Complementary dosimetry for a 6 MeV electron beam

Results in Physics 14 (2019) 102377

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Complementary dosimetry for a 6 MeV electron beam

T

D. Ticoş, A. Scurtu, M. Oane, C. Diplaşu, G. Giubega, I. Călina, C.M. Ticoş National Institute for Lasers, Plasma and Radiation, P.O. Box MG-36, RO-077125 Bucharest-Magurele, Romania

A R T I C LE I N FO

A B S T R A C T

Keywords: Electron beam Dosimetry Calorimetry Faraday cup Thermistor

Two methods for inferring the dose of the electron beam (EB) provided by the ALID-7 linear accelerator (LINAC) are compared. The main parameters of the electron beam are: energy 6 MeV , pulse duration 4 μs and frequency 53 Hz . The reference dosimeter is a graphite calorimeter built in-house, whose measured dose depends on the irradiation time. In order to modify the dose for a given irradiation time, the voltage applied on the filament of the electron gun is varied in the range 8–12 V. The calorimeter can provide reliable measurements (doses above 0.48 kGy ) for irradiation times sufficiently long (above 10 s) and for filament voltages where stable operation of the LINAC is achieved (above 9 V). The measured dose is compared with that deduced from measurements of the beam fluence given by a Faraday cup (FC), by taking into account the stopping power features of the electron beam into graphite. The electron beam charge per pulse measured at the exit of the LINAC is between 3.7 × 10−9 C at 8 V, and 2.4 × 10−7 C at 12 V. A good match is obtained particularly at 12 V, which is the typical operating filament voltage.

Introduction The effect produced in a material by ionizing radiation is quantified by the absorbed dose, the amount of energy absorbed in the mass unit [1]. Dosimetry is a well-established technique used to characterize and control an irradiation process. Several important aspects have to be taken into account in order to choose the adequate dosimetry system, such as its detection limit (i.e. its minimum and maximum dose rate), the radiation dose range, the dosimeter response to energy, the irradiation time, the temperature effect during the irradiation process, its stability, its spatial scale, resolution, price, etc. Dosimetry is essential for any irradiation facility but also for a routine control of the irradiation technology. There are many known dosimetry techniques for electron beams produced by a LINAC, which depend on many factors. In industrial applications, the use of electron beams requires medium to high dose measuring capabilities [2]. Among them we mention the dosimetry techniques based on calorimeters [3], radio-chromic films (RCF) [4–6], cellulose triacetate films [7], polyvinyl chloride [8,9], plane parallel chambers [10], single mode optical fibre [11,12], alanine and chemical solutions such as dichromate [13], Fricke [14], cericcereous[15]. Calorimetry is a dosimetry technique reliable in terms of dose measurement and relatively easy to implement [3,16–18]. With the advent of new radiation sources such as the laser-plasma particle accelerators new dosimetry methods were developed for beams that have particular characteristics such as very short pulse duration (tens of femtoseconds to few picoseconds), various energy distributions,

and low fluence [19]. As an example, the detection of electrons accelerated with ultra-intense lasers is very challenging [20]. A Faraday cup (FC) is often used for the characterization of short electron bunches which gives information about the total charge of the particles in the pulse. Other detection methods rely on the use of RCFs or LANEX fast screens scintillating detectors. On the long run one of the applications of femtoseconds electron and proton bunches is in radiation therapy [21–23]. It is of interest therefore to see how one can establish a correspondence between these different dosimetric techniques [24,25]. In the followings we comparatively describe the output of a calorimeter and a FC in an attempt to establish an equivalency between these two diagnostic techniques in the case of a pulsed EB with energy 6 MeV delivered by a LINAC. Methods and materials ALID-7 electron accelerator The LINAC ALID-7 was designed and built in the 80′s in our institute and was optimized for efficient X-ray generation and for nondestructive testing [26,27]. Since then the accelerator has been also used in diverse applications and research projects [28–30]. The LINAC is a traveling wave-type which uses microwaves in the S-band at 2.99 GHz propagating in a disk-loaded tube of about 2 m long. The microwaves are produced by a magnetron (model EEV-M5125) delivering 2 MW of power in pulses of 4 μs . The actual frequency may be slightly adjusted

E-mail addresses: dorina.toader@inflpr.ro (D. Ticoş), catalin.ticos@inflpr.ro (C.M. Ticoş). https://doi.org/10.1016/j.rinp.2019.102377 Received 18 February 2019; Received in revised form 21 May 2019; Accepted 21 May 2019 Available online 25 May 2019 2211-3797/ © 2019 Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/).

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working calorimeter reached this temperature, it was replaced with a cool one and new readings started at the ambient temperature of about 20 °C. The absorbed dose in the calorimeter is given by [3]

by tuning the magnetron’s cavity with the aid of a motor located onto the magnetron. An input mode transformer converts the radio-frequency mode TE01 propagating in a rectangular waveguide WR284 into a TM01 which is further transmitted into the accelerating structure. The electrons are injected into the structure from a diode type gun operated at 70 kV . Both diode gun and magnetron are powered by modulators which can deliver 86 kV at 16 A and 45 kV at 100 A , respectively. A triggering unit found in the control panel of the accelerator delivers pulses which synchronize and overlap the outputs of the magnetron and gun modulators. During operation, the remaining RF power left in the accelerating structure is coupled through an output mode transformer to a matched, water cooled load. The filament in the diode gun is driven incandescent by a small voltage obtained from a transformer coupled to the gun modulator [31]. The variable filament voltage (Uf =8–12 V ) is used in the present paper to control the magnitude of the accelerated EB current. In the initial design of ALID-7 the peak EB current was set to attain 100 − 130 mA at a variable pulse frequency between 50 and 250 Hz, giving an average current in time of several tens of μA . The actual obtainable EB current is much smaller due to inherent physical aging of the machine (i.e. of the power sources, integrity of the accelerating structure, etc). The typical operation frequency is now set at fpulse = 53 Hz .

Dcal = (T2 − T1 − Ta ) cG

Calorimetry is based on the determination of the energy deposited by the EB in the irradiated sample as heat through inelastic interaction with the sample material. A calorimeter is typically made of a low-Z material (graphite, polystyrene or water), a temperature sensor (thermistor), and a heat insulator disposed around the material absorber [3]. The heat is deduced indirectly by measuring the temperature variation of the calorimeter body and by knowing its heat capacity. Three identical calorimeters made of graphite that were built in-house were used for these measurements. Superfine isomolded graphite grade GR001CC with density 1.8 g/cm3 has been used [32]. The graphite disks were cut in the shape of a disk with 130 mm diameter, 18 mm thickness and mass m = 0.423 kg. The calorimeter was inserted into an insulating polystyrene box with size 300 × 300 × 100 mm that weighs 0.179 kg, as shown in Fig. 1. A thermistor made by Betatherm (NTC-model 10K3A542i) was inserted at the center of the graphite disk. It has a standard resistance of 10 kΩ at 25 °C. The temperature variation with resistance was approximated by a fit function with an error ≲ 0.1% in the range 20–60 °C [18]:

A − 273.15 ln(R) + B

(Sel / ρ )G

k

(2)

where T1 and T2 are the temperatures before and after irradiation, respectively, Ta is the temperature rise due to the influence of the irradiation facility components, cG is graphite’s specific heat, (Sel / ρ )W and (Sel / ρ )W are the mass stopping powers of electron beams at 6 MeV in water and graphite, respectively, and k is a calibration constant. In our experiment Ta was negligible, (Sel / ρ )W (Sel / ρ )W ≈ 1.13, k ≈ 1 while the dependence of heat capacity with temperature was taken as cG = 720.3 + 2.36T . This is somewhat higher than that of ASTM and other reports [3,33,34], however it is comparable with the measurement reported in [35]. The calorimeters were tested and calibrated against similar ones at the Institute of Nuclear Chemistry and Technology from Poland. The doses measured with the calorimeter are given in Table 1. For irradiation times ≳ 60 s the values are accurate and the fluctuations from shot to shot are low, as seen from the standard deviations σcal . The smallest recorded dose is 0.48 kGy at the low filament voltage Uf = 9 V and 60 s irradiation time. It is almost one order of magnitude lower than the dose obtained at Uf = 12V , the nominal operating range of the electron gun. The shortest time for which a dose could be obtained (0.57 kGy ) was 10 s. After 360 s the highest recorded dose was 28.88 kGy .

Graphite calorimeters

T (°C) =

(Sel / ρ )W

Faraday cup The Faraday cup (FC) can be used to determine the charge in the electron beam of a LINAC [36]. Given that the electron beam produced by the LINAC is pulsed, one can determine the total number of electrons per each pulse. Considering the area crossed by the electron beam one can deduce the fluence and the flux associated with each pulse. We used a RadiaBeam FC, model FARC-04, as shown in Fig. 2a), that can measure the charge of particles in the energy range 1–135 MeV. The Faraday cup produces a signal that is directly proportional to the electrical charge of the beam and can be visualized on the oscilloscope in real time. Example of pulses are given in Fig. 2b). The measured τ charge of a single pulse is QFC [C ] = τ ∫0 VFC (t ) dt / Z , where VFC (t ) is the pulse signal detected by the FC, τ [s] is the pulse duration and Z [Ω] is the impedance matched oscilloscope (in our experiment τ = 4 × 10−6s, Z = 50 Ω). The fluence considering the area AFC [cm2] of the collecting surface (the diameter of the FC is 26.2 mm ) is given by

(1)

el Q ΦFC ⎡ 2 ⎤ = FC eAFC ⎣ cm ⎦

where R (Ω) is the resistance and A = 3932 , and B = 3.98 are constants. The reading of the resistance was carried out with a digital multimeter Multimetrix, model DMM240, having 0.06% accuracy. In order to insure a stable operation of the thermistor and protect it from overheating, the maximum achievable temperature was set at ∼50 °C. Every time the

(3)

while the flux is

el ⎤ QFC = ψFC ⎡ ⎣ s·cm2 ⎦ eAFC τ

(4)

where e = −1.6 × 10−19 C . The size of the EB spot at the exit of the accelerator is roughly elliptical with axes 22 × 17 mm. The divergence of the beam is ≈ 6°. Electron charge, beam fluence and beam flux measurements are given in Table 2 for various values of the filament voltage that generates the free electrons in the accelerator. The measurements were carried out at the exit window of the electron accelerator. We notice that the charge per pulse drops dramatically with over one order of magnitude as the filament voltage is lowered from 12 V which is in the regular operating range, down to 8V where electron beam formation and acceleration becomes problematic. The standard deviation of the measured charge per pulse increases up to a level where the uncertainty approaches almost 40–50%, at this low filament

Fig. 1. Graphite calorimeter used at the Electron Accelerator ALID-7. 2

Results in Physics 14 (2019) 102377

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Table 1 Absorbed dose measured with the graphite calorimeter for different exposure times. Filament voltage (V)

Dose (kGy)

Irrad. time 10 s

Irrad. time 30 s

Irrad. time 60 s

Irrad. time 120 s

Irrad. time 240 s

Irrad. time 360 s

12

Average dose Standard dev.σcal Average dose Standard dev.σcal Average dose Standard dev.σcal Average dose Standard dev.σcal

0.57 0.02 – – – – – –

2.21 0.08 1.38 0.10 0.52 0.05 – –

4.49 0.19 2.57 0.23 1.08 0.12 0.48 0.03

9.28 0.30 5.47 0.30 2.41 0.13 0.88 0.10

19.47 0.28 10.50 0.25 4.02 0.28 2.03 0.11

28.88 0.32 15.12 0.31 7.31 0.49 2.83 0.18

11 10 9

voltage. Thus, operation in this point is not quite practical as the EB becomes unstable with a large inaccuracy in the charge and current readings, in spite of the fact that it delivers a beam with a low fluence.

ΦFC = QFC / Acal . The fraction of backscattered electrons is quite small ( 0.2%) and thus their contribution does not affect significantly the electron flux crossing the calorimeter.

Results and discussions

Dose measurements

Calorimeter dosimetry vs. Faraday cup fluence

The results for the highest filament voltages (Uf = 11 and 12 V ) are shown in Fig. 3. We can see that the accuracy of the dose given by the FC is based on several assumptions. First, we derive the average dose of a single pulse by taking into account 5 to 10 measurements of the fluence ΦFC . Then we calculate the error in this dose by considering the standard deviation of the measured charge σFC from Table 2. We extrapolate this result for a time interval which comprises a large number of pulses Npulse and consider that all pulses are identical in terms of delivered fluence. The obtained values are shown in Fig. 3a) and b) with continuous line. The calorimeter readings are shown with dashed line. The error in the dose converted from the FC signal increases linearly with time (i.e. with the number of pulses), as expected from Eq. (1). At Uf = 12 V the two methods provide very close results with 5% accuracy. At Uf = 11 V , the charge measured with the FC has large fluctuations from pulse to pulse, quantified by the standard deviation σFC = −2.47 × 10−8 C. This leads to a larger error in the FC dose as shown in Fig. 3b). On the other hand, the dose measured with the calorimeter has a much lower standard deviation (σcal from Table 1) as shown in Fig. 3 with error bars. The results for the filament voltages Uf =8 to 10 V are shown in Fig. 4. At Uf = 10 V the doses given by the calorimeter are within the errors range of the FC dose. However, we can see a deviation from the linear increase of the dose with time, in Fig. 4a). This is correlated with the increased σcal = 0.49 kGy . At Uf = 9 V the two methods provide results that differ by 30%. At Uf = 8 V the calorimeter could not provide reliable measurements as the dose is too small and the standard deviation is comparable with the measured values. Data is presented only for the FC, which gives a total dose 1.5 kGy after a 360 s

In order to establish a correspondence between the dose measured with the calorimeter and the fluence given by the FC we follow Attix’s approach [37]. We consider the that electron beam with incident energy T0 = 6 MeV crosses the graphite plate with thickness h = 18 mm . It appears that at this energy the range of electrons in the continuously slowing down approximation (CSDA) is larger than h . We attempt to establish an equivalency between the measured doses provided by the two methods by employing the following formula:

DFC = 1.6 × 10−10ΦFC

ΔE Npulse ρcal h

(5)

where DFC [Gy] is the equivalent average dose that is received by the graphite plate as a result of the irradiation, ΦFC is the measured fluence per pulse, ΔE is the energy difference between the incident and exiting electrons, ρcal is the density of graphite and Npulse is the number of electron pulses within the irradiation time interval considered. The total number of pulses for a given irradiation time t [s] is Npulse = fpulse t. The range of electrons is RCSDA ≈ 3.488 g/cm2 while ρcal h=3.24 g/cm2 [38]. The residual range is res RCSDA = RCSDA − ρcal h ≈ 0.248 g/cm2 which corresponds to an exit energy Text ≈ 0.58 MeV . The radiation yield in this energy range is quite low: Y0 ≈ 0.022 at 6 MeV and Yext ≈ 2 × 10−3 at 0.58 MeV. The energy difference is thus ΔE = T0 (1 − Y0) − Text (1 − Yext ) ≈ 5.29 MeV . The fluence is deduced by taking the total charge in the beam divided by the cross section area of the calorimeter Acal = 132.73 cm2, positioned 52 cm away from the accelerator exit window:

Fig. 2. a) FC for charge and fluence measurements; b) Measured signal with FC for two filament voltages: 10 V and 12 V, respectively. 3

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Table 2 Electron beam parameters measured with the FC at about 2 cm from the exit window of the ALID 7 accelerator, the closest position where installation of the detector is possible. Filament voltage (V)

Charge per pulse (C)

el

el

Fluence per pulse ΦFC ⎡ 2 ⎤ ⎣ cm ⎦

⎤ Flux per pulse ψFC ⎡ ⎣ s·cm2 ⎦

Mean

Standard dev.σFC

Mean

Φ Standard dev.σFC

Mean

Ψ Standard dev.σFC

12

− 1.29 × 10−7

− 1.25 × 10−8

1.49 × 1011

1.73 × 1010

3.60 × 1016

3.81 × 1015

11

− 8.98 × 10−8

− 2.47 × 10−8

8.85 × 1010

4.77 × 1010

2.60 × 1016

6.60 × 1015

10

− 3.93 × 10−8

− 1.35 × 10−8

4.54 × 1010

1.50 × 1010

1.13 × 1016

3.71 × 1015

9

− 1.80 × 10−8

− 1.41 × 10−9

2.08 × 1010

1.89 × 109

5.25 × 1015

4.36 × 1014

8

− 6.58 × 10−9

− 3.04 × 10−9

7.78 × 109

3.73 × 109

1.90 × 1015

8.68 × 1014

Fig. 3. Dose measured with the calorimeter vs. dose converted from the fluence measured with the FC, for two filament voltages a) Uf = 12 V and b) Uf = 11 V .

Fig. 4. Dose measured with the calorimeter vs. dose converted from the fluence measured with the FC, for different filaments voltages: a) Uf = 10 V and b) Uf = 8 and 9 V.

irradiation time. We notice from Figs. 3 and 4 that the dose obtained with the FC is systematically larger than that of the calorimeter. This is a consequence of our assumption that all pulses are identical for the time period considered. The longer the time period, the larger is the dose given by Eq. (5), which does not really takes into considerations fluctuations of the fluence, from pulse to pulse. A more accurate result could be obtained by acquiring all pulses and averaging them to obtain the true value of the EB fluence. In the case of the 360 s irradiation time, it would consist of ∼ 1.9 × 10 4 pulse waveforms. Also Eq. (5) is a statistical approximation based on the stopping power in the calorimeter material. A more rigorous approach using Monte-Carlo simulations could provide a more realistic description of the attenuation and energy deposition rates of the EB [24,25].

bunches of very short duration (in the femto- to picoseconds range). Each of them has its own advantages. For high exposure times of the order of minutes and for larger irradiation area calorimetry is the most suitable. For short irradiation times of the order of seconds and for pulse-by-pulse irradiation a FC provides accurate values of the charge per pulse which can be converted into dose. The FC provides a precise determination of the beam flux which is one of the most important parameters to be determined when working with electron beams since it directly influences the absorbed dose. When the EB is stable and the voltage of the electron gun filament is in the nominal operating range the two methods give almost similar doses, in spite of the simplicity of our approach.

Conclusions

Acknowledgments

An attempt to compare two dosimetry techniques based on a calorimeter and a FC was carried out for electron beams with energy 6 MeV at the ALID-7 LINAC. The first one is standard in irradiation processes while the second one is often encountered in the field of hyper intense lasers interactions with matter which generate electron

The authors are grateful to the Ministry of Research and Innovation (MCI), Romania for providing a financial assistance through the projects IIN, PN-16-47-01-02 and Laplas VI 16N/08.02.2019. C. Diplasu, G. Giubega and C.M. Ticos have also been financially supported by the Institute of Atomic Physics (IFA), from project ELI-NP 23. 4

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