed in LiF:Mg,Ti for the investigated dose rates. For the highest dose rate, 4500 Gy s −1 , the TLD response is −5%, but one can observe that all TLDs irradiated in the same session (triangles in figure 9) but with different dose rates (1, 100, 3000) Gy s −1 showed a lower response and are not statistically different.
The response of the TLDs was then compared to the microDiamond and the EBT3 film signals. As described in section 3.2, the beam center dose of the microDiamond was obtained by correcting the measured dose for the averaging effects.
The comparison of the different detectors is shown in figure 10, where all detector responses were normalized to the average response of the TLDs. The different detectors agree within their uncertainties. The maximum deviation (−7%) of the TLDs from the reference detectors was measured at the highest dose rate. Such deviation can be due to the fitting procedure or to the calculated correction factor of the microDiamond. On average, the response of the TLD-100 TM Microcubes coincided with the response of the microDiamond, while a 1.4% discrepancy was measured with EBT3 films.
The precision in the measurement of the beam spread affects the precision of the dose rate response of the investigated detectors. To reduce the spread of the detector responses as a function of the dose rate, it would be necessary to measure the beam spot size at each irradiation, simultaneously with the investigated materials. Indeed, a variation of the beam spread in separate irradiation session was measured by Togno et al (2022), who showed that variations up to ±3% of the beam spread can lead to a 6% under-or over-estimation of the beam central dose.

Conclusions
The results of the investigations on possible dose rate effects in LiF:Mg,Ti (TLD-100 TM Microcubes) at ultrahigh dose rate narrow proton beams showed that volume signal averaging needs to be taken into account, if the beam central doses (and, consequently, dose rate effects) are to be correctly evaluated. This can be done either by estimating the correction factor based on the beam spread and detectors sizes, or using a matrix of TLDs and applying a beam reconstruction procedure.
Correction factors for volume signal averaging calculated for the TLD-100 TM Microcubes based on the lateral Gaussian profile of the proton beam were in the range between 1% at 1 Gy s −1 and 12% for the narrowest beam at 4500 Gy s −1 , depending on the beam alignment relative to the detector center. The obtained correction factors are applicableif the beam center hits the detector.
For the narrowest beam, corresponding to the highest dose rate, more robust results were obtained using the beam reconstruction procedure applied to a matrix of 5 × 5 TLDs. This procedure allowed to determine the dose at the beam center and the beam spread, in agreement with the results of the EBT3 films within 4% at 4500 Gy s −1 .
Additionally, LiF:Mg,Ti was shown to be dose rate independent up to 4500 Gy s −1 and in agreement with the reference detectors within their uncertainties.
The results demonstrate the applicability of LiF:Mg,Ti for dosimetry of ultra-high dose rate proton beams, even for pencil beams down to a beam spread of 1.4 mm (Gaussian sigma). The TLD-100 TM Microcubes small size makes them suitable to support biological experiments for FLASH effects.
Nevertheless, the investigation was carried out at proton energies where the ionization quenching can be neglected. To extend the study to the Bragg peak region it is necessary to take into account the effects of higher ionization densities, which result in a supralinear and then sublinear response of LiF:Mg,Ti with increasing proton LET. Such effects need to be distinguished from possible dose rate effects.