Abstract Recombination chambers are linear energy transfer (LET)-dependent detectors and their applications are closely related to the problem of estimating radiation quality. The operational principle is based on the phenomenon of the initial recombination of ions in gases. Practical usefulness of the chambers is well confirmed by experimental results, however, the correlation of the response with LET is based on an approximated theoretical description of initial recombination of ions in gases. In this work, a precise numerical model of the REM-2 recombination chamber has been prepared, in order to calculate the dose distributions versus LET inside the chamber. The results form a set of data for further validation of recombination methods. INTRODUCTION The estimation of radiation quality by means of recombination methods is performed for more than 50 years(1, 2). Correlation of the amount of initial recombination in pressurized gases with local ionization density, ν, and linear energy transfer (LET), L, forms the basis for the use of the initial recombination phenomenon for radiation quality determination. The ion collection efficiency, f, of the recombination chamber can be described by an approximated formula(3): f=1D∫d(μ)1+μ1−fCsfcsdμ (1) where D is the total absorbed dose and d (μ) is the dose distribution versus μ. The relative ion density μ is defined as the ratio μ = υ/υ0 of the local ion density υ in tracks of the considered charged particles to a constant value υ0, which corresponds to the value of local ionization density in a reference radiation field of 137Cs radiation source, while ion collection efficiency in this field is fCs. The ion collection efficiency in the investigated field, f and fCs have to be determined under conditions of initial recombination of ions and at the same polarizing voltage. In order to achieve the initial recombination conditions, the gas pressure and polarization voltage should be chosen in such a way that volume recombination is negligible. For practical reasons it can be assumed(3–5) that μ≅LL0 (2) where L0 = 3.5 keV/μm. Equation (1), together with the Equation (2), became a basis for two measuring methods. One of them (recombination microdosimetric method(4, 5), RMM) includes a deconvolution procedure, which makes it possible to determine the D(L) distribution and to separate low-LET and high-LET dose components. The main advantage of the method is its usefulness in mixed radiation fields of unknown energy and composition, provided that the measurements of the ionization current are performed with an accuracy of not <0.2%. RMM method is used mainly for research purposes, while recombination chambers are most frequently used for radiation protection purposes. Then, the simplified approach is applied and a quantity called Recombination Index of Radiation Quality (RIQ, Q4) is used for estimation of the radiation quality factor. Q4 is derived from the measured values as follows(6, 7): Q4=1−f(UR)1−fc(UR)=1−f(UR)1−0.96 (3) where f (UR) and fc (UR) are the ion collection efficiencies at the voltage UR for the investigated radiation field and the reference gamma radiation field, respectively. The voltage UR that ensures 96% saturation in the reference gamma radiation field must be determined as a part of the calibration procedure for a particular chamber. The approximate dependence of the Q4 on the local ionization density, derived from theories of initial recombination of ions, can be expressed as follows(5, 6): Q4≅LL01+0.04(LL0−1)forL≥3.5keV/μm (4a) Q4≅0.85+0.15LL0forL<3.5keV/μm (4b) Practical usefulness of RIQ is well confirmed by experimental results, however, the correlation of RIQ with LET is based on approximated theoretical description of the initial recombination of ions in gases, so also the correlation of RIQ with the radiation quality factor is approximated with relatively high inaccuracy of ~20% in complex radiation fields(5). Moreover, the Q(L) relationship recommended by ICRP changed(8–10) from the time when the RIQ has been defined. Further validation of the methods is still desirable. That is why the need for D(L) distribution calculation in recombination chamber was indicated. Taking into account currently available numerical codes and presence of highly efficient computational clusters, the calculations may considerably improve physical justification and accuracy of recombination methods. METHODS A numerical model of the REM-2 type recombination chamber (Figure 1) was created for Monte Carlo calculations performed in this work. The chamber is a tissue equivalent, pressurized (1 MPa) ionization chamber, with a volume of ~1800 cm3, which contains 25 electrodes and is filled with a mixture of hydrocarbon and nitrogen gases. The distance between the electrodes is equal to 7 mm. Alternately mounted parallel-plate polarizing and collecting electrodes assure sufficient ion collection efficiency, and a domination of the local recombination over the volume recombination, in particular for low polarizing voltages. The chamber utilizes the dependence of the efficiency of collecting ions in the ionization chamber (which operates in the conditions of initial recombination) on the radiation quality of the measured radiation field. Figure 1. View largeDownload slide Cross section of the REM-2 recombination chamber—numerical model. The simulated part and the irradiation field are marked. Figure 1. View largeDownload slide Cross section of the REM-2 recombination chamber—numerical model. The simulated part and the irradiation field are marked. FLUKA version 2011.2c-5 was used for calculations performed in this work. It is a multi-purpose Monte Carlo code for calculations of particle transport and interactions with matter, covering an extended range of applications. It calculates energy losses due to electromagnetic interactions, energy loss fluctuations, Coulomb scattering, elastic and inelastic nuclear interactions of primary particles and all produced secondary particles(11, 12). A 2.3 × 14.0 cm2 monoenergetic parallel beam of neutrons with energy range from 500 keV to 200 MeV with no momentum spread and no divergence was dumped perpendicularly to the long axis of the chamber into a section of the REM-2 type recombination chamber. The simulated section covers a range equal to three parallel-plate electrodes, including gas cavities and housing of the chamber. The scoring region was defined as an active gas cavity placed between the collecting and the polarizing electrodes. For the simulations, the pre-defined ‘default precision’ configuration was chosen. It initializes the code with a standard set of particle production and transportation thresholds. Kinetic energy threshold for delta ray production was set to 100 eV, Rayleigh scattering and inelastic form factor corrections to Compton scattering and Compton profiles were activated. Particle transport threshold was set at 100 eV, except neutrons where it was equal to 0.01 meV. The double differential yield (d2/dL dE) of all charged particles produced due to interactions per primary incident neutron, with respect to LET and energy was calculated. The d/dL single differential yield with respect to LET was obtained from the double differential yield due to an unitary energy interval. The single differential yield with respect to LET was then multiplied by each LET bin width to get the yield per primary incident neutron at each LET bin. Finally, it was multiplied by the energy loss in each bin in order to get the L d (L) distribution per primary neutron. LET was scored in the range from 0.1 to 1000 keV/μm logarithmically divided into 100 bins. RESULTS AND DISCUSSION LET spectra of secondary charged particles released in the active volume of the REM-2 type recombination chamber were calculated for monoenergetic neutrons in the energy range from 500 keV to 200 MeV. The scoring area was defined on the border between the chamber electrodes and filling gas. Then, the distributions of the dose versus LET were obtained. It should be noted that in FLUKA code only the recoil protons and protons from N(n, p) reaction are produced and transported explicitly, taking into account the detailed kinematics of elastic scattering, continuous energy loss with energy straggling, delta ray production, multiple and single scattering, while all other charged secondary particles produced by neutrons at energy < 20 MeV are not transported but their energy is deposited at the point of interaction(11). Therefore, for neutrons with energies up to 20 MeV, the attention was paid only to the electron and proton secondary particles and their impact on total LET distribution. Because of the limitations, the results do not contain high-LET components. Above 20 MeV heavy ions are transported and they participate in total LET, what can be seen below (high-LET components above 100 keV/μm). Calculated spectra divided into four groups, according to neutron energy, are presented in the Figures 2–5. Figure 2. View largeDownload slide Calculated LET spectra in REM-2 chamber for monoenergetic neutrons of energy 500 keV, 1 MeV and 1.2 MeV. Figure 2. View largeDownload slide Calculated LET spectra in REM-2 chamber for monoenergetic neutrons of energy 500 keV, 1 MeV and 1.2 MeV. Figure 3. View largeDownload slide Calculated LET spectra in REM-2 chamber for monoenergetic neutrons of energy 2 MeV, 2.5 MeV and 5 MeV. Figure 3. View largeDownload slide Calculated LET spectra in REM-2 chamber for monoenergetic neutrons of energy 2 MeV, 2.5 MeV and 5 MeV. Figure 4. View largeDownload slide Calculated LET spectra in REM-2 chamber for monoenergetic neutrons of energy 8 MeV, 10 MeV and 14 MeV. Figure 4. View largeDownload slide Calculated LET spectra in REM-2 chamber for monoenergetic neutrons of energy 8 MeV, 10 MeV and 14 MeV. Figure 5. View largeDownload slide Calculated LET spectra for monoenergetic neutrons of energy 14.6 MeV, 20 MeV, 60 MeV and 100 MeV. Figure 5. View largeDownload slide Calculated LET spectra for monoenergetic neutrons of energy 14.6 MeV, 20 MeV, 60 MeV and 100 MeV. For incident neutrons at energy range up to 1.2 MeV, a strong peak at ~70 μm/keV is dominant. Generally, lowering the incident neutron energy increases the high-LET. For low energy neutrons (below 1 MeV) one can see the slope of LET spectra reaching 10 μm/keV, which for higher energy gets wider and shifts to lower LET values. As it could be expected, higher neutron energies give a wider spread of LET values (Figures 3–5). At the low-LET end, higher energy neutrons produce recoil protons of higher energy and lower LET. At energy equal to 14 MeV, the relative contribution of low-LET protons reaches its maximum intensity, and decreases as the incident neutron energy rises. At the high-LET of the spectrum, high-energy neutrons induce more nuclear reactions and transfer more energy to heavy oxygen, nitrogen and carbon recoils. As mentioned above, this part of the spectrum has not been included in the calculations. Above 15 MeV, because of the threshold reactions, there are additional heavy LET components, i.e. alpha particles, deuterium, triton and He-3 ions. For 20 MeV neutrons, there is significant component of deuterons but it is much weaker and wider than in the case of 60 MeV neutrons. There is a small contribution of tritons for 20 MeV incident neutrons. Contribution of He-3 is negligible in that case, while for 60 MeV they give noticeable impact on the total LET spectrum. The triton component for incident high-energy neutrons also gives a wide spectra contribution for total LET. An investigation of the components of the LET spectrum was performed for all the above mentioned incident neutron energies. For energies below 20 MeV only recoil protons and electrons were considered. The electron component has practically the same LET distribution. Electrons give strong contribution to total LET below 1 keV/μm, and reach 20 keV/μm maximum (e.g. 10 MeV neutrons is given in Figure 6). Figure 6. View largeDownload slide Calculated LET spectra for 10 MeV monoenergetic neutrons. p-proton and e-electron components. Figure 6. View largeDownload slide Calculated LET spectra for 10 MeV monoenergetic neutrons. p-proton and e-electron components. Component LET spectra of protons, deuterons, tritons, alphas and electrons for 20 MeV are presented in Figure 7. Figure 7. View largeDownload slide Calculated LET spectra for 20 MeV monoenergetic neutrons. p-proton, d-deuteron, t-triton, He-4-helium and e-electron components. Figure 7. View largeDownload slide Calculated LET spectra for 20 MeV monoenergetic neutrons. p-proton, d-deuteron, t-triton, He-4-helium and e-electron components. CONCLUSIONS A high precision numerical model of the recombination chamber REM-2 was prepared. LET distributions of secondary ionizing particles created inside the chamber cavity were calculated. The results are the first numerical set of data for validation of the results obtained by RMM and will be a basis for further investigation for RIQ(L) relationship for recombination methods. FUNDING This work was supported by the National Science Centre, Poland [2015/19/N/ST7/01202]. REFERENCES 1 Zielczynski , M. Use of columnar recombination for determination of relative biological efficiency of radiation . Nukleonika 7 , 175 – 182 ( 1962 ). 2 Sullivan , A. H. and Baarli , J. An ionization chamber for the estimation of the biological effectiveness of radiation. CERN Report 63-17. CERN, Geneva, Switzerland ( 1963 ). 3 Golnik , N. Recombination Methods in the Dosimetry of Mixed Radiation. Report IAE-20/A ( Poland : Institute of Atomic Energy, Świerk ) ( 1996 ). 4 Golnik , N. and Zielczynski , M. Determination of restricted LET distribution for mixed (n,g) radiation fields by high pressure ionization chamber . Radiat. Prot. Dosim. 52 , 35 – 38 ( 1994 ). Google Scholar CrossRef Search ADS 5 Golnik , N. Microdosimetry using a recombination chamber: method and applications . Radiat. Prot. Dosim. 61 , 125 – 128 ( 1995 ). Google Scholar CrossRef Search ADS 6 Zielczyński , M. , Golnik , N. , Makarewicz , M. and Sullivan , A. H. Definition of radiation quality by initial recombination of ions. Proceedings of 7th Symposium, Microdosimetry, Oxford (Harwood Academic Publishers for CEC, Luxembourg: EUR 7147), Vol. 2, pp. 853–862 ( 1980 ). 7 Zielczyński , M. and Golnik , N. Recombination Index of Radiation Quality—measuring and applications . Radiat. Prot. Dosim. 52 , 419 – 422 ( 1994 ). Google Scholar CrossRef Search ADS 8 ICRP Publication 21 . Data for Protection against Ionizing Radiation from External Sources—Supplement to ZCRP Publication IS, Pergamon Press, Oxford ( 1973 ). Superseded by ICRP Publications 33 and 51. 9 ICRP ( 1991 ). 1990 Recommendations of the International Commission on Radiological Protection. ICRP Publication 60. Ann. ICRP 21 (1–3). 10 ICRP ( 2007 ). The 2007 Recommendations of the International Commission on Radiological Protection. ICRP Publication 103. Ann. ICRP 37 (2–4). 11 Böhlen , T. T. , Cerutti , F. , Chin , M. P. W. , Fassò , A. , Ferrari , A. , Ortega , P. G. , Mairani , A. , Sala , P. R. , Smirnov , G. and Vlachoudis , V. The FLUKA Code: developments and challenges for high energy and medical applications . Nucl. Data Sheets 120 , 211 – 214 ( 2014 ). Google Scholar CrossRef Search ADS 12 Ferrari , A. , Sala , P. R. , Fasso , A. and Ranft , J. FLUKA: a multi-particle transport code. INFN/TC_05/11, SLAC-R-773 ( 2005 ). © The Author(s) 2018. Published by Oxford University Press. 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Radiation Protection Dosimetry – Oxford University Press
Published: Aug 1, 2018
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