Three-dimensional modelling of plasma structure with generating algorithm of optimal starting points for magnetic field line tracing
The magnetic fields confining plasma in fusion reactors are analyzed using Poincaré plots, which show intersections of magnetic field lines on a poloidal crosssection. Traditional methods for designing vacuum vessels and related structures involve slicing the reactor vertically and analyzing these p...
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| Published in | Journal of Advanced Simulation in Science and Engineering Vol. 12; no. 1; pp. 249 - 266 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Japan Society for Simulation Technology
01.01.2025
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| ISSN | 2188-5303 2188-5303 |
| DOI | 10.15748/jasse.12.249 |
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| Abstract | The magnetic fields confining plasma in fusion reactors are analyzed using Poincaré plots, which show intersections of magnetic field lines on a poloidal crosssection. Traditional methods for designing vacuum vessels and related structures involve slicing the reactor vertically and analyzing these plots, but this approach is inefficient for understanding plasma shapes globally. Key challenges include the computational cost of magnetic field line tracing and the difficulty in constructing continuous surfaces for the divertor legs due to the limited number of magnetic field lines reaching this area. To address these issues, a new and automatic method has been proposed to increase the number of magnetic field lines constituting the divertor legs by predicting optimal starting points for tracing. The proposed method involves placing starting points on orthogonal lines through the magnetic axis, resulting in a better representation of divertor legs. This new algorithm enhances the efficiency of generating Poincaré plots that depict divertor leg regions more clearly than previous methods. Neural Networks predict voxel data representing the shape of magnetic field lines. Considering the Larmor radius, we calculate an envelope surface that encompasses the region where plasma exists and create 3D modeling data. |
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| AbstractList | The magnetic fields confining plasma in fusion reactors are analyzed using Poincaré plots, which show intersections of magnetic field lines on a poloidal crosssection. Traditional methods for designing vacuum vessels and related structures involve slicing the reactor vertically and analyzing these plots, but this approach is inefficient for understanding plasma shapes globally. Key challenges include the computational cost of magnetic field line tracing and the difficulty in constructing continuous surfaces for the divertor legs due to the limited number of magnetic field lines reaching this area. To address these issues, a new and automatic method has been proposed to increase the number of magnetic field lines constituting the divertor legs by predicting optimal starting points for tracing. The proposed method involves placing starting points on orthogonal lines through the magnetic axis, resulting in a better representation of divertor legs. This new algorithm enhances the efficiency of generating Poincaré plots that depict divertor leg regions more clearly than previous methods. Neural Networks predict voxel data representing the shape of magnetic field lines. Considering the Larmor radius, we calculate an envelope surface that encompasses the region where plasma exists and create 3D modeling data. |
| Author | Koyamada, Koji Hu, Kunqi Ohtani, Hiroaki |
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| Cites_doi | 10.1007/s12650-021-00768-w 10.13182/FST10-A10803 10.1585/pfr.6.2406027 10.15748/jasse.7.151 10.1585/pfr.8.2403072 10.1016/j.fusengdes.2012.01.030 10.1088/0029-5515/46/2/013 10.1585/pfr.14.1405163 10.1016/j.fusengdes.2013.02.124 10.1143/JPSJ.71.1684 10.1016/0010-4655(86)90058-5 10.1007/978-3-540-88606-8_11 10.1088/1741-4326/ab15c3 10.1016/j.nme.2016.12.020 10.1585/pfr.8.1402134 10.1063/1.864116 10.1016/j.cag.2006.07.021 10.1088/0741-3335/53/10/105007 10.1109/TPS.2011.2157174 |
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| References | [11] H. Ohtani, A. Kageyama, Y. Tamura, S. Ishiguro, M. Shohji: Integrated Visualization of Simulation Results and Experimental Devices in Virtual-Reality Space, Plasma and Fusion Research, 6 (2011), 2406027. [18] Project webpage: https://github.com/yasuhiro-suzuki/MGTRC, last accessed 2024/05/14. [9] A. G. Chiariello, A. Formisano, R. Martone: Fast magnetic field computation in fusion technology using gpu technology, Fusion Engineering and Design, 88:9-10 (2013), 1635-1639. [23] T. Watanabe: Alpha-particle confinement control of the geodesic winding of lhd-type fusion reactors, Plasma and Fusion Research, 8 (2013), 2403072. [19] Y. Matsumoto, S. Oikawa, T. Watanabe.: Field line and particle orbit analysis in the periphery of the Large Helical Device, Journal of the Physical Society of Japan, 71:7 (2002), 1684-1693. [7] R. Peikert, F. Sadlo: Flow topology beyond skeletons: Visualization of features in recirculating flow, Topology-Based Methods in Visualization II, Kloster Nimbschen, 2009, 145-160. [8] H. Tanaka, G. Kawamura, S. Masuzaki, M. Kobayashi, T. Akiyama, B.J. Peterson, K. Mukai, R. Sano, S.Y. Dai, R. Sakamoto, T. Morisaki, N. Ohno, LHD Experiment Group: Toroidally symmetric/asymmetric effect on the divertor flux due to neon/nitrogen seeding in LHD, Nuclear Materials and Energy, 12 (2017), 241-246. [10] T. Watanabe, M. Yoshida, S. Masuzaki, M. Emoto and Y. Nagayama: How to use the numerical system. 'LHD LINES OF FORCE.EXE' for the visualization of lines of force in the Large Helical Device (NIFS-TECH-14), NIFS-TECH, National Institute for Fusion Science, Toki, 2006. (in Japanese) [13] K. Hu, Q. Wang, K. Koyamada, H. Ohtani, T. Goto, J. Miyazawa: Visualization of the plasma shape in a force free helical reactor, FFHR, Journal of Advanced Simulation in Science and Engineering, 7:1 (2020), 151-167. [24] A. Y. Chang: A survey of geometric data structures for ray tracing, Department of Computer and Information Science, Polytechnic University, Ph.D thesis (2001). [4] M. Itagaki, T. Maeda, T. Ishimaru, G. Okubo, K. Watanabe, R. Seki, Y. Suzuki: Three-dimensional cauchy-condition surface method to identify the shape of the last closed magnetic surface in the large helical device, Plasma Physics and Controlled Fusion, 53:10 (2011), 105007. [6] R. Peikert, F. Sadlo: Visualization methods for vortex rings and vortex breakdown bubbles, in Proceedings of the 9th Joint Eurographics/IEEE VGTC conference on Visualization (EuroVis07), Norrköping, 2007, 211-218. [5] M. Itagaki, K. Ishimaru, Y. Matsumoto,K. Watanabe, R. Seki, Y. Suzuki: Improved three-dimensional ccs method analysis for the reconstruction of the peripheral magnetic field structure in a finite beta helical plasma, Plasma and Fusion Research, 8 (2013), 1402134. [22] K. Y. Watanabe, Y. Suzuki, S. Sakakibara, T. Yamaguchi, Y. Narushima, Y. Nakamura, K. Ida, N. Nakajima, H. Yamada, LHD Experiment Group: Characteristics of mhd equilibrium and related issues on LHD, Fusion Science and Technology, 58:1 (2010), 160-175. [17] S. P. Hirshman, W.I. van RIJ, P. Merkel: Three-dimensional free boundary calculations using a spectral Green's function method, Computer Physics Communications, 43:1 (1986), 143-155. [2] T. Goto, J. Miyazawa, H. Tamura, T. Tanaka, R. Sakamoto, C. Suzuki, R. Seki, S. Satake, M. Nunami, M. Yokoyama, N. Yanagi, A. Sagara and the FFHR Design Group: Conceptual design of a compact helical fusion reactor FFHR-c1 for the early demonstration of year-long electric power generation, Nuclear Fusion, 59:7 (2019), 076030. [25] S. Timothy, Y. Hong: A survey of the marching cubes algorithm. Computers & Graphics, 30:5 (2006), 854–879. [14] K. Hu, K. Koyamada, H. Ohtani, T. Goto, J. Miyazawa: Visualization of plasma shape in the LHD-type helical fusion reactor, FFHR, by a deep learning technique, Journal of Visualization, 24:6 (2021), 1141-1154. [21] T. Watanabe, Y. Matsumoto, M. Hishiki, S. Oikawa, H. Hojo, M. Shoji, S. Masuzaki, R. Kumazawa, K. Saito, T. Seki, T. Mutoh, A. Komori and LHD Experimental Group: Magnetic field structure and confinement of energetic particles in the LHD, Nuclear Fusion, 46:2 (2006), 291. [1] J. Miyazawa, H. Tamura, T. Tanaka, Y. Hamaji, M. Kobayashi, T. Murase, S. Nakagawa, T. Goto, N. Yanagi, A. Sagara, the FFHR Design Group: Improved design of a cartridge-type helical blanket system for the helical fusion reactor FFHR-b1, Plasma and Fusion Research, 14 (2019), 1405163. [16] S. P. Hirshman, J. C. Whitson: Steepest-descent moment method for threedimensional magnetohydrodynamic equilibria, Physics of Fluids, 26:12 (1983), 3553-3568. [20] T. Goto: private communication. [12] H. Ohtani, Y. Tamura, A. Kageyama, S. Ishiguro: Scientific visualization of plasma simulation results and device data in virtual-reality space, IEEE Transactions on Plasma Science, 39:11 (2011), 2472-2473. [3] A. Sagara, T. Goto, J. Miyazawa, N. Yanagi, T. Tanaka, H. Tamura, R. Sakamoto, M. Tanaka, K. Tsumori, O. Mitarai, S. Imagawa, T. Muroga, The FFHR design group: Design activities on helical demo reactor FFHR-d1, Fusion Engineering and Design, 87:5-6 (2012), 594-602. [15] K. Hu: Improving efficiency and quality on modeling 3D plasma shape in FFHR by introducing Neural Networks. Kyoto University, Ph.D thesis (2024). 22 23 24 25 10 11 12 13 14 15 16 17 18 19 1 2 3 4 5 6 7 8 9 20 21 |
| References_xml | – reference: [3] A. Sagara, T. Goto, J. Miyazawa, N. Yanagi, T. Tanaka, H. Tamura, R. Sakamoto, M. Tanaka, K. Tsumori, O. Mitarai, S. Imagawa, T. Muroga, The FFHR design group: Design activities on helical demo reactor FFHR-d1, Fusion Engineering and Design, 87:5-6 (2012), 594-602. – reference: [9] A. G. Chiariello, A. Formisano, R. Martone: Fast magnetic field computation in fusion technology using gpu technology, Fusion Engineering and Design, 88:9-10 (2013), 1635-1639. – reference: [13] K. Hu, Q. Wang, K. Koyamada, H. Ohtani, T. Goto, J. Miyazawa: Visualization of the plasma shape in a force free helical reactor, FFHR, Journal of Advanced Simulation in Science and Engineering, 7:1 (2020), 151-167. – reference: [24] A. Y. Chang: A survey of geometric data structures for ray tracing, Department of Computer and Information Science, Polytechnic University, Ph.D thesis (2001). – reference: [22] K. Y. Watanabe, Y. Suzuki, S. Sakakibara, T. Yamaguchi, Y. Narushima, Y. Nakamura, K. Ida, N. Nakajima, H. Yamada, LHD Experiment Group: Characteristics of mhd equilibrium and related issues on LHD, Fusion Science and Technology, 58:1 (2010), 160-175. – reference: [16] S. P. Hirshman, J. C. Whitson: Steepest-descent moment method for threedimensional magnetohydrodynamic equilibria, Physics of Fluids, 26:12 (1983), 3553-3568. – reference: [15] K. Hu: Improving efficiency and quality on modeling 3D plasma shape in FFHR by introducing Neural Networks. Kyoto University, Ph.D thesis (2024). – reference: [8] H. Tanaka, G. Kawamura, S. Masuzaki, M. Kobayashi, T. Akiyama, B.J. Peterson, K. Mukai, R. Sano, S.Y. Dai, R. Sakamoto, T. Morisaki, N. Ohno, LHD Experiment Group: Toroidally symmetric/asymmetric effect on the divertor flux due to neon/nitrogen seeding in LHD, Nuclear Materials and Energy, 12 (2017), 241-246. – reference: [12] H. Ohtani, Y. Tamura, A. Kageyama, S. Ishiguro: Scientific visualization of plasma simulation results and device data in virtual-reality space, IEEE Transactions on Plasma Science, 39:11 (2011), 2472-2473. – reference: [20] T. Goto: private communication. – reference: [21] T. Watanabe, Y. Matsumoto, M. Hishiki, S. Oikawa, H. Hojo, M. Shoji, S. Masuzaki, R. Kumazawa, K. Saito, T. Seki, T. Mutoh, A. Komori and LHD Experimental Group: Magnetic field structure and confinement of energetic particles in the LHD, Nuclear Fusion, 46:2 (2006), 291. – reference: [10] T. Watanabe, M. Yoshida, S. Masuzaki, M. Emoto and Y. Nagayama: How to use the numerical system. 'LHD LINES OF FORCE.EXE' for the visualization of lines of force in the Large Helical Device (NIFS-TECH-14), NIFS-TECH, National Institute for Fusion Science, Toki, 2006. (in Japanese) – reference: [14] K. Hu, K. Koyamada, H. Ohtani, T. Goto, J. Miyazawa: Visualization of plasma shape in the LHD-type helical fusion reactor, FFHR, by a deep learning technique, Journal of Visualization, 24:6 (2021), 1141-1154. – reference: [1] J. Miyazawa, H. Tamura, T. Tanaka, Y. Hamaji, M. Kobayashi, T. Murase, S. Nakagawa, T. Goto, N. Yanagi, A. Sagara, the FFHR Design Group: Improved design of a cartridge-type helical blanket system for the helical fusion reactor FFHR-b1, Plasma and Fusion Research, 14 (2019), 1405163. – reference: [4] M. Itagaki, T. Maeda, T. Ishimaru, G. Okubo, K. Watanabe, R. Seki, Y. Suzuki: Three-dimensional cauchy-condition surface method to identify the shape of the last closed magnetic surface in the large helical device, Plasma Physics and Controlled Fusion, 53:10 (2011), 105007. – reference: [7] R. Peikert, F. Sadlo: Flow topology beyond skeletons: Visualization of features in recirculating flow, Topology-Based Methods in Visualization II, Kloster Nimbschen, 2009, 145-160. – reference: [17] S. P. Hirshman, W.I. van RIJ, P. Merkel: Three-dimensional free boundary calculations using a spectral Green's function method, Computer Physics Communications, 43:1 (1986), 143-155. – reference: [23] T. Watanabe: Alpha-particle confinement control of the geodesic winding of lhd-type fusion reactors, Plasma and Fusion Research, 8 (2013), 2403072. – reference: [25] S. Timothy, Y. Hong: A survey of the marching cubes algorithm. Computers & Graphics, 30:5 (2006), 854–879. – reference: [5] M. Itagaki, K. Ishimaru, Y. Matsumoto,K. Watanabe, R. Seki, Y. Suzuki: Improved three-dimensional ccs method analysis for the reconstruction of the peripheral magnetic field structure in a finite beta helical plasma, Plasma and Fusion Research, 8 (2013), 1402134. – reference: [11] H. Ohtani, A. Kageyama, Y. Tamura, S. Ishiguro, M. Shohji: Integrated Visualization of Simulation Results and Experimental Devices in Virtual-Reality Space, Plasma and Fusion Research, 6 (2011), 2406027. – reference: [6] R. Peikert, F. Sadlo: Visualization methods for vortex rings and vortex breakdown bubbles, in Proceedings of the 9th Joint Eurographics/IEEE VGTC conference on Visualization (EuroVis07), Norrköping, 2007, 211-218. – reference: [19] Y. Matsumoto, S. Oikawa, T. Watanabe.: Field line and particle orbit analysis in the periphery of the Large Helical Device, Journal of the Physical Society of Japan, 71:7 (2002), 1684-1693. – reference: [2] T. Goto, J. Miyazawa, H. Tamura, T. Tanaka, R. Sakamoto, C. Suzuki, R. Seki, S. Satake, M. Nunami, M. Yokoyama, N. Yanagi, A. Sagara and the FFHR Design Group: Conceptual design of a compact helical fusion reactor FFHR-c1 for the early demonstration of year-long electric power generation, Nuclear Fusion, 59:7 (2019), 076030. – reference: [18] Project webpage: https://github.com/yasuhiro-suzuki/MGTRC, last accessed 2024/05/14. – ident: 14 doi: 10.1007/s12650-021-00768-w – ident: 18 – ident: 22 doi: 10.13182/FST10-A10803 – ident: 11 doi: 10.1585/pfr.6.2406027 – ident: 13 doi: 10.15748/jasse.7.151 – ident: 23 doi: 10.1585/pfr.8.2403072 – ident: 3 doi: 10.1016/j.fusengdes.2012.01.030 – ident: 21 doi: 10.1088/0029-5515/46/2/013 – ident: 10 – ident: 1 doi: 10.1585/pfr.14.1405163 – ident: 9 doi: 10.1016/j.fusengdes.2013.02.124 – ident: 19 doi: 10.1143/JPSJ.71.1684 – ident: 24 – ident: 17 doi: 10.1016/0010-4655(86)90058-5 – ident: 7 doi: 10.1007/978-3-540-88606-8_11 – ident: 20 – ident: 2 doi: 10.1088/1741-4326/ab15c3 – ident: 8 doi: 10.1016/j.nme.2016.12.020 – ident: 5 doi: 10.1585/pfr.8.1402134 – ident: 16 doi: 10.1063/1.864116 – ident: 25 doi: 10.1016/j.cag.2006.07.021 – ident: 4 doi: 10.1088/0741-3335/53/10/105007 – ident: 12 doi: 10.1109/TPS.2011.2157174 – ident: 15 – ident: 6 |
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| SubjectTerms | Divertor legs Magnetic field line tracing Magnetically confined plasma Poincaré plots three-dimensional model |
| Title | Three-dimensional modelling of plasma structure with generating algorithm of optimal starting points for magnetic field line tracing |
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