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Track structure of carbon ions: New measurements and simulations
Radiation Physics and Chemistry 168 (2020) 108576
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Radiation Physics and Chemistry journal homepage: www.elsevier.com/locate/radphyschem
Track structure of carbon ions: New measurements and simulations ∗
T
V. Conte , A. Selva, P. Colautti Istituto Nazionale di Fisica Nucleare INFN, Laboratori Nazionali di Legnaro, Viale dell’Università 2, Legnaro, Padova, Italy
A B S T R A C T :
It is recognized today that the observable radiobiological effects of ionizing radiations are strongly correlated to the local density of lesions produced in micrometerand nanometer-sized subcellular structures, and thus to the track structure properties of interacting particles. In view of the emerging interest of carbon ions in radiotherapy, an experimental study was done for characterizing the track structure of carbon ions at different energies close to the Bragg peak. Ionization cluster size distributions for nanometer-sized target volumes were measured with the Startrack-Counter installed at the TANDEM-ALPI accelerator complex at LNL, and calculated by means of a dedicated Monte Carlo code. Measurements and simulations were performed for particle tracks crossing directly the target volume or passing nearby at specified impact parameters. Results will be presented and discussed for 12C-ions at 6, 8, 12.5 and 20 MeV per nucleon.
1. Introduction The scientific community recognizes today that the effectiveness of ionizing radiation to produce biological observable damage is strongly correlated to the clustering of damages at the level of DNA helix (Ward, 1985), hence to the particle track structure. The characteristic properties of track structure are directly measurable nowadays, for instance, with the Startrack-Counter (De Nardo et al., 2002) developed at the Legnaro National Laboratories (LNL) of the Italian Istituto Nazionale di Fisica Nucleare (INFN), and installed there at the TANDEM-ALPI accelerator complex. Based on the gas scaling principle, when filled with propane gas at 300 Pa the Counter simulates a cylindrical water-target volume of about 25 nm in diameter and height (Grosswendt, 2004; B. Grosswendt et al., 2004): this is to say, the stochastics of ionizations simulated in millimetric volumes of mass per area (Dρ)(gas) filled with propane at low gas pressure are in satisfactory agreement with the distributions simulated in nanometric volumes of liquid water, with diameter (Dρ)(water ) calculated according to the following equation:
(Dρ)(water ) = (Dρ)(gas) × (water ) (λρ)ion
(water ) (λρ)ion (gas ) (λρ)ion (gas ) (λρ)ion
(1)
and are the mean-free ionization path Here, lengths of the primary ionizing particle in water and in the gas respectively. Equation (1) is based on the assumption that the production of secondary electrons and the electron degradation are similar in both materials. It was found that the agreement between distributions simulated in propane gas and in water is satisfactory when a ratio (gas ) (water ) (λρ)ion /(λρ)ion = 1.24 is considered (B. Grosswendt et al., 2004). The target volume can be moved transversally with respect to a
∗
narrow primary particle beam, thus allowing the characterization of the so-called “track-core” region, a narrow central zone with high-density energy deposition that includes interactions of the primary particle, and the “penumbra” region, a peripheral zone enveloping the core where energetic secondary electrons are the exclusive agents of energy deposition (Chatterjee and Schaefer, 1976; Kase et al., 1985). Considering the emerging interest for carbon ions in radiotherapy, the particle track-structure properties of 12C-ions at different energies were studied experimentally and by means of Monte Carlo simulations, by measuring the number ν of ionizations (the ionization cluster size) which is caused in a target volume (SV) by single ionizing particles when penetrating through or passing nearby the target at specified impact parameter d. By repeating the measurement for a large number of primary particles (typically 106), the relative frequency Pν(Q,dρ) of cluster size formation is derived, representing the expectation value of cluster size ν produced by ionizing particles of radiation quality Q. Particular descriptors of the track structure can be derived from these distributions, as the cumulative probability Fk of measuring a number ν ≥ k of ionizations. These quantities are particularly interesting, because a higher probability of large clusters of ionizations naturally corresponds to a higher probability of clustering of DNA lesions, thus to an enhanced biological effect. By comparison with radiobiological data for radio-resistant cells available in the literature, it was found in previous work (Conte et al., 2018) that the probabilities F1, F2 and F3 are strongly correlated to cellular inactivation cross sections measured at different end-points.
Corresponding author. E-mail address: [email protected] (V. Conte).
https://doi.org/10.1016/j.radphyschem.2019.108576 Received 30 July 2019; Received in revised form 29 October 2019; Accepted 9 November 2019 Available online 11 November 2019 0969-806X/ © 2019 Elsevier Ltd. All rights reserved.
Radiation Physics and Chemistry 168 (2020) 108576
V. Conte, et al.
Fig. 1. Schematic view of the Startrack Counter. The bottom-right box represents a picture of the efficiency map ε (X,Y), which describes the probability that a slow electron from position (X,Y) is detected by the single electron counter at the MSAC. The red square represents the cylindrical target volume SV of 3.7 mm in width and 3.7 mm in height; the yellow circles represent the confining electrode rings of 0.1 mm in diameter. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
2. Material and methods
meaning that, on average, 20 out of 100 initial electrons generated in the SV are counted at the MSAC and recorded by the acquisition system. The electron counting starts when the primary particle interacts with a solid state detector placed at the end of the beam line. The use of an external trigger allows to record also the “zero-events”, that is the particle tracks that pass at defined impact parameter without producing any detectable signal in the Startrack-counter. For these measurements the sensitive volume was filled with propane gas at a pressure of 300 Pa, corresponding to a mass per area of about 2.0 μg cm−2 for the SV diameter, which is equivalent to 20 nm at a density of 1 g/cm³. The measurement of cluster size distributions were performed by counting the number of ionizations which are caused by a large number of single primary ionizing particles when penetrating through or passing nearby the target volume at specified impact parameter d. If the primary particle traverses the target all the ionizations are counted, both those produced in ionization processes of the primary particle and those produced by secondary electrons. When the primary particle trajectory passes nearby, ionizations inside the target are produced by δ-electrons only. The irradiation geometry is schematically depicted in Fig. 2. The particle beam was collimated to 0.8 mm in diameter (equivalent to 0.44 μg/cm2 or to 4.4 nm at 1 g/cm³). Cluster size distributions were
2.1. Experimental procedure The measurements discussed in the present paper were carried out with the LNL Startrack Counter (De Nardo et al., 2002), which measures the ionizations by counting the electrons set free in the ionization process. The counter consists of a target volume (SV) and a single electron counter, made of a long cylindrical drift column and a multi‒step avalanche chamber (MSAC). A schematic view of the device components is given in Fig. 1. The sensitive volume is defined by the static electric field produced with several miniaturized circular electrodes, delineating a right cylinder 3.7 mm in diameter and height. Electrons generated inside the SV are transferred into the drift column, where they drift towards the MSAC. Due to the diffusion process, electrons which belong to the initial cluster reach the MSAC individually, thus allowing to be counted. The efficiency with which electrons are transferred from the SV into the drift column changes from point to point, being higher at the centre of the SV and decreasing towards its borders, as shown in the bottom-right box of Fig. 1. More details can be found in the work by Conte V. et al. (Conte et al., 2012). The average electron detection efficiency is approximately ε = 0.2, 2
Radiation Physics and Chemistry 168 (2020) 108576
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Fig. 2. Schematic view of the Startrack measuring geometry. The blue circles show the 12C-ions beam size, as defined by 0.8 mm collimators. Three measuring positions are shown, at d = 0.0, 2.3 and 7.0 mm (equivalent to 0.0, 13 and 38 nm at 1 g/cm³). The yellow halo is a schematic representation of the penumbra region. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
measured for 12C-ions at 6, 8, 12.5 and 20 MeV per nucleon, at different impact parameters d of the primary ion trajectories with respect to the centre of the target volume SV. As it can be seen in Fig. 2, when d > 2.25 mm (∼12 nm at 1 g/cm³) the primary ion trajectories pass always outside SV. To study separately the track-core region (when the primary particle directly traverses SV) and the penumbra region (the particle passes nearby SV and the measured ionizations are produced only by secondary electrons emerging from the primary particle trajectory), the impact parameter d was varied between 0 mm and 7 mm, which corresponds to 0 μg/cm³ ≤ dρ ≤ 3.8 μg/cm2. A full description of the experimental procedure and of the data processing can be found in the publication of Conte et al. (2012).
where Ñ is the molecular number density of the target medium. The determination of σion (T ) is based on the analytical model of Rudd et al. (1985) for the integrated ionization cross section, which however is actually valid only for protons in methane. The procedure followed to get the data for 12C-ions in propane is described in ref (De Nardo et al., 2002). The spectral distribution of δ-electrons set in motion in propane was calculated by applying the model by Rudd et al. (1992). The simulation of the ionization component due to the δ-electrons takes into account elastic electron scattering, impact excitation, and impact ionization, assuming that the electrons always travel along straight lines between successive interaction points. The history of each electron is simulated until it leaves a pre-defined interaction volume, or until its energy is smaller than or equal to 10 eV which is close to the ionization threshold energy of about 11.08 eV in propane. To determine the cluster size distributions these low energy electrons are counted if they appear inside the target volume. The maximum energy, Tmax , transferred to an electron by a primary particle at energy T and relative atomic mass M can be approximated, in the case of non-relativistic energies, as follows:
2.2. Monte Carlo simulations To simulate the measurements, a dedicated track structure Monte Carlo code was used, which has been developed by B. Grosswendt (De Nardo et al., 2002; Grosswendt et al., 2014), to calculate the ionization component of the tracks of light ions penetrating propane thicknesses of small mass per area. The model is based on the assumption that in thin layers of gaseous propane elastic scattering, charge changing effects and impact excitation processes of the primary particles can be neglected. Consistently, it is assumed that the particles’ track structure and the resulting cluster size distributions Pν(Q,dρ) are determined only by the path lengths of the primary ion between two successive ionizing collisions, by the spectral and angular distributions of emerging secondary electrons, and by the properties of electron degradation in the target medium. The mean free ionization path length λion(T) of the carbon ion at energy T is determined by the corresponding ionization cross section σion (T ) :
λion (T ) =
1 N˜ × σion (T )
Tmax =
4mel T T × ⎛ ⎞ ≈ 2 × 10−3 × ⎛ ⎞ u ⎝M⎠ ⎝M⎠
(3)
where mel is the mass of an electron at rest, u is the atomic mass unit and (T / M ) is the energy per nucleon of the primary particle. Thus, the maximum energy of δ-electrons, Tmax , depends only on the primary ion velocity but not on its charge or mass. The maximum energy of δ-electrons, the penumbra radius (Rρ)P as given by the continuous-slowing-down mass range of electrons in propane (ESTAR), the ionization mean free path length (λρ)ion and the ratio (Dρ)/(λρ)ion of the particles investigated in this study are listed in Table 1. The ratio (Dρ)/(λρ)ion represents the mean number of ionizations produced by the primary ion along a path length equal to the diameter of the target volume, Dρ.
(2) 3
Radiation Physics and Chemistry 168 (2020) 108576
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From the ionization cluster size distributions Pν(Q,dρ) specific descriptors of the radiation quality can be derived, in particular the mean cluster size M1(Q,dρ) and the cumulative probabilities F1(Q,dρ), F2(Q,dρ) and F3(Q,dρ). The values obtained at impact parameter dρ = 0 μg/cm2, as derived from the spectra shown in Fig. 3, are summarized in Table 2. The value M1(Q,d=0) can be easily explained by considering the number of ionizations caused directly by the primary particles inside the target volume along its diameter. This number is equal to the ratio of the particles’ travelling lengths inside the target to their mean free ionization path lengths, (Dρ)/(λρ)ion. The number of primary ionizing interactions (D/λion) is about 76 for the 8 MeV/u 12C-ions, about 52 for the 12.5 MeV/u and about 35 for the 20 MeV/u ions. In view of the counting efficiency of the track-nanodosimeter of 20%, these numbers nicely agree with the measured mean cluster sizes M1. In a similar way, the mean value M1 = 11.2 for the 6 MeV/u ions is in good agreement with (D/λion) = 96 and a mean counting efficiency of 10%. In order to analyse the influence of radiation quality on the cluster size distributions caused by ionizing particles in a nanometer-sized target volume V in the penumbra region in a greater detail, Fig. 4 shows the measured cluster size distributions due to carbon-ions at 8, 12.5 and 20 MeV/u at the same impact parameter dρ = 2.7 μg/cm2. In the penumbra region, the three distributions Pν(Q) have the same shape for ν > 0, independent of the primary particle velocity. They differ only by a constant factor, corresponding to the number of initial δ-electrons set in motion along a relevant path length. The Pν(Q) for carbon ions at 6 MeV/u is not included in the previous figure, because, due to the reduced efficiency, it has a steeper slope with respect to the other ones. The number of initial δ-electrons set in motion along a relevant path length equal to target diameter Dρ is given by the ratio (Dρ)/(λρ)ion. Fig. 5 shows the scaled distributions relative to the 8 MeV/u 12C-ions, obtained by multiplying the P ν ≥ 1 by the factor k(Q) = (λρ)ion-Q/ (λρ)ion-8 MeV/u. It is clear that, when scaled to the same number of initial electrons set in motion by primary ionization processes, the cluster size distributions in the penumbra region are almost the same, invariant with the velocity of the primary particles. This invariance of the scaled distributions clearly demonstrates that the shape of the cluster size distributions at larger impact parameters in the penumbra region is independent of radiation quality, and that the relative cluster size frequencies for ν > 0 are directly proportional to the number of δ-electrons set in motion by the primary particles. The cluster size distribution for 6 MeV/u 12C-ions is also shown in Fig. 5, and it decreases more rapidly with ν, due to the reduced counting efficiency. To further investigate the shape of cluster size distributions in the penumbra region, Fig. 6 shows the measured cluster size distributions due to carbon-ions at 12.5 MeV/u and at impact parameter dρ = 2.6 μg/ cm2, dρ = 2.9 μg/cm2, dρ = 3.1 μg/cm2 and dρ = 3.7 μg/cm2, approximately corrected for the solid angle, i.e. multiplying P ν≥1 by (dρ)2. The scaled distributions are the same within statistical uncertainties, confirming that the cluster size distributions in the penumbra depend on the impact parameter almost exclusively through the solid angle. Similar results on the independence of impact parameter were also found for other ions (Conte et al., 2012), as well as in the measurements with the Ion-counter, a different nanodosimeter based on the counting of ions instead of electrons (Bashkirov et al., 2009; Hilgers et al., 2017). Considered the fact that the ionization-counting efficiency ε of the Startrack-Counter is spatially-dependent with a mean value ε ≈ 0.2 , the question arises whether it is possible to define an effective site size of uniform counting efficiency ε = 1, at least for primary particles traversing the target volume centrally (d = 0). The correspondence of ionization cluster size distributions measured in the target volume of Startrack with those simulated in a smaller volume with uniform efficiency ε = 1 was therefore investigated. As already described, the Startrack target volume is a cylinder with equal diameter and height equal to 3.7 mm. Filled with gaseous
Table 1 The maximum energy of δ-electrons, the penumbra radius (Rρ)P as given by the continuous-slowing-down mass range of electrons in propane (ESTAR), the primary ionization mean free path length (λρ)ion and the ratio (Dρ)/(λρ)ion of the 12C-ions at different energy per nucleon. Energy per nucleon (MeV/u)
Max energy of δelectrons (keV)
Penumbra radius (Rρ)p (μg/cm2)
(λρ)ion (μg/cm2)
(Dρ)/ (λρ)ion
6 8 12.5 20
13 17 27 44
300 600 1300 3000
0.021 0.026 0.038 0.057
96 76 52 35
The efficiency-map of the Startrack-counter is included in the Startrack-Monte Carlo code. As the detector loses efficiency for cluster sizes larger than 10, a time correction factor is afterwards applied to the simulated cluster size distributions. More details on the model and implemented cross sections can be found in References (De Nardo et al., 2002; Grosswendt et al., 2014). Two sets of simulations were performed. The aim of the first set was to reproduce the detector and the experimental conditions, in terms of real SV size, gas pressure and detection efficiency. Ionization cluster size distributions were simulated for 12C-ions passing at several impact parameters with respect to the sensitive volume, and compared with experimental results. Considered that the efficiency of our detector is only 20% on average, and furthermore it is also not uniform inside the target volume, a second set of simulations was performed, aiming to find an equivalent sensitive volume at efficiency 1, such that the ionization cluster size distributions produced in this volume are similar to those measured by the Startrack counter, at least for central passage (d = 0 mm) of the primary ions. Simulations were done in several smaller cylinders of different size, taking the same gas pressure (300 Pa) but considering a uniform 100% efficiency, until obtaining the good match with experimental data, and thus the associated SV of density 1 g/cm3 of our detector. 3. Results and discussion In order to investigate the track structure of particles at different velocity, we looked at the ionization cluster size distributions Pν(Q,dρ), measured and simulated by means of Monte Carlo calculations, at different impact parameter dρ. In Fig. 3 both experimental and calculated ionization cluster size distributions are shown at six impact parameters from dρ = 0 μg/cm2 to dρ = 3.8 μg/cm2. From (a) to (d) Fig. 3 shows the results obtained for 12C ions at 6, 8, 12.5 and 20 MeV per nucleon. A first glance at Fig. 3 immediately shows two different shapes of the cluster size distributions. In the track-core region of particle tracks (dρ < 1 μg cm−2), with the primary particles directly crossing the volume, the distributions are peaked, with a cluster size at maximum that increases with decreasing particle velocity, reflecting the shortening of the ionization mean free path (λρ)ion. For the carbon-ions at 72 MeV one must consider that the detector-parameters where set as to reduce the detecting efficiency by a factor of 2. In the penumbra region, for dρ > 1.2 μg/cm2, ionizations are produced inside SV only via δ-electron interactions. The probability that a δ-ray traverses SV also decreases with impact parameter dρ, mainly due to the decreasing solid angle. The most probable cluster size is always zero and the probability P0(Q,dρ) increases with increasing impact parameter dρ. The shape of the distributions is similar at any carbon-ion velocity and independent of the impact parameter: Pν(Q,V) decreases monotonically with increasing ν, and shows an almost exponential shape for ν ≥ 3. Both in the track-core and in the penumbra regions the agreement between measured and calculated distributions is very satisfactory. 4
Radiation Physics and Chemistry 168 (2020) 108576
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Fig. 3. Ionization cluster size distributions Pν(Q,dρ) produced in the nanometric target volume SV by 12C-ions at 6, 8, 12.5 and 20 MeV/u passing at six different impact parameters dρ: measurements (symbols) and simulations (lines). Error bars on experimental data represent statistical errors only. Statistical errors in the simulations are negligible. The sensitive volume of the detector has a diameter (Dρ)SV = 2.0 μg cm−2. The ion beam diameter, as defined by the collimators, is (Rρ)beam = 0.4 μg cm−2. Table 2 The ratio (Dρ)/(λρ)ion, the measured mean ionization cluster size M1 and the cumulative probabilities F1, F2 and F3 derived from experimental spectra shown in Fig. 3. 12C-ions crossing the target volume at its centre, at different energies per nucleon. Energy per nucleon (MeV/u)
(Dρ)/ (λρ)ion
M1
F1
F2
F3
6a 8 12.5 20
96 76 52 35
11.2 15.5 10.0 8.1
0.99999 1.0000 0.99997 0.99950
0.99981 1.0000 0.99963 0.99676
0.99895 1.0000 0.99795 0.98566
a Measurements performed at reduced detection efficiency (mean value ε ≈ 0.1).
propane at 300 Pa, the mass thickness of the diameter is approximately 2.0 μg/cm2 at T = 25 °C, corresponding to a length of 20 nm when scaled at a density of 1 g/cm3. By taking into account the mean value ε ≈ 0.2 of the spatially-dependent efficiency applied in the measurements, simulations were performed in different target volumes varying the diameter length between 0.7 and 0.8 mm with step of 0.02 mm. After the correction for the time-resolution of the experimental set-up, simulated cluster size distributions were compared with measured distributions. The best agreement on the mean value M1 and on the cumulative probabilities F1, F2 and F3 was found for D = 0.8 mm. For 6 MeV/u 12C-ions, which were measured with a reduced mean efficiency ε ≈ 0.1, the best agreement was found for D = 0.5 mm. Both measured and simulated cluster size distributions are shown in Figs. 7 and 8. The agreement is very satisfactory. In consequence, it can
Fig. 4. Measured cluster size distributions Pν(Q) for 12C-ions at 96, 150 and 240 MeV passing the target volume at impact parameter dρ = 2.7 μg/cm2. Error bars represent statistical errors only.
be assumed that the cluster size distributions measured by the Startrack-counter at 300 Pa C3H8 are close to those produced in the case of a smaller target volume and an ideal constant detection efficiency of 100%, at least for light-ions crossing the target volume at its centre. In this sense, the “effective-target size” of the Startrack counter is 0.8 mm, or 0.44 μg/cm2, at 300 Pa and standard operational conditions, and 0.5 mm, or 0.27 μg/cm2, when the operational conditions reduce the mean detecting efficiency to ε ≈ 0.1. 5
Radiation Physics and Chemistry 168 (2020) 108576
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Fig. 5. Measured cluster size distributions Pν(Q) for 6, 8, 12.5 and 20 MeV/u 12 C-ions passing the target volume SV at impact parameter dρ = 2.7 μg/cm2, normalized to the same number of initial δ-electrons set in motion along a relevant path length = Dρ. Error bars represent statistical errors only.
Fig. 8. Cluster size distributions Pν(Q) for 6 MeV/u 12C-ions traversing the target volume centrally, measured (symbols) and simulated (dashed black line) in the Startrack target volume, and simulated in a smaller volume with higher counting efficiency (continuous red line). See text for details. Error bars on experimental data represent statistical errors only. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
Table 3 The simulated mean ionization cluster size M1 and the cumulative probabilities F1, F2 and F3 for 12C-ions crossing the target volume along the diameter at its centre, at different energy per nucleon. The diameter of the simulated target is D = 0.8 mm, the target gas is propane at 300 Pa, the uniform detection efficiency is ε = 1. Energy per nucleon (MeV/u) a
6 8 12.5 20 a
Fig. 6. Measured cluster size distributions Pν(Q)x(dρ)2 for 12.5 MeV/u 12C-ions passing the target volume SV at impact parameter dρ = 2.6, 2.9, 3.2 and 3.7 μg/ cm2. Error bars represent statistical errors only.
M1
F1
F2
F3
11.4 15.2 10.5 8.00
1.00000 1.00000 0.99997 0.99937
0.99989 1.00000 0.99968 0.99498
0.99930 1.00000 0.99804 0.97958
Simulation performed in a target with D = 0.5 mm.
The values for M1, F1, F2 and F3 resulting from the simulations performed in the effective target volumes with efficiency ε = 1 are given in Table 3.
4. Conclusions The track structure of carbon ions was studied by measuring the ionization cluster size distributions produced in a nanometric target volume SV by Carbon ions traversing SV or passing by at specified distances. Measurements and simulations were performed for four different energies close to the Bragg peak. The cluster size distributions in the track-core and in the penumbra regions of particle tracks confirmed the general shape that had already been observed. In particular, the shape of the distributions at large distances, where only δ-electrons contribute to the ionization yield inside SV, is invariant with the velocity of the primary particle and also with the distance, at least in the limited range of investigated energies and distances. In order to study how this invariance correlates with the degradation spectra of secondary electrons, for different velocities of the primary ions, a new extended set of Monte Carlo simulations is planned for a future work. The possibility to define an effective target volume was also investigated by means of Monte Carlo simulations. The outcome is that, at least for the particles traversing the target at its centre, the cluster size distributions measured in the 3.7 mm of the Startrack target (mean efficiency 20%) are very close to those simulated in a 0.80 mm target with uniform 100% efficiency. In this sense the effective target size of
Fig. 7. Cluster-size distributions Pν(Q) for 8, 12.5 and 20 MeV/u 12C-ions traversing the target volume centrally, measured in the Startrack target volume (symbols) and simulated in a smaller volume with efficiency ε = 1 (lines). See text for details. Error bars on experimental data represent statistical errors only.
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the Startrack counter is 0.80 mm, or 0.44 μg/cm2 at 300 Pa of propane, which corresponds to a length of 4.4 nm at a density of 1 g/cm3. Taking into account the ratio of the ionization mean free path in liquid water and in gaseous propane, our detector measures cluster size distributions equivalent to those for a liquid water cylinder 5.5 nm in diameter (Grosswendt, 2004; Grosswendt et al., 2004). Considered that in previous work (Conte et al., 2018) the relevant target size had been suggested to be in the range 1–1.5 nm, it is clear that a modification is necessary for the operational conditions of Startrack counter, in order to reduce the effective target size. It is therefore important to investigate the possibility to operate the detector at gas pressures lower than 300 Pa, and to study the effect of this pressure reduction on the mean detection efficiency. Future work will be devoted to this subject.
Experimental validation of track structure models. IEEE Trans. Nucl. Sci. 56 (5), 2859–2863. Chatterjee, A., Schaefer, H.J., 1976. Microdosimetric structure of heavy ion tracks in tissue. Radiat. Environ. Biophys. 13, 215. Conte, V., Colautti, P., Grosswendt, B., Moro, D., De Nardo, L., 2012. Track structure of light ions: experiments and simulations. New J. Phys. 14, 093010. Conte, V., Selva, A., Colautti, P., Hilgers, G., Rabus, H., Bantsar, A., Pietrzak, M., Nanodosimetry, Pszona S., 2018. Towards a new concept of radiation quality. Radiat. Prot. Dosim. 180 (1–4), 150–156. De Nardo, L., Colautti, P., Conte, V., Baek, W.Y., Grosswendt, B., Tornielli, G., 2002. Ionization-cluster distributions of α-particles in nanometric volumes of propane: measurement and calculation. Radiat. Environ. Biophys. 41, 235–256. ESTAR: Stopping powers and ranges for electrons. http://physics.nist.gov/PhysRefData/ Star/Text/method.html. Grosswendt, B., 2004. Recent advances of nanodosimetry. Radiat. Prot. Dosim. 110, 789–799. Grosswendt, B., De Nardo, L., Colautti, P., Pszona, S., Conte, V., Tornielli, G., 2004. Experimental equivalent cluster size distributions in nanometric liquid volumes of liquid water. Radiat. Prot. Dosim. 110, 851–857. Grosswendt, B., Conte, V., Colautti, P., 2014. An upgraded track structure model: experimental validation. Radiat. Prot. Dosim. 161 (1–4), 464–468. Hilgers, G., Bug, M.U., Rabus, H., 2017. Measurement of track structure parameters of low and medium energy helium and carbon ions in nanometric volumes. Phys. Med. Biol. 62 (19), 7569–7597. Kase, K.R., Bjarngard, B.E., Attix, F.H. (Eds.), 1985. The Dosimetry of Ionizing Radiation, vol. I Academic Press, Orlando, FL, USA. Rudd, M.E., Kim, Y.-K., Madison, D.H., Gallagher, J.W., 1985. Electron production in proton collisions: total cross sections. Rev. Mod. Phys. 57, 965–994. Rudd, M.E., Kim, Y.-K., Madison, D.H., Gay, T.J., 1992. Electron production in proton collisions with atoms and molecules: energy distributions. Rev. Mod. Phys. 64, 441–490. Ward, J.F., 1985. Biochemistry of DNA lesions. Radiat. Res. Suppl. 8, 104 S-103-S-111.
Acknowledgement This work has been supported by the 5th Commission of INFN (Italian National Institute for Nuclear Physics), Frascati-Italy, under the research project NIRVANA. Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.radphyschem.2019.108576. References Bashkirov, V., Schulte, R., Wroe, A., Sadrozinski, H., Gargioni, E., Grosswendt, B., 2009.
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Track structure of carbon ions: New measurements and simulations ∗
T
V. Conte , A. Selva, P. Colautti Istituto Nazionale di Fisica Nucleare INFN, Laboratori Nazionali di Legnaro, Viale dell’Università 2, Legnaro, Padova, Italy
A B S T R A C T :
It is recognized today that the observable radiobiological effects of ionizing radiations are strongly correlated to the local density of lesions produced in micrometerand nanometer-sized subcellular structures, and thus to the track structure properties of interacting particles. In view of the emerging interest of carbon ions in radiotherapy, an experimental study was done for characterizing the track structure of carbon ions at different energies close to the Bragg peak. Ionization cluster size distributions for nanometer-sized target volumes were measured with the Startrack-Counter installed at the TANDEM-ALPI accelerator complex at LNL, and calculated by means of a dedicated Monte Carlo code. Measurements and simulations were performed for particle tracks crossing directly the target volume or passing nearby at specified impact parameters. Results will be presented and discussed for 12C-ions at 6, 8, 12.5 and 20 MeV per nucleon.
1. Introduction The scientific community recognizes today that the effectiveness of ionizing radiation to produce biological observable damage is strongly correlated to the clustering of damages at the level of DNA helix (Ward, 1985), hence to the particle track structure. The characteristic properties of track structure are directly measurable nowadays, for instance, with the Startrack-Counter (De Nardo et al., 2002) developed at the Legnaro National Laboratories (LNL) of the Italian Istituto Nazionale di Fisica Nucleare (INFN), and installed there at the TANDEM-ALPI accelerator complex. Based on the gas scaling principle, when filled with propane gas at 300 Pa the Counter simulates a cylindrical water-target volume of about 25 nm in diameter and height (Grosswendt, 2004; B. Grosswendt et al., 2004): this is to say, the stochastics of ionizations simulated in millimetric volumes of mass per area (Dρ)(gas) filled with propane at low gas pressure are in satisfactory agreement with the distributions simulated in nanometric volumes of liquid water, with diameter (Dρ)(water ) calculated according to the following equation:
(Dρ)(water ) = (Dρ)(gas) × (water ) (λρ)ion
(water ) (λρ)ion (gas ) (λρ)ion (gas ) (λρ)ion
(1)
and are the mean-free ionization path Here, lengths of the primary ionizing particle in water and in the gas respectively. Equation (1) is based on the assumption that the production of secondary electrons and the electron degradation are similar in both materials. It was found that the agreement between distributions simulated in propane gas and in water is satisfactory when a ratio (gas ) (water ) (λρ)ion /(λρ)ion = 1.24 is considered (B. Grosswendt et al., 2004). The target volume can be moved transversally with respect to a
∗
narrow primary particle beam, thus allowing the characterization of the so-called “track-core” region, a narrow central zone with high-density energy deposition that includes interactions of the primary particle, and the “penumbra” region, a peripheral zone enveloping the core where energetic secondary electrons are the exclusive agents of energy deposition (Chatterjee and Schaefer, 1976; Kase et al., 1985). Considering the emerging interest for carbon ions in radiotherapy, the particle track-structure properties of 12C-ions at different energies were studied experimentally and by means of Monte Carlo simulations, by measuring the number ν of ionizations (the ionization cluster size) which is caused in a target volume (SV) by single ionizing particles when penetrating through or passing nearby the target at specified impact parameter d. By repeating the measurement for a large number of primary particles (typically 106), the relative frequency Pν(Q,dρ) of cluster size formation is derived, representing the expectation value of cluster size ν produced by ionizing particles of radiation quality Q. Particular descriptors of the track structure can be derived from these distributions, as the cumulative probability Fk of measuring a number ν ≥ k of ionizations. These quantities are particularly interesting, because a higher probability of large clusters of ionizations naturally corresponds to a higher probability of clustering of DNA lesions, thus to an enhanced biological effect. By comparison with radiobiological data for radio-resistant cells available in the literature, it was found in previous work (Conte et al., 2018) that the probabilities F1, F2 and F3 are strongly correlated to cellular inactivation cross sections measured at different end-points.
Corresponding author. E-mail address: [email protected] (V. Conte).
https://doi.org/10.1016/j.radphyschem.2019.108576 Received 30 July 2019; Received in revised form 29 October 2019; Accepted 9 November 2019 Available online 11 November 2019 0969-806X/ © 2019 Elsevier Ltd. All rights reserved.
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Fig. 1. Schematic view of the Startrack Counter. The bottom-right box represents a picture of the efficiency map ε (X,Y), which describes the probability that a slow electron from position (X,Y) is detected by the single electron counter at the MSAC. The red square represents the cylindrical target volume SV of 3.7 mm in width and 3.7 mm in height; the yellow circles represent the confining electrode rings of 0.1 mm in diameter. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
2. Material and methods
meaning that, on average, 20 out of 100 initial electrons generated in the SV are counted at the MSAC and recorded by the acquisition system. The electron counting starts when the primary particle interacts with a solid state detector placed at the end of the beam line. The use of an external trigger allows to record also the “zero-events”, that is the particle tracks that pass at defined impact parameter without producing any detectable signal in the Startrack-counter. For these measurements the sensitive volume was filled with propane gas at a pressure of 300 Pa, corresponding to a mass per area of about 2.0 μg cm−2 for the SV diameter, which is equivalent to 20 nm at a density of 1 g/cm³. The measurement of cluster size distributions were performed by counting the number of ionizations which are caused by a large number of single primary ionizing particles when penetrating through or passing nearby the target volume at specified impact parameter d. If the primary particle traverses the target all the ionizations are counted, both those produced in ionization processes of the primary particle and those produced by secondary electrons. When the primary particle trajectory passes nearby, ionizations inside the target are produced by δ-electrons only. The irradiation geometry is schematically depicted in Fig. 2. The particle beam was collimated to 0.8 mm in diameter (equivalent to 0.44 μg/cm2 or to 4.4 nm at 1 g/cm³). Cluster size distributions were
2.1. Experimental procedure The measurements discussed in the present paper were carried out with the LNL Startrack Counter (De Nardo et al., 2002), which measures the ionizations by counting the electrons set free in the ionization process. The counter consists of a target volume (SV) and a single electron counter, made of a long cylindrical drift column and a multi‒step avalanche chamber (MSAC). A schematic view of the device components is given in Fig. 1. The sensitive volume is defined by the static electric field produced with several miniaturized circular electrodes, delineating a right cylinder 3.7 mm in diameter and height. Electrons generated inside the SV are transferred into the drift column, where they drift towards the MSAC. Due to the diffusion process, electrons which belong to the initial cluster reach the MSAC individually, thus allowing to be counted. The efficiency with which electrons are transferred from the SV into the drift column changes from point to point, being higher at the centre of the SV and decreasing towards its borders, as shown in the bottom-right box of Fig. 1. More details can be found in the work by Conte V. et al. (Conte et al., 2012). The average electron detection efficiency is approximately ε = 0.2, 2
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Fig. 2. Schematic view of the Startrack measuring geometry. The blue circles show the 12C-ions beam size, as defined by 0.8 mm collimators. Three measuring positions are shown, at d = 0.0, 2.3 and 7.0 mm (equivalent to 0.0, 13 and 38 nm at 1 g/cm³). The yellow halo is a schematic representation of the penumbra region. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
measured for 12C-ions at 6, 8, 12.5 and 20 MeV per nucleon, at different impact parameters d of the primary ion trajectories with respect to the centre of the target volume SV. As it can be seen in Fig. 2, when d > 2.25 mm (∼12 nm at 1 g/cm³) the primary ion trajectories pass always outside SV. To study separately the track-core region (when the primary particle directly traverses SV) and the penumbra region (the particle passes nearby SV and the measured ionizations are produced only by secondary electrons emerging from the primary particle trajectory), the impact parameter d was varied between 0 mm and 7 mm, which corresponds to 0 μg/cm³ ≤ dρ ≤ 3.8 μg/cm2. A full description of the experimental procedure and of the data processing can be found in the publication of Conte et al. (2012).
where Ñ is the molecular number density of the target medium. The determination of σion (T ) is based on the analytical model of Rudd et al. (1985) for the integrated ionization cross section, which however is actually valid only for protons in methane. The procedure followed to get the data for 12C-ions in propane is described in ref (De Nardo et al., 2002). The spectral distribution of δ-electrons set in motion in propane was calculated by applying the model by Rudd et al. (1992). The simulation of the ionization component due to the δ-electrons takes into account elastic electron scattering, impact excitation, and impact ionization, assuming that the electrons always travel along straight lines between successive interaction points. The history of each electron is simulated until it leaves a pre-defined interaction volume, or until its energy is smaller than or equal to 10 eV which is close to the ionization threshold energy of about 11.08 eV in propane. To determine the cluster size distributions these low energy electrons are counted if they appear inside the target volume. The maximum energy, Tmax , transferred to an electron by a primary particle at energy T and relative atomic mass M can be approximated, in the case of non-relativistic energies, as follows:
2.2. Monte Carlo simulations To simulate the measurements, a dedicated track structure Monte Carlo code was used, which has been developed by B. Grosswendt (De Nardo et al., 2002; Grosswendt et al., 2014), to calculate the ionization component of the tracks of light ions penetrating propane thicknesses of small mass per area. The model is based on the assumption that in thin layers of gaseous propane elastic scattering, charge changing effects and impact excitation processes of the primary particles can be neglected. Consistently, it is assumed that the particles’ track structure and the resulting cluster size distributions Pν(Q,dρ) are determined only by the path lengths of the primary ion between two successive ionizing collisions, by the spectral and angular distributions of emerging secondary electrons, and by the properties of electron degradation in the target medium. The mean free ionization path length λion(T) of the carbon ion at energy T is determined by the corresponding ionization cross section σion (T ) :
λion (T ) =
1 N˜ × σion (T )
Tmax =
4mel T T × ⎛ ⎞ ≈ 2 × 10−3 × ⎛ ⎞ u ⎝M⎠ ⎝M⎠
(3)
where mel is the mass of an electron at rest, u is the atomic mass unit and (T / M ) is the energy per nucleon of the primary particle. Thus, the maximum energy of δ-electrons, Tmax , depends only on the primary ion velocity but not on its charge or mass. The maximum energy of δ-electrons, the penumbra radius (Rρ)P as given by the continuous-slowing-down mass range of electrons in propane (ESTAR), the ionization mean free path length (λρ)ion and the ratio (Dρ)/(λρ)ion of the particles investigated in this study are listed in Table 1. The ratio (Dρ)/(λρ)ion represents the mean number of ionizations produced by the primary ion along a path length equal to the diameter of the target volume, Dρ.
(2) 3
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From the ionization cluster size distributions Pν(Q,dρ) specific descriptors of the radiation quality can be derived, in particular the mean cluster size M1(Q,dρ) and the cumulative probabilities F1(Q,dρ), F2(Q,dρ) and F3(Q,dρ). The values obtained at impact parameter dρ = 0 μg/cm2, as derived from the spectra shown in Fig. 3, are summarized in Table 2. The value M1(Q,d=0) can be easily explained by considering the number of ionizations caused directly by the primary particles inside the target volume along its diameter. This number is equal to the ratio of the particles’ travelling lengths inside the target to their mean free ionization path lengths, (Dρ)/(λρ)ion. The number of primary ionizing interactions (D/λion) is about 76 for the 8 MeV/u 12C-ions, about 52 for the 12.5 MeV/u and about 35 for the 20 MeV/u ions. In view of the counting efficiency of the track-nanodosimeter of 20%, these numbers nicely agree with the measured mean cluster sizes M1. In a similar way, the mean value M1 = 11.2 for the 6 MeV/u ions is in good agreement with (D/λion) = 96 and a mean counting efficiency of 10%. In order to analyse the influence of radiation quality on the cluster size distributions caused by ionizing particles in a nanometer-sized target volume V in the penumbra region in a greater detail, Fig. 4 shows the measured cluster size distributions due to carbon-ions at 8, 12.5 and 20 MeV/u at the same impact parameter dρ = 2.7 μg/cm2. In the penumbra region, the three distributions Pν(Q) have the same shape for ν > 0, independent of the primary particle velocity. They differ only by a constant factor, corresponding to the number of initial δ-electrons set in motion along a relevant path length. The Pν(Q) for carbon ions at 6 MeV/u is not included in the previous figure, because, due to the reduced efficiency, it has a steeper slope with respect to the other ones. The number of initial δ-electrons set in motion along a relevant path length equal to target diameter Dρ is given by the ratio (Dρ)/(λρ)ion. Fig. 5 shows the scaled distributions relative to the 8 MeV/u 12C-ions, obtained by multiplying the P ν ≥ 1 by the factor k(Q) = (λρ)ion-Q/ (λρ)ion-8 MeV/u. It is clear that, when scaled to the same number of initial electrons set in motion by primary ionization processes, the cluster size distributions in the penumbra region are almost the same, invariant with the velocity of the primary particles. This invariance of the scaled distributions clearly demonstrates that the shape of the cluster size distributions at larger impact parameters in the penumbra region is independent of radiation quality, and that the relative cluster size frequencies for ν > 0 are directly proportional to the number of δ-electrons set in motion by the primary particles. The cluster size distribution for 6 MeV/u 12C-ions is also shown in Fig. 5, and it decreases more rapidly with ν, due to the reduced counting efficiency. To further investigate the shape of cluster size distributions in the penumbra region, Fig. 6 shows the measured cluster size distributions due to carbon-ions at 12.5 MeV/u and at impact parameter dρ = 2.6 μg/ cm2, dρ = 2.9 μg/cm2, dρ = 3.1 μg/cm2 and dρ = 3.7 μg/cm2, approximately corrected for the solid angle, i.e. multiplying P ν≥1 by (dρ)2. The scaled distributions are the same within statistical uncertainties, confirming that the cluster size distributions in the penumbra depend on the impact parameter almost exclusively through the solid angle. Similar results on the independence of impact parameter were also found for other ions (Conte et al., 2012), as well as in the measurements with the Ion-counter, a different nanodosimeter based on the counting of ions instead of electrons (Bashkirov et al., 2009; Hilgers et al., 2017). Considered the fact that the ionization-counting efficiency ε of the Startrack-Counter is spatially-dependent with a mean value ε ≈ 0.2 , the question arises whether it is possible to define an effective site size of uniform counting efficiency ε = 1, at least for primary particles traversing the target volume centrally (d = 0). The correspondence of ionization cluster size distributions measured in the target volume of Startrack with those simulated in a smaller volume with uniform efficiency ε = 1 was therefore investigated. As already described, the Startrack target volume is a cylinder with equal diameter and height equal to 3.7 mm. Filled with gaseous
Table 1 The maximum energy of δ-electrons, the penumbra radius (Rρ)P as given by the continuous-slowing-down mass range of electrons in propane (ESTAR), the primary ionization mean free path length (λρ)ion and the ratio (Dρ)/(λρ)ion of the 12C-ions at different energy per nucleon. Energy per nucleon (MeV/u)
Max energy of δelectrons (keV)
Penumbra radius (Rρ)p (μg/cm2)
(λρ)ion (μg/cm2)
(Dρ)/ (λρ)ion
6 8 12.5 20
13 17 27 44
300 600 1300 3000
0.021 0.026 0.038 0.057
96 76 52 35
The efficiency-map of the Startrack-counter is included in the Startrack-Monte Carlo code. As the detector loses efficiency for cluster sizes larger than 10, a time correction factor is afterwards applied to the simulated cluster size distributions. More details on the model and implemented cross sections can be found in References (De Nardo et al., 2002; Grosswendt et al., 2014). Two sets of simulations were performed. The aim of the first set was to reproduce the detector and the experimental conditions, in terms of real SV size, gas pressure and detection efficiency. Ionization cluster size distributions were simulated for 12C-ions passing at several impact parameters with respect to the sensitive volume, and compared with experimental results. Considered that the efficiency of our detector is only 20% on average, and furthermore it is also not uniform inside the target volume, a second set of simulations was performed, aiming to find an equivalent sensitive volume at efficiency 1, such that the ionization cluster size distributions produced in this volume are similar to those measured by the Startrack counter, at least for central passage (d = 0 mm) of the primary ions. Simulations were done in several smaller cylinders of different size, taking the same gas pressure (300 Pa) but considering a uniform 100% efficiency, until obtaining the good match with experimental data, and thus the associated SV of density 1 g/cm3 of our detector. 3. Results and discussion In order to investigate the track structure of particles at different velocity, we looked at the ionization cluster size distributions Pν(Q,dρ), measured and simulated by means of Monte Carlo calculations, at different impact parameter dρ. In Fig. 3 both experimental and calculated ionization cluster size distributions are shown at six impact parameters from dρ = 0 μg/cm2 to dρ = 3.8 μg/cm2. From (a) to (d) Fig. 3 shows the results obtained for 12C ions at 6, 8, 12.5 and 20 MeV per nucleon. A first glance at Fig. 3 immediately shows two different shapes of the cluster size distributions. In the track-core region of particle tracks (dρ < 1 μg cm−2), with the primary particles directly crossing the volume, the distributions are peaked, with a cluster size at maximum that increases with decreasing particle velocity, reflecting the shortening of the ionization mean free path (λρ)ion. For the carbon-ions at 72 MeV one must consider that the detector-parameters where set as to reduce the detecting efficiency by a factor of 2. In the penumbra region, for dρ > 1.2 μg/cm2, ionizations are produced inside SV only via δ-electron interactions. The probability that a δ-ray traverses SV also decreases with impact parameter dρ, mainly due to the decreasing solid angle. The most probable cluster size is always zero and the probability P0(Q,dρ) increases with increasing impact parameter dρ. The shape of the distributions is similar at any carbon-ion velocity and independent of the impact parameter: Pν(Q,V) decreases monotonically with increasing ν, and shows an almost exponential shape for ν ≥ 3. Both in the track-core and in the penumbra regions the agreement between measured and calculated distributions is very satisfactory. 4
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Fig. 3. Ionization cluster size distributions Pν(Q,dρ) produced in the nanometric target volume SV by 12C-ions at 6, 8, 12.5 and 20 MeV/u passing at six different impact parameters dρ: measurements (symbols) and simulations (lines). Error bars on experimental data represent statistical errors only. Statistical errors in the simulations are negligible. The sensitive volume of the detector has a diameter (Dρ)SV = 2.0 μg cm−2. The ion beam diameter, as defined by the collimators, is (Rρ)beam = 0.4 μg cm−2. Table 2 The ratio (Dρ)/(λρ)ion, the measured mean ionization cluster size M1 and the cumulative probabilities F1, F2 and F3 derived from experimental spectra shown in Fig. 3. 12C-ions crossing the target volume at its centre, at different energies per nucleon. Energy per nucleon (MeV/u)
(Dρ)/ (λρ)ion
M1
F1
F2
F3
6a 8 12.5 20
96 76 52 35
11.2 15.5 10.0 8.1
0.99999 1.0000 0.99997 0.99950
0.99981 1.0000 0.99963 0.99676
0.99895 1.0000 0.99795 0.98566
a Measurements performed at reduced detection efficiency (mean value ε ≈ 0.1).
propane at 300 Pa, the mass thickness of the diameter is approximately 2.0 μg/cm2 at T = 25 °C, corresponding to a length of 20 nm when scaled at a density of 1 g/cm3. By taking into account the mean value ε ≈ 0.2 of the spatially-dependent efficiency applied in the measurements, simulations were performed in different target volumes varying the diameter length between 0.7 and 0.8 mm with step of 0.02 mm. After the correction for the time-resolution of the experimental set-up, simulated cluster size distributions were compared with measured distributions. The best agreement on the mean value M1 and on the cumulative probabilities F1, F2 and F3 was found for D = 0.8 mm. For 6 MeV/u 12C-ions, which were measured with a reduced mean efficiency ε ≈ 0.1, the best agreement was found for D = 0.5 mm. Both measured and simulated cluster size distributions are shown in Figs. 7 and 8. The agreement is very satisfactory. In consequence, it can
Fig. 4. Measured cluster size distributions Pν(Q) for 12C-ions at 96, 150 and 240 MeV passing the target volume at impact parameter dρ = 2.7 μg/cm2. Error bars represent statistical errors only.
be assumed that the cluster size distributions measured by the Startrack-counter at 300 Pa C3H8 are close to those produced in the case of a smaller target volume and an ideal constant detection efficiency of 100%, at least for light-ions crossing the target volume at its centre. In this sense, the “effective-target size” of the Startrack counter is 0.8 mm, or 0.44 μg/cm2, at 300 Pa and standard operational conditions, and 0.5 mm, or 0.27 μg/cm2, when the operational conditions reduce the mean detecting efficiency to ε ≈ 0.1. 5
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Fig. 5. Measured cluster size distributions Pν(Q) for 6, 8, 12.5 and 20 MeV/u 12 C-ions passing the target volume SV at impact parameter dρ = 2.7 μg/cm2, normalized to the same number of initial δ-electrons set in motion along a relevant path length = Dρ. Error bars represent statistical errors only.
Fig. 8. Cluster size distributions Pν(Q) for 6 MeV/u 12C-ions traversing the target volume centrally, measured (symbols) and simulated (dashed black line) in the Startrack target volume, and simulated in a smaller volume with higher counting efficiency (continuous red line). See text for details. Error bars on experimental data represent statistical errors only. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
Table 3 The simulated mean ionization cluster size M1 and the cumulative probabilities F1, F2 and F3 for 12C-ions crossing the target volume along the diameter at its centre, at different energy per nucleon. The diameter of the simulated target is D = 0.8 mm, the target gas is propane at 300 Pa, the uniform detection efficiency is ε = 1. Energy per nucleon (MeV/u) a
6 8 12.5 20 a
Fig. 6. Measured cluster size distributions Pν(Q)x(dρ)2 for 12.5 MeV/u 12C-ions passing the target volume SV at impact parameter dρ = 2.6, 2.9, 3.2 and 3.7 μg/ cm2. Error bars represent statistical errors only.
M1
F1
F2
F3
11.4 15.2 10.5 8.00
1.00000 1.00000 0.99997 0.99937
0.99989 1.00000 0.99968 0.99498
0.99930 1.00000 0.99804 0.97958
Simulation performed in a target with D = 0.5 mm.
The values for M1, F1, F2 and F3 resulting from the simulations performed in the effective target volumes with efficiency ε = 1 are given in Table 3.
4. Conclusions The track structure of carbon ions was studied by measuring the ionization cluster size distributions produced in a nanometric target volume SV by Carbon ions traversing SV or passing by at specified distances. Measurements and simulations were performed for four different energies close to the Bragg peak. The cluster size distributions in the track-core and in the penumbra regions of particle tracks confirmed the general shape that had already been observed. In particular, the shape of the distributions at large distances, where only δ-electrons contribute to the ionization yield inside SV, is invariant with the velocity of the primary particle and also with the distance, at least in the limited range of investigated energies and distances. In order to study how this invariance correlates with the degradation spectra of secondary electrons, for different velocities of the primary ions, a new extended set of Monte Carlo simulations is planned for a future work. The possibility to define an effective target volume was also investigated by means of Monte Carlo simulations. The outcome is that, at least for the particles traversing the target at its centre, the cluster size distributions measured in the 3.7 mm of the Startrack target (mean efficiency 20%) are very close to those simulated in a 0.80 mm target with uniform 100% efficiency. In this sense the effective target size of
Fig. 7. Cluster-size distributions Pν(Q) for 8, 12.5 and 20 MeV/u 12C-ions traversing the target volume centrally, measured in the Startrack target volume (symbols) and simulated in a smaller volume with efficiency ε = 1 (lines). See text for details. Error bars on experimental data represent statistical errors only.
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the Startrack counter is 0.80 mm, or 0.44 μg/cm2 at 300 Pa of propane, which corresponds to a length of 4.4 nm at a density of 1 g/cm3. Taking into account the ratio of the ionization mean free path in liquid water and in gaseous propane, our detector measures cluster size distributions equivalent to those for a liquid water cylinder 5.5 nm in diameter (Grosswendt, 2004; Grosswendt et al., 2004). Considered that in previous work (Conte et al., 2018) the relevant target size had been suggested to be in the range 1–1.5 nm, it is clear that a modification is necessary for the operational conditions of Startrack counter, in order to reduce the effective target size. It is therefore important to investigate the possibility to operate the detector at gas pressures lower than 300 Pa, and to study the effect of this pressure reduction on the mean detection efficiency. Future work will be devoted to this subject.
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Acknowledgement This work has been supported by the 5th Commission of INFN (Italian National Institute for Nuclear Physics), Frascati-Italy, under the research project NIRVANA. Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.radphyschem.2019.108576. References Bashkirov, V., Schulte, R., Wroe, A., Sadrozinski, H., Gargioni, E., Grosswendt, B., 2009.
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