CC BY
12
УДК: 539.12
V.M. LAZURIK, V.T. LAZURIK, G.F. POPOV
V.N. Karasin Kharkiv National University,
Z. ZIMEK
Institute of Nuclear Chemistry and Technology
ESTIMATION OF ACCURACY AT DETERMINATION OF ELECTRON ENERGY BASED ON TWO PARAMETRIC MODEL OF ELECTRON BEAM
Accuracy of computational method for determining the energy of electron radiation, which was developed on the basis of two parametric electron beam models, is estimated for case when the electron source in the radiation-technological process has an energy spread. Accuracy is estimated with numerical methods using the electron spectra measured in different operating modes of the radiation-technological line.
Key words: parametric model of electron beam, electron spectrum, depth distribution of dose.
В.М. ЛАЗУРИК, В.Т. ЛАЗУРИК, Г.Ф. ПОПОВ
Харгавський нацюнальний ушверситет iM. В.Н.Каразша,
З. З1МЕК
1нститут Ядерно! XiMii i Технологш, Варшава, Польща
ОЦ1НКА ТОЧНОСТ1 ВИЗНАЧЕННЯ ЕНЕРГП ЕЛЕКТРОННОГО ВИПРОМ1НЮВАННЯ НА ОСНОВ1 ДВОПАРАМЕТРИЧНО1 МОДЕЛ1 ЕЛЕКТРОННОГО ПУЧКА
Оцтюеться похибка обчислювального методу визначення енергИ електронного випромтювання, який був розроблений на основi двопараметрично'1 модел1 електронного пучка, для випадку, коли джерело електронгв в радiацiйно-технологiчному процеа мае енергетичний розкид. Похибка оцтюеться чисельними методами i3 використанням спектрiв електротв, вимiряних в рiзних режимах роботи радiацiйно-технологiчноi лтИ.
Ключовi слова: параметрична модель електронного пучка, спектр електротв, глибинний розподш
дози.
В.М. ЛАЗУРИК, В.Т. ЛАЗУРИК, Г.Ф. ПОПОВ
Харковский национальный университет им. В.Н.Каразина,
З.ЗИМЕК
Институт Ядерной Химии и Технологий, Варшава, Польша
ОЦЕНКА ТОЧНОСТИ ОПРЕДЕЛЕНИЯ ЭНЕРГИИ ЭЛЕКТРОННОГО ИЗЛУЧЕНИЯ НА ОСНОВЕ ДВУХПАРАМЕТРИЧЕСКОЙ МОДЕЛИ ЭЛЕКТРОННОГО ПУЧКА
Оценивается погрешность вычислительного метода определения энергии электронного излучения, который был разработан на основе двухпараметрической модели электронного пучка, для случая, когда источник электронов в радиационно-технологическом процессе имеет энергетический разброс. Погрешность оценивается численными методами с использованием спектров электронов, измеренных в различных режимах работы радиационно-технологической линии.
Ключевые слова: параметрическая модель электронного пучка, спектр электронов, глубинное распределение дозы.
The problem formulation
At present, a large volume of products undergoes radiation treatment using electron beams [1]. At planning stage, the choice of optimal regime of the radiation-technological process can be performed on basis of computer modeling of the dose distribution of electron radiation in the objects undergoing processing [2,3]. At the stage of realization of the chosen mode of technological process, dosimetry methods of ionizing radiation are needed, which allow to determine with high accuracy the energy of electron radiation source in the process of radiation treatment. Certainly, today, there are methods and equipment capable of determining the characteristics of electron radiation with high accuracy. However, these methods are designed to solve scientific research problems and, as a rule, cannot be used to control the processes of irradiation in radiation technologies. Therefore, development of methods that allow with high accuracy to determine the electron beam energy of source is an actual task for realization of radiation technologies.
Analysis of recent investigations and publications
Influence of the energy spread of electron beam on the depth dose distribution was studied in [4]. To describe the energy spread of electrons, it was used the model of electron spectra in form of a triangular probability distribution. The depth distribution of the dose of electron radiation in an aluminum target was simulated by the Monte Carlo method in a detailed physical model using RT-Office software [5]. Obtained results of computer simulation were processed with standard computational methods of dosimetry electron radiation, which are used in processing the results of measurements of depth dose distributions performed by the dosimetric wedge or stack method [6]. The results of numerical studies show that the practical range of electrons Rp depends strongly on the
energy spread of electrons and weakly correlates with the value of the most probable electron energy Ep for asymmetric electron spectra. Relatively the depths of half dose reduction R50, it was shown that a correlation is observed between this value and the average electron energy in the beam EAv, even for large values of the electron energy spread.
Thus, when the source of electrons has an energy spread, for dosimetry of electron radiation, along with the traditionally used value of the practical range of electrons Rp, the depth of half-reduction of the dose is
important R50 . In this connection, the method of dosimetry of electron radiation based on two parametric electron
beam models [7] is of interest, using which one can simultaneously determine Rp and R50 - standard characteristics
of depth distributions of the electron radiation dose. It should be note that the main assumption that ensures agreement of the results obtained using this method with the results obtained on the basis of standard procedures for processing measurements, is the possibility of approximating the measurements results in a semi-empirical model of the depth distribution of the dose of monoenergetic electron radiation.
Since electron sources in radiation-technological processes can differ substantially from monoenergetic ones, it is necessary to estimates accuracy in determining the standard characteristics of the electron-beam energy obtained with method proposed in [7] for the cases when the electron sources have the energy spread.
Formulation of research objective
Accuracy of the computational method for determining the energy of electron radiation based on two parametric electron beam models, which was previously proposed and tested on the results of measurements, was studied. Accuracy was estimated by numerical methods using a set of electron spectra measured in various operating modes of the radiation-technological line of the Sterilization Center of the Institute of Nuclear Chemistry and Technology in Warsaw.
The errors in the method for determining of electron radiation energy in the presence of an electrons energy spread
The depth distribution of the electron radiation dose in case of a non-monoenergetic electron beam can be represented in the form
E max
DM (x) = 0. j DM (x, E) • S(E)dE (1)
E min
Here DM (x) - depth-dose distribution of electrons radiation in the material M, DM (x, E) - depth-dose distribution in the material at irradiation with mono-energetic electron beam with fluency O e = 1 and energy electrons E, S(E) - electron beam spectrum, O e - electron fluency.
The main assumption of the two parametric model of the electron beam is fact that the results of measurements of the depth dose distributions of electron radiation can be well approximated by a function
D*(x,X0,E0)that depends only on the distance x to the target boundary and contains three free parameters (Oo, X0, E0)
D*M( x, X0, E0) -O 0 • Dm (x + X0, E0) (2)
O 0 - scale factor, X0 - displacement and E0 - effective energy of electrons.
At that the approximating function is superimposed on the condition, that provide the law of conservation of energy Qtot transferred by the electron radiation to the target material in the depth interval from Xmin to Xmax.
X max
Qoot = j D*( x, X0, E0)dx (3)
The energy Qtot transferred to the target material by electron radiation is determined on the basis of the dose distribution measured in the target in the depth interval from Xmin to Xmax.
X max
Qoot = J DM (X )dx
X min
Condition (3) allows us to determine two independent parameters (X 0, E0)of the approximating function by the method of least squares. In this case, the scale factor can be determined from equation
X max
Qtot =Ф 0 J Dm (X + X 0, Eo)dx (4)
X min
Thus, the use of condition (3) makes it possible to realize a conservative computational method [8] for determining the values of three free parameters of function (2) on the basis of two parametric electron beam models. Software that implements the procedures for determining the parameters of the electron beam model from the measurement results is described in [9].
To estimate accuracy of the method for calculating the characteristics of the radiation energy, in the presence
of an energy spread of electrons, the electron spectrum S(E) of the radiation source was used. Based on the electron spectrum, the depth dose distributions of electron radiation in an aluminum target are simulated by the Monte Carlo method [5]. The results of computer modeling assume as the results of measurements of deep dose distributions performed by the method of dosimetric wedge or stack, and processed with standard methods of dosimetry of electron radiation [6]. Accuracy of values were obtained as values of the deviations of the results of calculating the practical ranges of electrons R and the depths of the half-reduction of the dose R50, calculated
using standard methods [6] and a method based on two parametric electron beam models [7]. Spectra of electrons from a radiation source
To estimate accuracy of the method for calculating the characteristics of radiation energy, we used the electron beam spectra from the linear electron accelerator Elektronika 10/10 with electron beam energy of 10 MeV at Institute of Nuclear Chemistry and Technology, Warsaw, Poland. The spectra of electrons are shown in Fig.1.
Fig. 1. Spectra of electrons S (E) for different accelerator parameters (Si - magnetron RF source average current: 600 mA; pulse current of electron gun: 400 mA, and respectively: S2 - 700 mA; 500 mA, S3 - 550 mA; 300 mA)
Characteristics of spectra: Ep - is the maximum possible electron energy, EAv - average electron energy,
D - dispersion of the energy distribution of electrons, u - root-mean-square deviation of electron energy (energy spread of electrons) calculated from the data presented in Figure 1 are shown in Table 1. In the figure, vertical dashed curves indicate values for each of the spectra.
As can be seen from the Fig. 1 - the spectra of electron beam 1 and 3 are asymmetric; the spectrum 2 is close to the symmetric one. The indicator of asymmetry can be the relative deviation of the average electron energy
from the maximum probable electron energy. KAs = (Ep — EAv) /EAv .
Table 1
Characteristics of spectra from the source of electrons radiation
Spectrum Ep, [MeV] EAv , [MeV] D, [MeV2] G, [MeV] g/EAv , [%] KAs, [%]
S3 8.30 8.01 0.17 0.41 5.14 3.62
S2 8.80 8.72 0.05 0.23 2.59 0.92
Si 9.30 8.79 0.46 0.68 7.75 5.78
As follows from the Table 1, the value of asymmetry index KAs for the spectrum of S2 ,is much smaller
than the values for the spectra Sj and S3
The depth-dose distribution of electron radiation in an aluminum target
The depth-dose distribution of electron radiation in an aluminum target was simulated by the Monte Carlo method in a detailed physical model using RT-Office software [5]. Figure 2 shows the results of calculations for sources with different electron spectra.
Fig. 2. Depth-dose distributions of the electron radiation in an aluminum target. Histogram D1 - calculation of the dose for the source of electrons with the spectrum S1, D2 - spectrum of the source S2, and D3 - spectrum of the source S3.
Note, that for the spectra of S2 and S3, all characteristics given in Table 1 differ greatly except for the quantities EAv . As can be seen in Fig. 2, the depth distributions of dose D2 and D3 from electron sources with these
spectra differ insignificantly. Otherwise, when characteristics of the spectra differ significantly (for example, for spectra S2 and S3), the differences in depth distributions of the dose D2 and D3 can be significant (see D2 and D3 in Fig. 2). Furthermore, we note, that difference in characteristic values for the spectra of S1 and S2 and for the spectra of S2 and S3 is close (about 0.5 MeV). However, this difference in values of the characteristics does not lead to significant differences in depth distributions of the dose D2 and D3 (electron sources with spectra S2 and S3). These facts confirm the conclusions of paper [4] about more important role of the spectrum characteristic EAv with respect to the characteristic Ep in estimation of depth distributions of the electron radiation dose, in
presence of an electron energy spread.
Processing results of computer modeling the depth-dose distributions
The results of computer simulation were processed with a method that was developed on the basis of two parametric electron beam models [7] and standard computational methods for radiation dosimetry [6]. The results of processing the depth dose distribution from sources with different electron spectra are presented in Table 2.
Characteristics of the depth dose distributions, calculated using two parametric electron beam model (Rp standard methods (R*p, R*50) of electron radiation dosimetry.
Table 2 , R50) and
Dose Eo Xo Rp R50 R*P R 50
Di 8.01 -0.006 1.61 1.26 1.60 1.25
D2 8.66 0.007 1.75 1.37 1.73 1.37
D3 8.97 -0.091 1.78 1.39 1.77 1.38
As follows from a comparison of the practical range of electrons and the half-dose reduction depths presented in Table 2, accuracy of computational method, which was developed on the basis of two parametric electron beam models, does not exceed 1% relative to standard methods.
Results and conclusions
It is shown in the paper, that use of a computational method, developed on the basis of two parametric models of an electron beam, makes it possible to determine, with a small relative error, the energy characteristics of not monoenergetic electron radiation. The proposed computational method for dosimetry of electron radiation can be successfully applied also in the case of sufficiently large (<10%) energy spread of electrons in the beam.
An important advantage of the method is the ability, in a consistent calculation scheme, to determine simultaneously two standard characteristics of electrons depth dose distributions, such as the practical range of electrons Rp and the depth at which the dose equals half of the maximum dose R50. The relative error in
calculating these characteristics does not exceed 1%.
In the future, it is necessary to study the possibilities of using two parametric electron beam model for processing special data samples from a set of results of measurements of deep dose distributions made using the dosimetric wedge or stack methods. Such possibilities of computational method will make it possible to eliminate errors in the results of measurements that arise due to edge effects in construction of the dosimeter wedge and nonlinear response of dosimetric film to transferred energy of the electron radiation.
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References
ISO/ASTM Standard 51649, Practice for dosimetry in an e-beam facility for radiation processing at energies between 300 keV and 25 MeV. Annual Book of ASTM Standards. Vol. 2005.12.02.
ASTM Standard Е2322-02 Standard Guide for Selection and Use of Mathematical Methods for Calculating Absorbed Dose in Radiation Processing Applications, Annual Book of ASTM Standards 12.2002. "Nuclear Energy Agency, Data Base" The abstracts of the computer programs. http://www.nea.fr/html/dbprog. Z. Zimek, V.M. Lazurik, V.T. Lazurik, G. Popov. Evaluation of electron beam energy spread variation on quality of radiation processing.//IRaP 2016, The 12th meeting of the "Ionizing radiation and polymers" symposium (September 25-30, 2016) - Peninsula of Giens, France, 2016 - P. 143.
V.M. Lazurik, V.T. Lazurik, G. Popov, Yu. Rogov, Z. Zimek. Book "Information System and Software for Quality Control of Radiation Processing", IAEA Collaborating Center for Radiation Processing and Industrial Dosimetry, Warsaw, Poland, 2011, 220 p
ICRU REPORT 35. Radiation dosimetry: electron beams with energies between 1 and 50MeV, 1984-160 p. V.M. Lazurik, V.T. Lazurik, G. Popov, Z. Zimek. Two-parametric model of electron beam in computational dosimetry for radiation processing. // Radiation Physics and Chemistry, - 2016. - Vol. 124. - P. 230-234. Pochynok A.V., Lazurik V.T., Sarukhanyan G.E The parametric method of the determination of electron energy on the data obtained by the method of a dosimetric wedge //Bulletin Kherson National Technical University. - 2012. - Vol. 2(45). - P.298-302.
Лазурик В.М., Шаптала Ю.А., Салах Саван. Программная реализация определения энергии электронов по экспериментальным данным, полученным методом дозиметрического клина // ВЕСТНИК Херсонского национального технического университета - 2016. - № 3(58). - С. 245-248.
