- Email: [email protected]
Magnetic field and structure analysis of a superconducting dipole magnet for a rotating gantry
Physica C 471 (2011) 1445–1448
Contents lists available at ScienceDirect
Physica C journal homepage: www.elsevier.com/locate/physc
Magnetic field and structure analysis of a superconducting dipole magnet for a rotating gantry T. Obana a,⇑, T. Ogitsu b a b
National Institute for Fusion Science, 322-6 Oroshi, Toki, Gifu 509-5292, Japan KEK High Energy Accelerator Research Organization, 1-1, OHO, Tsukuba, Ibaraki 305-0801, Japan
a r t i c l e
i n f o
Article history: Available online 13 May 2011 Keywords: Superconducting magnet Magnetic field analysis Structural analysis
a b s t r a c t The conceptual design of a superconducting dipole magnet for a rotating gantry has been conducted. The dipole magnet is composed of a saddle shaped (cosine theta) multi-pole coil, which is wound with a NbTi superconducting wire, surrounded by an iron collar. In terms of a design parameter, a magnetic field strength of not only 1.5 T but also 3.0 T at the magnet center is required within the field quality of 1.0 10 3. In this study, the magnetic field analysis and structural analysis of the superconducting dipole magnet are described. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction A rotating gantry is essential to irradiate a tumor effectively with charged particles in particle radiotherapy for cancer [1,2]. As a main component of the rotating gantry, conventional magnets have been used to transfer the charged particles from the accelerator to the patient. The weight and size of the conventional magnet are key issues in terms of the development and operation of the rotating gantry. In order to address these issues, we have been trying to replace the conventional magnets with superconducting magnets in the rotating gantry. In this study, a superconducting dipole magnet, in which a saddle shape (cosine theta) multilayered coil is surrounded by an iron collar, has been proposed as an efficient bending magnet for a heavy ion beam of 400 MeV/u. The saddle shape multilayered coil is wound with NbTi wire, the diameter of which is about 1 mm, by using the surface winding technology [3] and is impregnated with resin. In this paper, magnetic field analysis and structural analysis of the dipole superconducting magnet are described. 2. Superconducting dipole magnet for a rotating gantry Fig. 1 illustrates the half cross-section of a superconducting dipole magnet for a rotating gantry. Design parameters of the dipole magnet for the rotating gantry are listed in Table 1. The magnet is composed of a superconducting multilayered coil, an iron collar, a SUS pipe, and a vacuum vessel. The coil consists of a cosine theta current distribution. The design of the coil cross-section was con⇑ Corresponding author. Tel.: +81 572 58 2137; fax: +81 572 58 2616. E-mail address: [email protected] (T. Obana). 0921-4534/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2011.05.213
ducted while taking into account the influence of the iron collar so as to fulfill the design requirements. The detail of the design process was described in Ref. [4]. In the optimized coil cross-section, there are 26th coil layers and 3588 coil windings. Fig. 2 illustrates the cross-section of the optimized coil. The coil cross-sections from the 1st to the 25th layer were designed with high filling factors to increase magnetic field strength effectively. On the other hand, at the 26th layer which is the outermost layer, the coil cross-section was designed to correct the error of the magnetic field generated by the coil cross-sections from the 1st layer to the 25th layer. 3. Magnetic field analysis A magnetic field generated by the designed magnet was obtained in 2-dimension by using ANSYS [5]. Fig. 3 shows the distribution of the magnetic field strength in the case that an operating current is 140 A. The peak field is about 3.0 T in the coil crosssection, and there are saturated parts, where the magnetic field strength is over 1.5 T, in the iron collar surrounding the coil. On the contrary, the vacuum vessel is not saturated because the magnetic field leaked from the iron collar is less than 1.0 T. The magnetic field strength on the mid-plane is shown in Fig. 4. By using the vacuum vessel and iron collar, the leak field can be prevented up to an acceptable value which is above 5 10 4 T. Multipole coefficients bn of the magnetic field were obtained for the purpose of evaluating the magnetic field in the bore of the magnet. In Table 2, the multipole coefficients for each operating current at the reference radius of 40 mm are expressed in units that are normalized with respect to the dipole field B1 and scaled by a factor of 10,000. All of bn, except b1, must be within ±10 units in
1446
T. Obana, T. Ogitsu / Physica C 471 (2011) 1445–1448
Vaccum vessel
3
Magnetic field strength [T]
2
1.5
1
0.5
Fig. 1. Half cross-section of the superconducting dipole magnet for the rotating gantry.
0
0
0.1
0.2
0.3
0.4
x [m]
Table 1 Design parameters of the dipole magnet for the rotating gantry.
Fig. 4. Magnetic field strength on the mid-plane.
Nominal magnetic field
1.5 T and 3 T at coil center
Coil inner diameter Good field region Conductor Cu ratio Diameter
150 mm 80 mm NbTi/Cu 4 0.9 mm
Table 2 Multipole coefficients bn of the superconducting dipole magnet for each current at the reference radius of 40 mm. B1 is the dipole magnetic field strength at the magnet center.
0.15 Conductor (Plus) Conductor (Minus) 0.1
0.05
y [m]
Iron collar
Coil
2.5
1 (A) B1 (T) b1 b2 b3 b4 b5 b6 b7 b8 b9 b10
70.0 1.5 10,000.0 0.0 2.3 0.0 2.8 0.0 0.7 0.0 0.1 0.0
140.0 3.0 10,000.0 0.0 3.8 0.0 2.8 0.0 0.1 0.0 0.1 0.0
Target 10,000.0 0 0 0 0 0 0 0 0 0
0 Table 3 Characteristics of materials used in the structural model.
-0.05
Conductor Epoxy resin Iron collar
-0.1
-0.15 -0.15
-0.1
-0.05
0
0.05
0.1
0.15
x [m]
Young’s modulus (Pa)
Poisson’s ratio
1.08E+10 6.87E+9 2.11E+11
0.328 0.3 0.293
terms of field quality of a magnet for the rotating gantry. Therefore, the field quality of the designed magnet is acceptable at each operating current value.
Fig. 2. Cross-section of the superconducting dipole coil. (Pods show the conductor position.)
4. Structural analysis In order to understand the influence of electromagnetic force on the dipole magnet, the structural analysis of the magnet was conducted by using ANSYS [5]. 4.1. Model and boundary conditions
Fig. 3. Magnetic field strength distribution in the case an operating current is 140 A.
A structural model is composed of the coil and iron collar to simplify the model, which is shown in Fig. 1, in the structural analysis. In the model, the coil consists of conductors and epoxy resin. The characteristics of materials used in the model are listed in Table 3. Conditions of constraint are as follows: the model’s points contacting on the mid-plane do not move in the vertical direction. In addition, one point at the innermost coil does not move in the horizontal and vertical direction for the purpose of preventing the
T. Obana, T. Ogitsu / Physica C 471 (2011) 1445–1448
1447
Fig. 5. Displacement in the cross-section of the superconducting dipole magnet.
Fig. 6. Stress distribution in the cross-section of the superconducting dipole magnet.
solution of the analysis from divergence. In the superconducting dipole magnet, the coil is surrounded with the iron collar. The boundary between the coil and the iron collar is not glued but contacted. Hence, contact elements are utilized on the boundary between the coil and the iron so as not to constrain the movements of the coil and the iron collar. On the other hand, the boundary between the conductor and epoxy resin is glued in the coil. Before the structural analysis, the electromagnetic force on the strands was obtained by magnetic field analysis in which the magnetic field strength was 3 T at the magnetic center.
magnetic force generated in the coil circumferential direction. The maximum distortion is about 0.6 10 4 m at the central part of the coil. The stress distribution of the magnet is shown in Fig. 6. The stress in the iron collar is higher than that in the coil, the maximum stress is about 15.1 106 Pa at the innermost part of the iron collar. The maximum stress is significantly small and within the allowable stress of the iron collar. Hence, the cross-section of the designed magnet is suitable for the magnet structure in the case that the magnet field strength is 3 T at the magnet center.
4.2. Analytical results
5. Conclusion and further plan
Fig. 5 shows the analytical result of displacement in the magnet which is subjected to electromagnetic force. The coil configuration is slightly distorted in the vertical direction by the effect of electro-
The conceptual design of a superconducting dipole magnet, which is composed of a superconducting multilayer coil surrounded by an iron collar, for a rotating gantry was carried
1448
T. Obana, T. Ogitsu / Physica C 471 (2011) 1445–1448
out. The cross-section of the coil was optimized taking into account saturation of the iron collar so as to fulfill the design requirement. The structure analysis of the magnet was also conducted to evaluate displacement and stress of the magnet which is subjected to electromagnetic force. The cross-section of the magnet was suitable for the magnet structure at the nominal current. As a further plan, the influence of the electromagnetic force on the field quality is going to be investigated while taking into account the structural analysis result. Acknowledgments This study was supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Young Scientists (B). The
authors would like to thank Mr. T. Orikasa of TOSHIBA for his support of this study. References [1] M. Pavlovic, Adv. Nucl. Inst. Meth. Phys. Res. A 434 (1999) 454. [2] Y. Takada, Jpn. J. Med. Phys. 15 (1995) 270 (in Japanese). [3] T. Obana, T. Ogitsu, A. Yamamoto, M. Yoshimoto, IEEE Trans. Appl. Supercond. 19 (2009) 1199. [4] T. Obana, T. Ogitsu, in: Proc. ICEC 23-ICMC 2010, in press. [5] ANSYS is a Trademark of Cybernet Systems Co., Ltd.
Contents lists available at ScienceDirect
Physica C journal homepage: www.elsevier.com/locate/physc
Magnetic field and structure analysis of a superconducting dipole magnet for a rotating gantry T. Obana a,⇑, T. Ogitsu b a b
National Institute for Fusion Science, 322-6 Oroshi, Toki, Gifu 509-5292, Japan KEK High Energy Accelerator Research Organization, 1-1, OHO, Tsukuba, Ibaraki 305-0801, Japan
a r t i c l e
i n f o
Article history: Available online 13 May 2011 Keywords: Superconducting magnet Magnetic field analysis Structural analysis
a b s t r a c t The conceptual design of a superconducting dipole magnet for a rotating gantry has been conducted. The dipole magnet is composed of a saddle shaped (cosine theta) multi-pole coil, which is wound with a NbTi superconducting wire, surrounded by an iron collar. In terms of a design parameter, a magnetic field strength of not only 1.5 T but also 3.0 T at the magnet center is required within the field quality of 1.0 10 3. In this study, the magnetic field analysis and structural analysis of the superconducting dipole magnet are described. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction A rotating gantry is essential to irradiate a tumor effectively with charged particles in particle radiotherapy for cancer [1,2]. As a main component of the rotating gantry, conventional magnets have been used to transfer the charged particles from the accelerator to the patient. The weight and size of the conventional magnet are key issues in terms of the development and operation of the rotating gantry. In order to address these issues, we have been trying to replace the conventional magnets with superconducting magnets in the rotating gantry. In this study, a superconducting dipole magnet, in which a saddle shape (cosine theta) multilayered coil is surrounded by an iron collar, has been proposed as an efficient bending magnet for a heavy ion beam of 400 MeV/u. The saddle shape multilayered coil is wound with NbTi wire, the diameter of which is about 1 mm, by using the surface winding technology [3] and is impregnated with resin. In this paper, magnetic field analysis and structural analysis of the dipole superconducting magnet are described. 2. Superconducting dipole magnet for a rotating gantry Fig. 1 illustrates the half cross-section of a superconducting dipole magnet for a rotating gantry. Design parameters of the dipole magnet for the rotating gantry are listed in Table 1. The magnet is composed of a superconducting multilayered coil, an iron collar, a SUS pipe, and a vacuum vessel. The coil consists of a cosine theta current distribution. The design of the coil cross-section was con⇑ Corresponding author. Tel.: +81 572 58 2137; fax: +81 572 58 2616. E-mail address: [email protected] (T. Obana). 0921-4534/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2011.05.213
ducted while taking into account the influence of the iron collar so as to fulfill the design requirements. The detail of the design process was described in Ref. [4]. In the optimized coil cross-section, there are 26th coil layers and 3588 coil windings. Fig. 2 illustrates the cross-section of the optimized coil. The coil cross-sections from the 1st to the 25th layer were designed with high filling factors to increase magnetic field strength effectively. On the other hand, at the 26th layer which is the outermost layer, the coil cross-section was designed to correct the error of the magnetic field generated by the coil cross-sections from the 1st layer to the 25th layer. 3. Magnetic field analysis A magnetic field generated by the designed magnet was obtained in 2-dimension by using ANSYS [5]. Fig. 3 shows the distribution of the magnetic field strength in the case that an operating current is 140 A. The peak field is about 3.0 T in the coil crosssection, and there are saturated parts, where the magnetic field strength is over 1.5 T, in the iron collar surrounding the coil. On the contrary, the vacuum vessel is not saturated because the magnetic field leaked from the iron collar is less than 1.0 T. The magnetic field strength on the mid-plane is shown in Fig. 4. By using the vacuum vessel and iron collar, the leak field can be prevented up to an acceptable value which is above 5 10 4 T. Multipole coefficients bn of the magnetic field were obtained for the purpose of evaluating the magnetic field in the bore of the magnet. In Table 2, the multipole coefficients for each operating current at the reference radius of 40 mm are expressed in units that are normalized with respect to the dipole field B1 and scaled by a factor of 10,000. All of bn, except b1, must be within ±10 units in
1446
T. Obana, T. Ogitsu / Physica C 471 (2011) 1445–1448
Vaccum vessel
3
Magnetic field strength [T]
2
1.5
1
0.5
Fig. 1. Half cross-section of the superconducting dipole magnet for the rotating gantry.
0
0
0.1
0.2
0.3
0.4
x [m]
Table 1 Design parameters of the dipole magnet for the rotating gantry.
Fig. 4. Magnetic field strength on the mid-plane.
Nominal magnetic field
1.5 T and 3 T at coil center
Coil inner diameter Good field region Conductor Cu ratio Diameter
150 mm 80 mm NbTi/Cu 4 0.9 mm
Table 2 Multipole coefficients bn of the superconducting dipole magnet for each current at the reference radius of 40 mm. B1 is the dipole magnetic field strength at the magnet center.
0.15 Conductor (Plus) Conductor (Minus) 0.1
0.05
y [m]
Iron collar
Coil
2.5
1 (A) B1 (T) b1 b2 b3 b4 b5 b6 b7 b8 b9 b10
70.0 1.5 10,000.0 0.0 2.3 0.0 2.8 0.0 0.7 0.0 0.1 0.0
140.0 3.0 10,000.0 0.0 3.8 0.0 2.8 0.0 0.1 0.0 0.1 0.0
Target 10,000.0 0 0 0 0 0 0 0 0 0
0 Table 3 Characteristics of materials used in the structural model.
-0.05
Conductor Epoxy resin Iron collar
-0.1
-0.15 -0.15
-0.1
-0.05
0
0.05
0.1
0.15
x [m]
Young’s modulus (Pa)
Poisson’s ratio
1.08E+10 6.87E+9 2.11E+11
0.328 0.3 0.293
terms of field quality of a magnet for the rotating gantry. Therefore, the field quality of the designed magnet is acceptable at each operating current value.
Fig. 2. Cross-section of the superconducting dipole coil. (Pods show the conductor position.)
4. Structural analysis In order to understand the influence of electromagnetic force on the dipole magnet, the structural analysis of the magnet was conducted by using ANSYS [5]. 4.1. Model and boundary conditions
Fig. 3. Magnetic field strength distribution in the case an operating current is 140 A.
A structural model is composed of the coil and iron collar to simplify the model, which is shown in Fig. 1, in the structural analysis. In the model, the coil consists of conductors and epoxy resin. The characteristics of materials used in the model are listed in Table 3. Conditions of constraint are as follows: the model’s points contacting on the mid-plane do not move in the vertical direction. In addition, one point at the innermost coil does not move in the horizontal and vertical direction for the purpose of preventing the
T. Obana, T. Ogitsu / Physica C 471 (2011) 1445–1448
1447
Fig. 5. Displacement in the cross-section of the superconducting dipole magnet.
Fig. 6. Stress distribution in the cross-section of the superconducting dipole magnet.
solution of the analysis from divergence. In the superconducting dipole magnet, the coil is surrounded with the iron collar. The boundary between the coil and the iron collar is not glued but contacted. Hence, contact elements are utilized on the boundary between the coil and the iron so as not to constrain the movements of the coil and the iron collar. On the other hand, the boundary between the conductor and epoxy resin is glued in the coil. Before the structural analysis, the electromagnetic force on the strands was obtained by magnetic field analysis in which the magnetic field strength was 3 T at the magnetic center.
magnetic force generated in the coil circumferential direction. The maximum distortion is about 0.6 10 4 m at the central part of the coil. The stress distribution of the magnet is shown in Fig. 6. The stress in the iron collar is higher than that in the coil, the maximum stress is about 15.1 106 Pa at the innermost part of the iron collar. The maximum stress is significantly small and within the allowable stress of the iron collar. Hence, the cross-section of the designed magnet is suitable for the magnet structure in the case that the magnet field strength is 3 T at the magnet center.
4.2. Analytical results
5. Conclusion and further plan
Fig. 5 shows the analytical result of displacement in the magnet which is subjected to electromagnetic force. The coil configuration is slightly distorted in the vertical direction by the effect of electro-
The conceptual design of a superconducting dipole magnet, which is composed of a superconducting multilayer coil surrounded by an iron collar, for a rotating gantry was carried
1448
T. Obana, T. Ogitsu / Physica C 471 (2011) 1445–1448
out. The cross-section of the coil was optimized taking into account saturation of the iron collar so as to fulfill the design requirement. The structure analysis of the magnet was also conducted to evaluate displacement and stress of the magnet which is subjected to electromagnetic force. The cross-section of the magnet was suitable for the magnet structure at the nominal current. As a further plan, the influence of the electromagnetic force on the field quality is going to be investigated while taking into account the structural analysis result. Acknowledgments This study was supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Young Scientists (B). The
authors would like to thank Mr. T. Orikasa of TOSHIBA for his support of this study. References [1] M. Pavlovic, Adv. Nucl. Inst. Meth. Phys. Res. A 434 (1999) 454. [2] Y. Takada, Jpn. J. Med. Phys. 15 (1995) 270 (in Japanese). [3] T. Obana, T. Ogitsu, A. Yamamoto, M. Yoshimoto, IEEE Trans. Appl. Supercond. 19 (2009) 1199. [4] T. Obana, T. Ogitsu, in: Proc. ICEC 23-ICMC 2010, in press. [5] ANSYS is a Trademark of Cybernet Systems Co., Ltd.