The experiments were carried out at the Metrological Electron Accelerator Facility (MELAF) [33] of the German National Metrology Institute, PTB. The facility provides a research linear accelerator (commissioned in 2012) for research in dosimetry for radiation therapy which features increased intensity for ultra-high DPP and considerably larger energy ranges (0.5–50 MeV) than conventional medical accelerators (typically 4 to 22 MeV). The accelerator provides a pulsed beam with about 2.5 μs pulse width. All irradiations reported in this work were carried out with 5 Hz pulse repetition frequency.

The research electron accelerator works on the same principle as medical accelerators but is equipped with beam line instrumentations for a precise characterization of the beam parameters. For the accurate determination of the energy, a magnetic spectrometer is used. As a non-destructive beam current monitor an Integrating Current Transformer (ICT) from Bergoz (in-flange version, windings ratio 50:1) is integrated in the beamline. The beam pulse charge can be typically varied in a range from 1 to 150 nC. The precision for the measurement of the charge of a single beam pulse is +/- 0.015 nC (k = 1) [34], i.e., for pulses > 10 nC that were mainly used in this work, the contribution to the uncertainty of the measured pulse charge is <0.15%. The profile of a typical beam in the beam line has a Gaussian shape with a FWHM of about 4 mm [34]. At the end of the beam line the electrons pass through a vacuum window consisting of a 0.1 mm thick Cu foil which scatters the beam. The diameter of this beam exit window is much larger (diameter > 3 cm) than the width of the beam, thus all electrons detected by the ICT contribute to the radiation field.

The ion collection efficiency of a plane-parallel Advanced Markus ionization chamber (PTW, type 34045, s/n: 1279) in an ultra-high DPP beam of up to 2.5 Gy/pulse was investigated. The chamber was placed in a 30 × 30 × 30 cm water phantom with 2 cm thick poly-methyl methacrylate (PMMA) walls and a 0.3 cm thick PMMA entrance window, positioned 70 cm in front of the beam exit window (see Figure 1). The chamber was mounted on a precise motorized 3D positioning system which allowed for controlled longitudinal movement of the ionization chamber along the central beam axis for depth dose measurements and controlled lateral movement to determine a cross-sectional dose distribution of the radiation field.

A 24 MeV electron beam was used. The chosen energy is not important for the comparison of the dosimeters. However, with higher energies higher DPP values can be achieved. In addition, the depth dose curve has a flatter slope with larger penetration depth, so the measurement position is less critical.

For the read-out of the ionization chamber, an analog electrometer (Keithley 616) was used in the current mode. The reading, M, of the electrometer returned via an output voltage was recorded by means of a 16-bit analog-to-digital converter and analyzed by in-house-developed software. A calibrated current source (Keithley 6430) was used to calibrate the electrometer with its read-out system. The Advanced Markus chamber was calibrated at PTB's ⁶⁰Co reference field in terms of absorbed dose to water traceable to the PTB's primary standard water calorimeter [35]. The conversion of the ionization chamber signal to absorbed dose to water followed the German protocol DIN 6800-2 [30]:

where NCo60,Dw′ is the calibration factor of the detector with respect to ⁶⁰Co radiation, M is the reading of the dosimeter corrected for the reading without irradiation M₀, k_E is the quality correction factor accounting for the difference in the detector's response between ⁶⁰Co radiation and high-energy electron radiation, and k_S is the correction factor for ion recombination. The factors k_pol and k_TP take into account the polarity effect and effects associated with the ambient conditions, respectively.

The radiation quality correction factor k_E can be determined with lowest uncertainty at the reference depth z_ref. Thus, the chamber was positioned there. The reference depth depends on the radiation quality index R₅₀ which was determined according to DIN 6800-2 [30] from the measured depth dose distribution. For the current setup end energy, z_ref was found to be 5.5 cm. Air pressure and temperature as well as the polarity effect were measured for k_TP and k_pol. The response of the chamber without taking into account any ion recombination correction factor D_w/k_S was determined applying Equation 2 without k_S. The DPP reference value was determined from the charge per beam pulse measured by means of the ICT, calibrated using alanine dosimeters positioned at the same position (z_ref) as the chamber.

Reference dose measurements were performed using cylindrical alanine pellets with a diameter of 5 mm and a height of 3 mm. The alanine pellets were irradiated to an approximate dose of 14 Gy at different charge per beam pulse values. The charge of each beam pulse was recorded by means of the ICT. For the highest used pulse charge (~120 nC) only 6 pulses were irradiated, for the lowest (~2 nC) 463 pulses were irradiated.

For each different charge per pulse setting, a stack of eight alanine pellets were irradiated simultaneously in a PMMA tube positioned in the water phantom at z_ref instead of the ionization chamber (see Figure 1) with the rotational axis of the stack perpendicular to the beam central axis. The dose response of alanine is known to depend on the temperature during irradiation (0.19%/°C) [36]. Thus, enough time (~10 min) was allowed for the alanine pellets to achieve temperature equilibrium in the water phantom. The temperature T of the water phantom was close to the reference temperature T₀ = 293.15 K. It was measured during irradiation using a Pt100 platinum resistance temperature sensor.

Ionizing radiation produces stable free radicals in alanine, which can be detected via electron spin resonance (ESR). The irradiated alanine pellets were read out using a Bruker EMX 1327 electron spin resonance (ESR) spectrometer at PTB. The alanine/ESR dosimetry system was calibrated at the ⁶⁰Co reference of the PTB. Thus, the alanine dose measurement is traceable to PTB's primary standard water calorimeter [35]. Uncertainties of 0.4–0.6% (k = 1) were reached for ⁶⁰Co radiation in the range of 5–25 Gy [36]. The methodology at PTB's alanine/ESR dosimetry system is standardized and extensively tested. Further details of the methodology can be found elsewhere [36–38]. A correction factor k_T = 1 – c_T · (T – T₀) for the temperature during the irradiation was applied, where the temperature coefficient c_T = (1.9 ± 0.2) 10⁻³ K. The relative uncertainty of k_T is 0.04%. A beam quality correction factor kEAlanine=1.012 (the equivalent of k_E for an ionization chamber) was applied for the used 24 MeV electron beam [38]. This factor does not depend on energy in the range of 6–22 MeV and is thus assumed to be valid for 24 MeV as well [39]. The relative uncertainty of kEAlanine is 1%. The absorbed dose to water determined from the alanine measurements was then used to cross-calibrate the ICT in terms of a dose per beam pulse charge in order to have a reference at the investigation of the ionization chambers response.

The majority of primary standard absorbed dose calorimeters have been optimized for operation at standard therapy dose rates, to measure a dose of around 2–4 Gy delivered over a period of 1–2 min. The radiation-induced temperature for such a delivered dose is of the order of mK and therefore complex calorimeter systems have been developed. The most common absorbing mediums are water and graphite and for either medium, thermal isolation (and hence long thermal time constants) is very desirable to minimize the corrections required for conductive heat loss. For a review of absorbed dose calorimetry see Renaud et al. [40].

FLASH delivery is very different from the irradiation conditions that these calorimetric standards have been designed for, and this means that a more flexible design is required, not tailored to a specific beam output (calorimeters should be applicable to electron, proton, and photon beams with ultra-high dose rates). Also, the ultra-high DPP (and hence high total dose delivered in a short time) means that thermal isolation is not such a constraint and a simpler design can be employed.

Calorimeters have been used for high dose rate measurements for the dosimetry of radiation processing beams [41] but there has been little investigation of few-pulse irradiations to date.

The calorimeter used in this investigation is an open-to-atmosphere aluminum calorimeter, whose design can be traced back to a graphite calorimeter developed at the NPL for industrial processing dose measurement [42]. In contrast to the more common graphite calorimeters used in a number of primary standards laboratories, the specific calorimeter employed here uses aluminum as an absorber material, which was chosen because a number of previous investigations had indicated that the granular nature of bulk graphite leads to inhomogeneities and impurities that can be difficult to quantify. Aluminum, in contrast, is obtainable in a very pure, highly homogenous form.

The calorimeter design is shown in Figure 2. The main features of the calorimeter are: a core of 21.7 mm diameter and 2.01 mm thickness of 99.999% aluminum; thermal isolation provided by a 1 mm air gap on all sides; the absorber is kept in position by a space constructed of a silica-based aerogel (Airloy®X103M, Aerogel Technologies, LLC), which is only in contact with the absorber at the edges of the aluminum disc. A pair of thermistors in series, combined with an AC bridge, are used to determine the radiation-induced temperature rise [43], for details see Bourgouin et al. [44] which used the same measurement system with an earlier calorimeter design. The outer parts of the calorimeter are constructed of 6061 aluminum alloy for ease of machining and reduced cost, only the core and the jacket are pure aluminum. The entire aluminum assembly is enclosed in expanded polystyrene foam (density 0.028 g/cm³) to provide thermal isolation from the environment.

Equation 1 also shows that the absorbed dose determined by a calorimeter is dependent on the medium used to absorb the energy and therefore a correction is required to convert it from the absorbed dose to the calorimeter medium to the equivalent absorbed dose to water value. This correction is independent of DPP and is usually calculated using Monte Carlo techniques (see e.g., [45]). In this initial investigation an approximated conversion factor from aluminum to water was used for presentation purposes, determined by averaging the mass restricted collisional stopping power ratio over the calculated energy spectrum yielding the relation D_w = 1.23 D_Al.

The specific heat capacity c in Equation 1 is independent of the dose rate and is assumed to be constant during the measurement as the temperature rise is of the order of a few mK. Both radiation field perturbation and beam non-uniformity correction factors are calculated here using Monte Carlo radiation transport techniques. These correction factors are dependent on the radiation beam energy and field size/shape. The heat loss correction factor is calculated here using finite element methods (FEM) using an energy map derived from a 2-D or 3-D dose distribution obtained from a Monte Carlo simulation. The heat loss correction factor is dependent on the radiation time [44] but independent of the dose rate. It was assumed that aluminum exhibits no heat defect (i.e., any radiochemical reactions have no significant impact on the radiation-induced temperature rise).

The calorimeter was positioned at a distance of 0.9 m from the beam exit window of the accelerator (Figure 3). The pencil electron beam was broadened by a double scattering foil system consisting of the copper foil of the vacuum exit window and a 1 mm thick disk of aluminum positioned 3.5 cm away on the beam central axis. A 10 × 10 cm standard clinical electron applicator from an Elekta Precise linear accelerator was used in order to generate a square radiation field with an approximately parabolic radial profile within the center portion. The radiation field was shaped to be similar to that from a previous experiment with this calorimeter [44], so that the existing simulations for field perturbation and beam non-uniformity correction factors were suitable.

The electron energy used for the investigation of the response of the calorimeter was 50 MeV. The choice of energy is somewhat arbitrary for the investigation where the focus is varying the DPP, but a very high energy provides a flatter depth-dose curve and therefore a more uniform temperature environment for the calorimeter core. For the measurements in the ultra-high DPP range 10 beam pulses were delivered within 2 s to the calorimeter while the charge of each beam pulse was measured simultaneously with the ICT. The pulse charge, and thus the DPP, was varied between 5 and 45 nC per pulse (0.3–1.8 Gy per pulse). The measurement was repeated five times for each pulse charge setting.

The radiation field from the research accelerator is not flat, as is typical for a clinical linear accelerator, and without any electron dual scattering foil systems [46, 47] for electron beam flattening (as used in the second experiment with the calorimeter) the radiation field shows a Gaussian shape (Figure 4). There is good agreement between the relative lateral ionization measurement with the Advanced Markus ionization chamber and the alanine measurements at different DPP. Both detectors average over a comparable range of the dose gradient (alanine 3 mm, ionization chamber 5 mm). For the determination of the absolute dose at the central beam axis (the position of the ionization chamber during the k_S determination) a 2nd order polynomial function was fitted to the alanine datapoints and the maximum at lateral position 0 was taken.

Figure 5 shows the dose per beam pulse (gray squares) determined this way as a function of the charge per beam pulse measured simultaneously by means of the ICT. The linear fit of the alanine data is used as the calibration function for the determination of the actual DPP at the position of the sensitive volume of the Advanced Markus ionization chamber from the measured beam pulse charge.

The blue dots in Figure 5 show the dose per beam pulse measured with the Advanced Markus ionization chamber at a 300 V operating voltage without taking into account any ion recombination correction factor Dw,pulseIC/kS as a function of the charge per beam pulse. The deviation from the dose per pulse reference Dw,pulseref measured by means of the ICT calibrated with alanine increases with the increasing charge per pulse/increasing dose per pulse. The blue dashed line represents the fit function given in Ref. [13] by Petersson et al. for experimentally determined k_S values for the Advanced Markus chamber at 300 V from, among others, comparison with radiochromic film measurements. This function is kS=(1+(Dw,pulseref/300)2.5)0.144, where Dw,pulseref is expressed in mGy.

At 1.5 Gy/pulse (as applied for the first treatment of a human with FLASH radiotherapy) the ion recombination correction amounts to 79%. The measurement uncertainty is therefore dominated by the uncertainty of the k_S factor and thus an uncertainty of the dose measurement comparable to those reached at conventional radiation therapy (<2%), seems not possible with this ionization chamber type.

A typical calorimeter temperature-trace recorded in this work is shown in Figure 6. The radiation-induced temperature rise, ΔT, is obtained by linearly extrapolating the pre- and post-irradiation traces to the center of the irradiation time as illustrated. The difference in the gradient of the pre- and post-irradiation traces is due to the relatively poor thermal isolation of the calorimeter, but this does not have a large effect on the accuracy of the results since the irradiation time is relative short compared to the heat transfer time constant. The good signal-to-noise ratio indicates that the calorimeter is sensitive enough to also measure a single pulse at ultra-high DPP. For a series of irradiations, the standard deviation of the temperature rise, normalized to the delivered beam charge, was typically 0.1%, comparable with primary standard calorimeters in electron beams (e.g., [48]).

There are variations in the post-irradiation gradient. These are random with respect to the DPP and therefore likely due to external environmental factors. The heat loss is significantly larger than for a water calorimeter, primarily due to the high thermal conductivity of the aluminum and the simple thermal isolation of the calorimeter core. However, the time constant for the heat loss is an order of magnitude larger than the irradiation time and therefore the calorimeter can be considered to be operating in a quasi-adiabatic mode. The heat loss correction, k_ht, is therefore small (<0.5%) and does not impact the overall uncertainty in the calorimeter dose determination.

The results for the calorimeter measurements (Figure 7), for measurements carried out on two different days, show that there is good repeatability between the two sets of measurements and that there is a linear relationship between the calorimeter dose and beam pulse.

The deviation of the calorimeter response from the linear fit function shown in Figure 7 was generally smaller than 0.5% (Figure 8). The bars in Figure 8 for the calorimeter represent only type A standard uncertainty for a sequence of 5 measurements in close succession with the same conditions and are therefore a measure of the short-term repeatability, not the actual uncertainty. The mean charge of the 10 delivered pulses are measured with absolute uncertainty of +/-0.005 nC, thus for the used pulse charges of more than 10 nC the uncertainty contribution is smaller than 0.05%. The uncertainty of the charge measurement is therefore probably not the main reason for the fluctuation of the values.

The deviations of the alanine dose measurements from the ICT calibration function shown in Figure 5, used as reference for the experiment with the ionization chamber, reveals a good linearity as well (squares in Figure 8). The corresponding bars in Figure 8 represent the statistical uncertainty contributions (k = 1) due to the variation in the homogeneity and mass as well as in the measured ESR signal of the alanine test pellets resulting in a relative uncertainty of 0.2% of the total dose measured with eight pellets. The absolute uncertainties for the delivered total doses (about 14 Gy) are ~30 mGy. The absolute uncertainty of the DPP increases with the DPP, since at low DPP about 500 beam pulses are needed to deliver 14 Gy while at the highest DPP only 6 pulses were irradiated to reach the same dose level. In the studied DPP range the deviation from the linear behavior is smaller than 0.5%. Good linearity was expected since the ICT signal was found to be linear with the pulse charge [34], the dose is proportional to the number of irradiated electrons and alanine is known to be independent of dose rate [19]. The data in Figure 8 indicate that the linearity of the calorimeter is comparable with the alanine dosimetry system.