- Email: [email protected]
Optimization of electron beam crosslinking for cables
Radiation Physics and Chemistry 94 (2014) 161–165
Contents lists available at ScienceDirect
Radiation Physics and Chemistry journal homepage: www.elsevier.com/locate/radphyschem
Optimization of electron beam crosslinking for cables Z. Zimek n, G. Przybytniak, A. Nowicki, K. Mirkowski, K. Roman Institute of Nuclear Chemistry and Technology, Warsaw, Poland
H I G H L I G H T S
Dose distribution simulation was performed using ModeCEB computer program. Simulated and experimental data on dose homogeneity were compared. High influence of EB divergence on the dose distribution was found.
art ic l e i nf o
a b s t r a c t
Article history: Received 7 November 2012 Accepted 4 July 2013 Available online 13 July 2013
Relationship between electron beam parameters (energy, energy spread, and electron beam distribution in irradiation zone), electrical cable geometry (thickness of polymer layers and metal wire diameter), construction (jacked, insulation) and dose distribution represented by the Dmax/Dmin coefficients were investigated. The simulations were performed using ModeCEB computer program (Lazurik et al., 2011) and then compared with the experimental data. It was demonstrated that computer simulations based on the ModeCEB program are sufficient for modeling absorbed dose distribution in the multi-layers circular objects irradiated with scanned electron beam. The calculations revealed (1) significant inhomogeneous circumferential dose distribution in polymeric sub-layers (2) relatively low influence of electron beam energy spectrum on homogeneity of irradiation and (3) high influence of beam divergence on the circumferential dose distribution. & 2013 Elsevier Ltd. All rights reserved.
Keywords: Monte Carlo simulation Electron beam Cable irradiation
1. Introduction Wire and cable radiation crosslinking is one of the most successful implementation of radiation technology and sustain to be attractive method for modification variety new polymer material implemented in cable industry (Chmielewski et al., 2005; Rouif, 2005). The process was found to be less expensive requiring less factory floor space, accepting wide range of insulating materials and offering faster processing rate in comparison with chemical methods. Electron beams applied for radiation processing of electrical wire and cable are the most frequently used within electron energy range 0.5–3 MeV and occasionally up to 10 MeV. The requirements associated with the construction of acceleratorbased facility are related to the product characteristics and process capacity. The throughput is directly linked with beam power level that can vary in the range of 20–500 kW depending on the accelerator type. Usually in wire and cable processing absorbed dose is situated in the range from 50 to 200 kGy. Difficulties in handling irradiation process may appear at a very high rate of irradiation what correspond to a very high beam power level. Wire
n
Corresponding author. Tel.: +48 22 504 13 84; fax: +48 22 504 13 13. E-mail address: [email protected] (Z. Zimek).
0969-806X/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.radphyschem.2013.07.005
and cable handling equipment should allow work with sufficiently high speed of the rewinding and obtain adequate homogeneity of irradiation what is directly related to the final product quality and reliability. The economical condition of any industrial activity requires process optimization to reduce unit cost of the operation but sustaining adequate quality of the final product. The computer simulation method becomes a very effective tool for optimization process providing necessary information in short time and reducing cost in comparison with conventional approach based on experimental dosimetry (Weiss et al., 1997; Kaluska et al., 2007; Ciappa et al., 2012). 2. Accelerator facility The quality of modified polymer is defined mostly by homogeneity of irradiation. The radiation technology (accelerator and rewinding or transport systems) should allow provide homogenous dose distribution of suitable level for all sizes and dimensions of processed wires and cables. The number of cable and wire handling techniques were developed and tested to obtain two, three and even four sided irradiation. The so-called rotary techniques and specific configuration of the irradiation zone provided by
162
Z. Zimek et al. / Radiation Physics and Chemistry 94 (2014) 161–165
the external magnets were tested as well. Accelerator is the crucial equipment which defines basic technical and economical parameters of any radiation facility. The under beam equipment which
Fig. 1. Dose distribution in irradiation zone measured at a distance of 45 cm bellow exit window (electron energy 1.5 MeV; scan path 40 cm).
Fig. 2. EB divergence angle versus electron energy for the distance 25–65 cm from the exit window.
is dedicated to rewinding wires and cables should be capable of utilize efficiently energy provided by electron beam. Electron beam spatial distribution in the irradiation zone is one of the important parameter of radiation processing. The detail knowledge is needed to select the most appropriate conditions and to optimize the radiation processing. Fig. 1 shows an example of electron beam spatial distribution measured by cellulose triacetate dosimetric foil to characterize spatial deposition of electron beam energy. The dosimetric foils where placed of 45 cm from the exit window. Length axis is defined as direction parallel to eb scanning path whereas width axis is perpendicular to eb scanning path as it can be seen on Fig. 1. Electron energy 1.5 MeV and scan path length 40 cm at exit window level were set during irradiation procedure. It should be noted that these particular measurements were performed in the pilot plant facility equipped with an electron accelerator ILU 6 type which is installed at INCT. ILU 6 accelerator is capable to accelerate electrons in 0.5–2 MeV range, up to 20 kW average beam power and is equipped with scan horn with adjustable scan width 30–80 cm (electron beam scan angle varies from 710 to 725 deg). Scan horn is mounted vertically at 90 deg to the product pathway. The specific constructions of different accelerators may lead to the slightly different spatial beam distribution measured at accelerator output due to different configuration of accelerating process, focusing system, beam current level, material and thickness of the exit foil, and finally electron energy and energy spread levels. The influence of electron beam intensity on spatial beam characteristics can be neglected in most cases. In practice only electron beam energy and beam current levels are being set according to process parameters. Electron energy spread and beam divergence effects can not be adjusted directly despite the fact that those parameters may have significant influence on radiation processing. On a basis of dosimetric measurements the electron beam divergence angle was calculated for various electron energy, taking into account the beam width observed below the level of exit window (Fig. 2). It was found that electron beam divergence angle has not been changed significantly over the distance of 25–65 cm from the exit window for selected electron energy. The electron beam divergence in accelerator facility described by Studer, 1979 revealed similar tendency, but beam divergence for 1 MeV was
Fig. 3. Cross section of electrical cable: (A) cable with segmented aluminum conductor; (B) equivalent dimensions of cable used for simulation of dose distribution. 1—Jacket; 2—insulation, 3—aluminum conductor.
Z. Zimek et al. / Radiation Physics and Chemistry 94 (2014) 161–165
found to be significantly lower (17 deg at a distance of 27 cm from exit window as it was derived from the data presented in the paper). That confirms specificity of the parameter which depends predominantly on the accelerator performances.
3. Optimization of electrical cables irradiation The cable rewinding equipment located under beam scanner at INCT facility enables two-sided cable irradiation. The experimental studies were conducted using the cable which construction and dimensions are presented on Fig. 3. It should be noted that conductor is made of seven separate aluminum segments tightly pressed to obtain not quite uniform cylindrical shape. The cable with diameter of metal aluminum conductor 6.5 mm and total polymer (PE composition) layer thickness 1.35 mm was used for the computer simulation of dose distribution (Fig. 3b). The aluminum conductor diameter and total polymer material thickness were calculated on the base of total amount of material in real cable (Fig. 3a). Polymer density was found to be 0.92 g/cm3. For some computer simulations the polymer layer was divided on two parts (jacket thickness 0.7 mm; insulation thickness 0.65 mm) to distinguish significant differences in dose distribution related to the polymer layer thickness. The sheath of real cable consists of relatively thin jacket (0.1 mm) and much thicker insulation layer which has not strictly
Fig. 4. Gel-fraction versus dose deposited in the polymer composition.
163
defined thickness what can be seen on Fig. 3a. Both layers are extruded from the same PE composition, but the jacket contains additionally colorant agent. Both materials in form of granules were irradiated separately with different doses to characterize their ability to be crosslinked, Fig. 4. The presence of colorant agent increased gel-fraction of a few percent over the entire range of doses and is not important from experimental point of view. The relation between electron beam parameters (energy, geometry of electron beam in irradiation zone), electrical cable geometry (thickness of polymer layers and metal wire diameter), construction (jacket, insulation) and dose distribution represented by Dmax/Dmin coefficients were investigated both experimentally and by Monte Carlo calculation based on ModeCEB computer program (Lazurik et al., 2004, 2011). The program was designed for simulations of dose distribution in multi-layer circular objects for the electron energy range 0.1–25 MeV. As input data the program ModeCEB uses a number of parameters related to radiation facility including electron beam parameters as well as material properties and dimensions. The requirements for computer modeling were chosen in such a way that the relative root mean square of statistical error was less than 1% in the selected range of absorbed doses. Figs. 5 and 6 show calculated and measured circumferential average dose and gel fraction distribution in single polymeric layer of electrical cable with aluminum conductor, for one- and twosided irradiation, respectively. The dose averaging was performed over the total thickness of polymer layer including jacket and insulation. The total thickness of polymer layer was 1.35 mm and aluminum wire diameter 6.5 mm. The accelerator parameters were as follows: electron energy 1 MeV, energy spread ΔE/ E¼ 20%, beam divergence 30 deg. The distance between wire axes was arranged on d ¼1.5 cm. The same accelerator parameters were used to perform experimentally one- and two-sided irradiation process, Figs. 5 and 6B. The circumferential crosslinking (gel fraction) distribution in the selected segments of the polymer layer was determined. For two-sided irradiation Dmax/Dmin coefficient was found to be as low as 1.057 and 1.044 for simulated and experimentally obtained results. The adequate tendencies obtained for calculated and measured data show that applied Monte Carlo calculation method can be a useful tool for assessing irradiation homogeneity and processing parameters. Quite different calculated dose distribution was achieved when beam divergence was set on 3 deg (narrow beam) instead of 30 deg used before, Fig. 7A. The Dmax/Dmin coefficient increased from 1.051 to 1.394 for a single layer configuration. When two
Fig. 5. Circumferential average dose distribution calculated (A) and measured gel fraction distribution (B) in polymer layer for one-sided irradiation.
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Z. Zimek et al. / Radiation Physics and Chemistry 94 (2014) 161–165
Fig. 6. Circumferential average dose distribution calculated (A) and measured gel fraction distribution (B) in polymer layer for two-sided irradiation.
Fig. 7. Circumferential average dose distribution calculated for single (A) and double (B) polymer layers for two sided irradiation (1 MeV, E/E¼ 20%, beam divergence 3 deg, d ¼1.5 cm).
separate polymer layers were investigated the change was much more dramatic, particularly for the jacket layer. The Dmax/Dmin coefficient increased from 1.151 to 1.756 for jacket layer and from 1.246 to 1.32 for insulation. It should be noted that high dose fluctuations may lead to the local changes of wire and cable parameters (Ciappa et al. 2011). The series of calculations were performed to establish the relationship between beam divergence angle and Dmax/Dmin coefficient for the polymer layer divided on two separate sub-layers. As seen from Fig. 8 for each layer there is an optimal range of electron beam divergence angle.
4. Conclusions Experimental and calculated with ModeCEB program data of circumferential dose distribution in the polymer layer of electrical cable with aluminum conductor are alike both for one- and twosided irradiations performed for electron energy 1 MeV, energy spread ΔE/E¼ 20%, beam divergence 30 deg and the distance between wires axes d ¼1.5 cm. Such a convergence demonstrates usefulness of Monte Carlo calculation method for modeling radiation induced effects in cables. The simulation revealed significant inhomogeneous circumferential dose distribution in sub-layers of polymer whereas average
Fig. 8. Effect of EB divergence angle on Dmax/Dmin coefficients calculated for polymer layer divided on two separate sub-layers for two-sided irradiation (1 MeV, ΔE/E ¼20%, d ¼ 1.5 cm).
depth dose distribution was quite uniform. Performed calculations demonstrated relatively low influence of electron beam energy spectrum on homogeneity of irradiation and high influence of beam divergence on the circumferential dose distribution.
Z. Zimek et al. / Radiation Physics and Chemistry 94 (2014) 161–165
References Chmielewski, A.G., Haji-Saeid, M., Ahmed, S., 2005. Progress in radiation processing of polymers. Nucl. Instrum. Methods Phys. Res., Sect. B 236, 44–54. Ciappa, M., Mangiacapra, L., Stangoni, M., Ott, S., Fichtner, W., 2011. Design of optimum electron beam irradiation processes for the reliability of electric cables used in critical applications. Microelectron. Reliab. 51, 1479–1483. Ciappa, M., Mangiacapra, L., Stangoni, M., Ott, S., 2012. High resolution twodimensional dose map ping of elektron beam processed polymers. Radiat. Phys. Chem. 81, 1270–1275. Kaluska, I., Lazurik, V.T., Lazurik, V.M., Popov, G.F., Rogov, Y.V., Zimek, Z., 2007. The features of electron dose distributions in circular objects: comparison of Monte Carlo calculation predictions with dosimetry. Radiat. Phys. Chem. 76, 1815–1819.
165
Lazurik, V.T., Lazurik, V.M., Popov, G.F., Rogov, Yu, 2004. RT-office for optimization of industrial EB and X-ray processing. Problems of atomic science and technology. N1. Ser.: Nucl. Phys. Invest. 43, 186–189. Lazurik, V.T., Lazurik, V.M., Popov, G., Rogov, Yu., Zimek, Z., 2011. Information System and Software for Quality Control of Radiation Processing. Warsaw, Poland. Rouif, S., 2005. Radiation cross-linked polymers: recent developments and new applications. Nucl. Instrum. Methods Phys. Res., Sect. B 236, 68–72. Studer, H.R., 1979. Irradiation of insulation and sheath for large wire and cable. Radiat. Phys. Chem. 14, 809–819. Weiss, D.E., Johnson, W.C., Kensek, R.P., 1997. Dose distribution in tubing irradiated by electron beam: Monte Carlo simulation and measurements. Radiat. Phys. Chem., 50; , pp. 475–485.
Contents lists available at ScienceDirect
Radiation Physics and Chemistry journal homepage: www.elsevier.com/locate/radphyschem
Optimization of electron beam crosslinking for cables Z. Zimek n, G. Przybytniak, A. Nowicki, K. Mirkowski, K. Roman Institute of Nuclear Chemistry and Technology, Warsaw, Poland
H I G H L I G H T S
Dose distribution simulation was performed using ModeCEB computer program. Simulated and experimental data on dose homogeneity were compared. High influence of EB divergence on the dose distribution was found.
art ic l e i nf o
a b s t r a c t
Article history: Received 7 November 2012 Accepted 4 July 2013 Available online 13 July 2013
Relationship between electron beam parameters (energy, energy spread, and electron beam distribution in irradiation zone), electrical cable geometry (thickness of polymer layers and metal wire diameter), construction (jacked, insulation) and dose distribution represented by the Dmax/Dmin coefficients were investigated. The simulations were performed using ModeCEB computer program (Lazurik et al., 2011) and then compared with the experimental data. It was demonstrated that computer simulations based on the ModeCEB program are sufficient for modeling absorbed dose distribution in the multi-layers circular objects irradiated with scanned electron beam. The calculations revealed (1) significant inhomogeneous circumferential dose distribution in polymeric sub-layers (2) relatively low influence of electron beam energy spectrum on homogeneity of irradiation and (3) high influence of beam divergence on the circumferential dose distribution. & 2013 Elsevier Ltd. All rights reserved.
Keywords: Monte Carlo simulation Electron beam Cable irradiation
1. Introduction Wire and cable radiation crosslinking is one of the most successful implementation of radiation technology and sustain to be attractive method for modification variety new polymer material implemented in cable industry (Chmielewski et al., 2005; Rouif, 2005). The process was found to be less expensive requiring less factory floor space, accepting wide range of insulating materials and offering faster processing rate in comparison with chemical methods. Electron beams applied for radiation processing of electrical wire and cable are the most frequently used within electron energy range 0.5–3 MeV and occasionally up to 10 MeV. The requirements associated with the construction of acceleratorbased facility are related to the product characteristics and process capacity. The throughput is directly linked with beam power level that can vary in the range of 20–500 kW depending on the accelerator type. Usually in wire and cable processing absorbed dose is situated in the range from 50 to 200 kGy. Difficulties in handling irradiation process may appear at a very high rate of irradiation what correspond to a very high beam power level. Wire
n
Corresponding author. Tel.: +48 22 504 13 84; fax: +48 22 504 13 13. E-mail address: [email protected] (Z. Zimek).
0969-806X/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.radphyschem.2013.07.005
and cable handling equipment should allow work with sufficiently high speed of the rewinding and obtain adequate homogeneity of irradiation what is directly related to the final product quality and reliability. The economical condition of any industrial activity requires process optimization to reduce unit cost of the operation but sustaining adequate quality of the final product. The computer simulation method becomes a very effective tool for optimization process providing necessary information in short time and reducing cost in comparison with conventional approach based on experimental dosimetry (Weiss et al., 1997; Kaluska et al., 2007; Ciappa et al., 2012). 2. Accelerator facility The quality of modified polymer is defined mostly by homogeneity of irradiation. The radiation technology (accelerator and rewinding or transport systems) should allow provide homogenous dose distribution of suitable level for all sizes and dimensions of processed wires and cables. The number of cable and wire handling techniques were developed and tested to obtain two, three and even four sided irradiation. The so-called rotary techniques and specific configuration of the irradiation zone provided by
162
Z. Zimek et al. / Radiation Physics and Chemistry 94 (2014) 161–165
the external magnets were tested as well. Accelerator is the crucial equipment which defines basic technical and economical parameters of any radiation facility. The under beam equipment which
Fig. 1. Dose distribution in irradiation zone measured at a distance of 45 cm bellow exit window (electron energy 1.5 MeV; scan path 40 cm).
Fig. 2. EB divergence angle versus electron energy for the distance 25–65 cm from the exit window.
is dedicated to rewinding wires and cables should be capable of utilize efficiently energy provided by electron beam. Electron beam spatial distribution in the irradiation zone is one of the important parameter of radiation processing. The detail knowledge is needed to select the most appropriate conditions and to optimize the radiation processing. Fig. 1 shows an example of electron beam spatial distribution measured by cellulose triacetate dosimetric foil to characterize spatial deposition of electron beam energy. The dosimetric foils where placed of 45 cm from the exit window. Length axis is defined as direction parallel to eb scanning path whereas width axis is perpendicular to eb scanning path as it can be seen on Fig. 1. Electron energy 1.5 MeV and scan path length 40 cm at exit window level were set during irradiation procedure. It should be noted that these particular measurements were performed in the pilot plant facility equipped with an electron accelerator ILU 6 type which is installed at INCT. ILU 6 accelerator is capable to accelerate electrons in 0.5–2 MeV range, up to 20 kW average beam power and is equipped with scan horn with adjustable scan width 30–80 cm (electron beam scan angle varies from 710 to 725 deg). Scan horn is mounted vertically at 90 deg to the product pathway. The specific constructions of different accelerators may lead to the slightly different spatial beam distribution measured at accelerator output due to different configuration of accelerating process, focusing system, beam current level, material and thickness of the exit foil, and finally electron energy and energy spread levels. The influence of electron beam intensity on spatial beam characteristics can be neglected in most cases. In practice only electron beam energy and beam current levels are being set according to process parameters. Electron energy spread and beam divergence effects can not be adjusted directly despite the fact that those parameters may have significant influence on radiation processing. On a basis of dosimetric measurements the electron beam divergence angle was calculated for various electron energy, taking into account the beam width observed below the level of exit window (Fig. 2). It was found that electron beam divergence angle has not been changed significantly over the distance of 25–65 cm from the exit window for selected electron energy. The electron beam divergence in accelerator facility described by Studer, 1979 revealed similar tendency, but beam divergence for 1 MeV was
Fig. 3. Cross section of electrical cable: (A) cable with segmented aluminum conductor; (B) equivalent dimensions of cable used for simulation of dose distribution. 1—Jacket; 2—insulation, 3—aluminum conductor.
Z. Zimek et al. / Radiation Physics and Chemistry 94 (2014) 161–165
found to be significantly lower (17 deg at a distance of 27 cm from exit window as it was derived from the data presented in the paper). That confirms specificity of the parameter which depends predominantly on the accelerator performances.
3. Optimization of electrical cables irradiation The cable rewinding equipment located under beam scanner at INCT facility enables two-sided cable irradiation. The experimental studies were conducted using the cable which construction and dimensions are presented on Fig. 3. It should be noted that conductor is made of seven separate aluminum segments tightly pressed to obtain not quite uniform cylindrical shape. The cable with diameter of metal aluminum conductor 6.5 mm and total polymer (PE composition) layer thickness 1.35 mm was used for the computer simulation of dose distribution (Fig. 3b). The aluminum conductor diameter and total polymer material thickness were calculated on the base of total amount of material in real cable (Fig. 3a). Polymer density was found to be 0.92 g/cm3. For some computer simulations the polymer layer was divided on two parts (jacket thickness 0.7 mm; insulation thickness 0.65 mm) to distinguish significant differences in dose distribution related to the polymer layer thickness. The sheath of real cable consists of relatively thin jacket (0.1 mm) and much thicker insulation layer which has not strictly
Fig. 4. Gel-fraction versus dose deposited in the polymer composition.
163
defined thickness what can be seen on Fig. 3a. Both layers are extruded from the same PE composition, but the jacket contains additionally colorant agent. Both materials in form of granules were irradiated separately with different doses to characterize their ability to be crosslinked, Fig. 4. The presence of colorant agent increased gel-fraction of a few percent over the entire range of doses and is not important from experimental point of view. The relation between electron beam parameters (energy, geometry of electron beam in irradiation zone), electrical cable geometry (thickness of polymer layers and metal wire diameter), construction (jacket, insulation) and dose distribution represented by Dmax/Dmin coefficients were investigated both experimentally and by Monte Carlo calculation based on ModeCEB computer program (Lazurik et al., 2004, 2011). The program was designed for simulations of dose distribution in multi-layer circular objects for the electron energy range 0.1–25 MeV. As input data the program ModeCEB uses a number of parameters related to radiation facility including electron beam parameters as well as material properties and dimensions. The requirements for computer modeling were chosen in such a way that the relative root mean square of statistical error was less than 1% in the selected range of absorbed doses. Figs. 5 and 6 show calculated and measured circumferential average dose and gel fraction distribution in single polymeric layer of electrical cable with aluminum conductor, for one- and twosided irradiation, respectively. The dose averaging was performed over the total thickness of polymer layer including jacket and insulation. The total thickness of polymer layer was 1.35 mm and aluminum wire diameter 6.5 mm. The accelerator parameters were as follows: electron energy 1 MeV, energy spread ΔE/ E¼ 20%, beam divergence 30 deg. The distance between wire axes was arranged on d ¼1.5 cm. The same accelerator parameters were used to perform experimentally one- and two-sided irradiation process, Figs. 5 and 6B. The circumferential crosslinking (gel fraction) distribution in the selected segments of the polymer layer was determined. For two-sided irradiation Dmax/Dmin coefficient was found to be as low as 1.057 and 1.044 for simulated and experimentally obtained results. The adequate tendencies obtained for calculated and measured data show that applied Monte Carlo calculation method can be a useful tool for assessing irradiation homogeneity and processing parameters. Quite different calculated dose distribution was achieved when beam divergence was set on 3 deg (narrow beam) instead of 30 deg used before, Fig. 7A. The Dmax/Dmin coefficient increased from 1.051 to 1.394 for a single layer configuration. When two
Fig. 5. Circumferential average dose distribution calculated (A) and measured gel fraction distribution (B) in polymer layer for one-sided irradiation.
164
Z. Zimek et al. / Radiation Physics and Chemistry 94 (2014) 161–165
Fig. 6. Circumferential average dose distribution calculated (A) and measured gel fraction distribution (B) in polymer layer for two-sided irradiation.
Fig. 7. Circumferential average dose distribution calculated for single (A) and double (B) polymer layers for two sided irradiation (1 MeV, E/E¼ 20%, beam divergence 3 deg, d ¼1.5 cm).
separate polymer layers were investigated the change was much more dramatic, particularly for the jacket layer. The Dmax/Dmin coefficient increased from 1.151 to 1.756 for jacket layer and from 1.246 to 1.32 for insulation. It should be noted that high dose fluctuations may lead to the local changes of wire and cable parameters (Ciappa et al. 2011). The series of calculations were performed to establish the relationship between beam divergence angle and Dmax/Dmin coefficient for the polymer layer divided on two separate sub-layers. As seen from Fig. 8 for each layer there is an optimal range of electron beam divergence angle.
4. Conclusions Experimental and calculated with ModeCEB program data of circumferential dose distribution in the polymer layer of electrical cable with aluminum conductor are alike both for one- and twosided irradiations performed for electron energy 1 MeV, energy spread ΔE/E¼ 20%, beam divergence 30 deg and the distance between wires axes d ¼1.5 cm. Such a convergence demonstrates usefulness of Monte Carlo calculation method for modeling radiation induced effects in cables. The simulation revealed significant inhomogeneous circumferential dose distribution in sub-layers of polymer whereas average
Fig. 8. Effect of EB divergence angle on Dmax/Dmin coefficients calculated for polymer layer divided on two separate sub-layers for two-sided irradiation (1 MeV, ΔE/E ¼20%, d ¼ 1.5 cm).
depth dose distribution was quite uniform. Performed calculations demonstrated relatively low influence of electron beam energy spectrum on homogeneity of irradiation and high influence of beam divergence on the circumferential dose distribution.
Z. Zimek et al. / Radiation Physics and Chemistry 94 (2014) 161–165
References Chmielewski, A.G., Haji-Saeid, M., Ahmed, S., 2005. Progress in radiation processing of polymers. Nucl. Instrum. Methods Phys. Res., Sect. B 236, 44–54. Ciappa, M., Mangiacapra, L., Stangoni, M., Ott, S., Fichtner, W., 2011. Design of optimum electron beam irradiation processes for the reliability of electric cables used in critical applications. Microelectron. Reliab. 51, 1479–1483. Ciappa, M., Mangiacapra, L., Stangoni, M., Ott, S., 2012. High resolution twodimensional dose map ping of elektron beam processed polymers. Radiat. Phys. Chem. 81, 1270–1275. Kaluska, I., Lazurik, V.T., Lazurik, V.M., Popov, G.F., Rogov, Y.V., Zimek, Z., 2007. The features of electron dose distributions in circular objects: comparison of Monte Carlo calculation predictions with dosimetry. Radiat. Phys. Chem. 76, 1815–1819.
165
Lazurik, V.T., Lazurik, V.M., Popov, G.F., Rogov, Yu, 2004. RT-office for optimization of industrial EB and X-ray processing. Problems of atomic science and technology. N1. Ser.: Nucl. Phys. Invest. 43, 186–189. Lazurik, V.T., Lazurik, V.M., Popov, G., Rogov, Yu., Zimek, Z., 2011. Information System and Software for Quality Control of Radiation Processing. Warsaw, Poland. Rouif, S., 2005. Radiation cross-linked polymers: recent developments and new applications. Nucl. Instrum. Methods Phys. Res., Sect. B 236, 68–72. Studer, H.R., 1979. Irradiation of insulation and sheath for large wire and cable. Radiat. Phys. Chem. 14, 809–819. Weiss, D.E., Johnson, W.C., Kensek, R.P., 1997. Dose distribution in tubing irradiated by electron beam: Monte Carlo simulation and measurements. Radiat. Phys. Chem., 50; , pp. 475–485.