- Email: [email protected]
Evaluation using m.c.n.p. code of the bremsstrahlung energy spectrum produced by interactions between structural materials and accelerated electrons
ARTICLE IN PRESS
Radiation Physics and Chemistry 71 (2004) 277–279
Evaluation using m.c.n.p. code of the bremsstrahlung energy spectrum produced by interactions between structural materials and accelerated electrons Elio Calderaro* Dipartimento di Ingegneria Nucleare, Universita` di Palermo, V.le delle Scienze, Palermo 90128, Italy
Abstract In order to design the biological shield of industrial accelerator plants, it is needed to have a good knowledge of the bremsstrahlung energy spectrum and the intensity of the bremsstrahlung produced by electron interactions with both products (usually water equivalent) and structural materials such as concrete, iron, aluminium. Using the MCNP code, a normalized bremsstrahlung energy spectrum was obtained for materials with average atomic number lower than or equal to 13 and irradiated with 5 and 10 Mev electrons, respectively; multiplying the spectrum by suitable coefficients, it was possible to obtain the real spectrum for materials such as water, concrete, aluminium and iron. The MCNP results have been obtained with relative error less than 2%. r 2004 Elsevier Ltd. All rights reserved. Keywords: Accelerated electrons; Bremsstrahlung energy spectrum; Radiation shielding
1. Objectives Different types of industrial electron beam processing systems are used in a wide and rising variety of applications. The processing room is a part of the facility and the thickness of the shield (often concrete) depends on the energy and the power of the electron beam accelerators. To estimate the wall thickness of the processing room, we need to know the energetic spectrum and the intensity of the bremsstrahlung produced by interactions of accelerated electrons with the absorbing materials.
energy interval DE, were calculated using the computer code MCNP for 5 and 10 MeV energy of the electron beam. The energy interval was 0.5 MeV. The examined materials were the ones most often present in an irradiation room: water, aluminium, concrete and iron. The simulated model for the evaluation of the bremsstrahlung, constituted a point isotropic monoenergetic source of electrons placed in the centre of a homogeneous sphere of examinated material, and with sphere radius equal to maximum electron range in the material and at the energy chosen.
2. Method
3. Results
The number of photons DNg produced by bremsstrahlung, per electron of the incident beam and in
The spectral distribution curves, Fig. 1, relative to 10 MeV electrons, normalized to photon number of the first energetic interval (0.0–0.5 MeV), can be approximately considered similar. This is true for the iron up to 8 MeV; above that, the results move 10% away.
*Fax: +39-091-232215. E-mail address: [email protected] (E. Calderaro).
0969-806X/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.radphyschem.2004.03.057
ARTICLE IN PRESS E. Calderaro / Radiation Physics and Chemistry 71 (2004) 277–279
278
of water, aluminium and concrete. For the studied materials and under the above discussed approximations, it is possible to draw from M3 values the bremsstrahlung spectral distribution for one of the materials multiplying them by the coefficients reported in Table 1. The M3 curves can be well represented by
1,E+00
[∆Nγ / (β- * ∆E)]
1,E-01
1,E-02
DNg ¼ mcnp H2O mcnp Al mcnp Conc mcnp Fe H2O n Al n Conc n Fe n M3
1,E-03
1,E-04
1,E-05 0
1
2
3
4
5
6
7
8
9
10
[ MeV ] Fig. 1. Bremsstrahlung produced by 10 MeV electron interactions with structural materials.
*
*
1,E-01
[∆Nγ / (β- * ∆E)]
*
1,E-02
Table 1 Coefficients to draw the bremsstrahlung spectral distribution
1,E-05 0
1
2
the adsorbed dose in the examined mass is very low: the MCNP code gives per particle source the adsorbed energy in a volume; it is erroneous to remove from the calculus the lowenergy particles since they prevalently contribute to dose; they undergo several interactions and so prolong calculus times very much; for a correct dose evaluation, the sensible volume must be as small as possible.
To overcome such inconveniences it has been used a physical-geometric cylindrical model: a circular plane
mcnp Fe mcnp Al mcnp Conc mcnp H2O Fe n Al n Conc n H2O n M3
1,E-04
ð1Þ
where DNg number of photons generated per electron of the beam in the energy interval DE in E; a, b, c, d coefficients (values reported in Table 2). Once the material target of the electron beam is defined, it is possible, using the Eq. (1) and the coefficients of Table 2, to compute, by the normal shielding calculus formulae (Jaeger, 1968; ICRU, 1984), the wall thickness of the irradiation room as a function of the power and energy (5 and 10 MeV) of the electron beam accelerators. The evaluation of the shield wall thickness of irradiation room through the MNCP code has been useless since very long calculus time is required; In fact (Briesmeister, 1997):
1,E+00
1,E-03
a þ bE ; 1 þ cE þ dE 2
3
4
5
[ MeV ] Fig. 2. Bremsstrahlung produced by 5 MeV electron interactions with structural materials.
Similar conclusions—Fig. 2—can be also drawn for 5 MeV electrons, but for the 4.5–5 MeV energy range the curve moves 6% away. The M3 curves reported in Figs. 1 and 2, were obtained from the average normalized values (n symbol)
Materials
5 MeV
10 MeV
Polyethylene Water Concrete Aluminium Iron
0.101 0.132 0.230 0.259 0.511
0.192 0.260 0.443 0.497 0.911
Table 2 Coefficients for Eq. (1) Coefficients
5 MeV
10 MeV
a b c d
2.356923 0.47994 2.839751 8.7625361
2.6404110 0.2661578 5.4616970 3.9917055
ARTICLE IN PRESS E. Calderaro / Radiation Physics and Chemistry 71 (2004) 277–279 Table 3 Coefficients for Eq. (2) MeV
a
b
3 5 10
0.0060 0.0125 0.0144
9.297 7.847 5.988
3.5
279
surface of the cylindrical shield are considered part of the dosimeter sensible volume. So we gain a considerable reduction of the calculus time. The obtained results, opportunely elaborated, lead to a relation that binds the shield thickness X (m) to the average current of the electron beam Ib (mA) at the dose rate of 2.78E-9 (Sv/s), according to the annual dose D of 20 (mSv) in 2000 h, per 3, 5 and 10 MeV electron beams X¼
1 Ib a lg ; bf D
ð2Þ
where f=r/2340 is the density correction factor; r=concrete density (kg/m3); a, b are the coefficients depending on electrons energy (Table 3). The graphic of Eq. (2) is shown in Fig. 3.
3 10 MeV
X [m]
5 MeV 3 Mev
4. Conclusions
2.5
The present study contributes to better knowledge of the bremsstrahlung spectrum generated by 3, 5 and 10 MeV electrons in materials with atomic number inferior to 13 and enables the evaluation of the shielding of irradiation room. The results are in reasonable agreement with the published values.
2
Acknowledgements
1.5 0
10
20
30
40
50
Ib [mA]
This work was supported by MIUR.
Fig. 3. Wall thickness of irradiation room vs. energy and power of electron beam accelerators for Do2.78E-09 (Sv/s).
References uniform bremsstrahlung source (generated by electron beam), 1 m in diameter, is put at a distance of 0.6 m from a cylindrical coaxial X m in thickness concrete shield. All the points of the horizontal plane lying on the bremsstrahlung source and intersecting the external
Briesmeister, J.F. (Ed.), 1997. MCNP general Monte Carlo n-particle transport code, version 4B, LA-12625-m. ICRU Report 35, 1984. Radiation dosimetry: electron beams with energies between 1 and 10 MeV. Jaeger, R.G. (Ed.), 1968. Engineering Compendium on Radiation Shielding.
Radiation Physics and Chemistry 71 (2004) 277–279
Evaluation using m.c.n.p. code of the bremsstrahlung energy spectrum produced by interactions between structural materials and accelerated electrons Elio Calderaro* Dipartimento di Ingegneria Nucleare, Universita` di Palermo, V.le delle Scienze, Palermo 90128, Italy
Abstract In order to design the biological shield of industrial accelerator plants, it is needed to have a good knowledge of the bremsstrahlung energy spectrum and the intensity of the bremsstrahlung produced by electron interactions with both products (usually water equivalent) and structural materials such as concrete, iron, aluminium. Using the MCNP code, a normalized bremsstrahlung energy spectrum was obtained for materials with average atomic number lower than or equal to 13 and irradiated with 5 and 10 Mev electrons, respectively; multiplying the spectrum by suitable coefficients, it was possible to obtain the real spectrum for materials such as water, concrete, aluminium and iron. The MCNP results have been obtained with relative error less than 2%. r 2004 Elsevier Ltd. All rights reserved. Keywords: Accelerated electrons; Bremsstrahlung energy spectrum; Radiation shielding
1. Objectives Different types of industrial electron beam processing systems are used in a wide and rising variety of applications. The processing room is a part of the facility and the thickness of the shield (often concrete) depends on the energy and the power of the electron beam accelerators. To estimate the wall thickness of the processing room, we need to know the energetic spectrum and the intensity of the bremsstrahlung produced by interactions of accelerated electrons with the absorbing materials.
energy interval DE, were calculated using the computer code MCNP for 5 and 10 MeV energy of the electron beam. The energy interval was 0.5 MeV. The examined materials were the ones most often present in an irradiation room: water, aluminium, concrete and iron. The simulated model for the evaluation of the bremsstrahlung, constituted a point isotropic monoenergetic source of electrons placed in the centre of a homogeneous sphere of examinated material, and with sphere radius equal to maximum electron range in the material and at the energy chosen.
2. Method
3. Results
The number of photons DNg produced by bremsstrahlung, per electron of the incident beam and in
The spectral distribution curves, Fig. 1, relative to 10 MeV electrons, normalized to photon number of the first energetic interval (0.0–0.5 MeV), can be approximately considered similar. This is true for the iron up to 8 MeV; above that, the results move 10% away.
*Fax: +39-091-232215. E-mail address: [email protected] (E. Calderaro).
0969-806X/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.radphyschem.2004.03.057
ARTICLE IN PRESS E. Calderaro / Radiation Physics and Chemistry 71 (2004) 277–279
278
of water, aluminium and concrete. For the studied materials and under the above discussed approximations, it is possible to draw from M3 values the bremsstrahlung spectral distribution for one of the materials multiplying them by the coefficients reported in Table 1. The M3 curves can be well represented by
1,E+00
[∆Nγ / (β- * ∆E)]
1,E-01
1,E-02
DNg ¼ mcnp H2O mcnp Al mcnp Conc mcnp Fe H2O n Al n Conc n Fe n M3
1,E-03
1,E-04
1,E-05 0
1
2
3
4
5
6
7
8
9
10
[ MeV ] Fig. 1. Bremsstrahlung produced by 10 MeV electron interactions with structural materials.
*
*
1,E-01
[∆Nγ / (β- * ∆E)]
*
1,E-02
Table 1 Coefficients to draw the bremsstrahlung spectral distribution
1,E-05 0
1
2
the adsorbed dose in the examined mass is very low: the MCNP code gives per particle source the adsorbed energy in a volume; it is erroneous to remove from the calculus the lowenergy particles since they prevalently contribute to dose; they undergo several interactions and so prolong calculus times very much; for a correct dose evaluation, the sensible volume must be as small as possible.
To overcome such inconveniences it has been used a physical-geometric cylindrical model: a circular plane
mcnp Fe mcnp Al mcnp Conc mcnp H2O Fe n Al n Conc n H2O n M3
1,E-04
ð1Þ
where DNg number of photons generated per electron of the beam in the energy interval DE in E; a, b, c, d coefficients (values reported in Table 2). Once the material target of the electron beam is defined, it is possible, using the Eq. (1) and the coefficients of Table 2, to compute, by the normal shielding calculus formulae (Jaeger, 1968; ICRU, 1984), the wall thickness of the irradiation room as a function of the power and energy (5 and 10 MeV) of the electron beam accelerators. The evaluation of the shield wall thickness of irradiation room through the MNCP code has been useless since very long calculus time is required; In fact (Briesmeister, 1997):
1,E+00
1,E-03
a þ bE ; 1 þ cE þ dE 2
3
4
5
[ MeV ] Fig. 2. Bremsstrahlung produced by 5 MeV electron interactions with structural materials.
Similar conclusions—Fig. 2—can be also drawn for 5 MeV electrons, but for the 4.5–5 MeV energy range the curve moves 6% away. The M3 curves reported in Figs. 1 and 2, were obtained from the average normalized values (n symbol)
Materials
5 MeV
10 MeV
Polyethylene Water Concrete Aluminium Iron
0.101 0.132 0.230 0.259 0.511
0.192 0.260 0.443 0.497 0.911
Table 2 Coefficients for Eq. (1) Coefficients
5 MeV
10 MeV
a b c d
2.356923 0.47994 2.839751 8.7625361
2.6404110 0.2661578 5.4616970 3.9917055
ARTICLE IN PRESS E. Calderaro / Radiation Physics and Chemistry 71 (2004) 277–279 Table 3 Coefficients for Eq. (2) MeV
a
b
3 5 10
0.0060 0.0125 0.0144
9.297 7.847 5.988
3.5
279
surface of the cylindrical shield are considered part of the dosimeter sensible volume. So we gain a considerable reduction of the calculus time. The obtained results, opportunely elaborated, lead to a relation that binds the shield thickness X (m) to the average current of the electron beam Ib (mA) at the dose rate of 2.78E-9 (Sv/s), according to the annual dose D of 20 (mSv) in 2000 h, per 3, 5 and 10 MeV electron beams X¼
1 Ib a lg ; bf D
ð2Þ
where f=r/2340 is the density correction factor; r=concrete density (kg/m3); a, b are the coefficients depending on electrons energy (Table 3). The graphic of Eq. (2) is shown in Fig. 3.
3 10 MeV
X [m]
5 MeV 3 Mev
4. Conclusions
2.5
The present study contributes to better knowledge of the bremsstrahlung spectrum generated by 3, 5 and 10 MeV electrons in materials with atomic number inferior to 13 and enables the evaluation of the shielding of irradiation room. The results are in reasonable agreement with the published values.
2
Acknowledgements
1.5 0
10
20
30
40
50
Ib [mA]
This work was supported by MIUR.
Fig. 3. Wall thickness of irradiation room vs. energy and power of electron beam accelerators for Do2.78E-09 (Sv/s).
References uniform bremsstrahlung source (generated by electron beam), 1 m in diameter, is put at a distance of 0.6 m from a cylindrical coaxial X m in thickness concrete shield. All the points of the horizontal plane lying on the bremsstrahlung source and intersecting the external
Briesmeister, J.F. (Ed.), 1997. MCNP general Monte Carlo n-particle transport code, version 4B, LA-12625-m. ICRU Report 35, 1984. Radiation dosimetry: electron beams with energies between 1 and 10 MeV. Jaeger, R.G. (Ed.), 1968. Engineering Compendium on Radiation Shielding.