The magnetic gradient scale length explains why certain plasmas require close external magnetic coils

Kappel, John; Landreman, Matt; Malhotra, Dhairya

doi:10.1088/1361-6587/ad1a3e

Title: The magnetic gradient scale length explains why certain plasmas require close external magnetic coils

Journal Article · 17 January 2024 · Plasma Physics and Controlled Fusion

DOI: https://doi.org/10.1088/1361-6587/ad1a3e · OSTI ID:2281754

;

Abstract The separation between the last closed flux surface of a plasma and the external coils that magnetically confine it is a limiting factor in the construction of fusion-capable plasma devices. This plasma-coil separation must be large enough so that components such as a breeding blanket and neutron shielding can fit between the plasma and the coils. Plasma-coil separation affects reactor size, engineering complexity, and particle loss due to field ripple. For some plasmas it can be difficult to produce the desired flux surface shaping with distant coils, and for other plasmas it is infeasible altogether. Here, we seek to understand the underlying physics that limits plasma-coil separation and explain why some configurations require close external coils. In this paper, we explore the hypothesis that the limiting plasma-coil separation is set by the shortest scale length of the magnetic field as expressed by the $\nabla B$ tensor. We tested this hypothesis on a database of $>$ 40 stellarator and tokamak configurations. Within this database, the coil-to-plasma distance compared to the minor radius varies by over an order of magnitude. The magnetic scale length is well correlated to the coil-to-plasma distance of actual coil designs generated using the REGCOIL method (Landreman 2017 Nucl. Fusion 57 046003). Additionally, this correlation reveals a general trend that larger plasma-coil separation is possible with a small number of field periods.

View Journal Article

Cite

Export

Save

Research Organization:: Univ. of California, Oakland, CA (United States); Univ. of Maryland, College Park, MD (United States)

Sponsoring Organization:: USDOE; USDOE Office of Science (SC); USDOE Office of Science (SC), Fusion Energy Sciences (FES)

Grant/Contract Number:: AC02-05CH11231; FG02-93ER54197

OSTI ID:: 2281754

Journal Information:: Plasma Physics and Controlled Fusion, Journal Name: Plasma Physics and Controlled Fusion Journal Issue: 2 Vol. 66; ISSN 0741-3335

Publisher:: IOP PublishingCopyright Statement

Country of Publication:: United Kingdom

Language:: English

References (52)

ESTELL: A Quasi-Toroidally Symmetric Stellarator Drevlak, M.; Brochard, F.; Helander, P. Contributions to Plasma Physics, Vol. 53, Issue 6 https://doi.org/10.1002/ctpp.201200055	journal	March 2013
Initial Vacuum Magnetic Field Mapping in the Compact Toroidal Hybrid Peterson, J. T.; Hartwell, G. J.; Knowlton, S. F. Journal of Fusion Energy, Vol. 26, Issue 1-2 https://doi.org/10.1007/s10894-006-9053-2	journal	December 2006
Quasi-helically symmetric toroidal stellarators Nührenberg, J.; Zille, R. Physics Letters A, Vol. 129, Issue 2 https://doi.org/10.1016/0375-9601(88)90080-1	journal	May 1988
Design of the national compact stellarator experiment (NCSX) Nelson, B. E.; Berry, L. A.; Brooks, A. B. Fusion Engineering and Design, Vol. 66-68 https://doi.org/10.1016/S0920-3796(03)00183-2	journal	September 2003
Towards assembly completion and preparation of experimental campaigns of Wendelstein 7-X in the perspective of a path to a stellarator fusion power plant Klinger, T.; Baylard, C.; Beidler, C. D. Fusion Engineering and Design, Vol. 88, Issue 6-8 https://doi.org/10.1016/j.fusengdes.2013.02.153	journal	October 2013
Single-stage gradient-based stellarator coil design: Optimization for near-axis quasi-symmetry Giuliani, Andrew; Wechsung, Florian; Cerfon, Antoine Journal of Computational Physics, Vol. 459 https://doi.org/10.1016/j.jcp.2022.111147	journal	June 2022
Advancing the physics basis for quasi-helically symmetric stellarators Bader, A.; Faber, B. J.; Schmitt, J. C. Journal of Plasma Physics, Vol. 86, Issue 5 https://doi.org/10.1017/S0022377820000963	journal	October 2020
Figures of merit for stellarators near the magnetic axis Landreman, Matt Journal of Plasma Physics, Vol. 87, Issue 1 https://doi.org/10.1017/S0022377820001658	journal	February 2021
Combined plasma–coil optimization algorithms Henneberg, S. A.; Hudson, S. R.; Pfefferlé, D. Journal of Plasma Physics, Vol. 87, Issue 2 https://doi.org/10.1017/S0022377821000271	journal	April 2021
Direct computation of magnetic surfaces in Boozer coordinates and coil optimization for quasisymmetry Giuliani, Andrew; Wechsung, Florian; Stadler, Georg Journal of Plasma Physics, Vol. 88, Issue 4 https://doi.org/10.1017/S0022377822000563	journal	July 2022
A single-field-period quasi-isodynamic stellarator Jorge, R.; Plunk, G. G.; Drevlak, M. Journal of Plasma Physics, Vol. 88, Issue 5 https://doi.org/10.1017/S0022377822000873	journal	September 2022
Mapping the space of quasisymmetric stellarators using optimized near-axis expansion Landreman, Matt Journal of Plasma Physics, Vol. 88, Issue 6 https://doi.org/10.1017/S0022377822001258	journal	December 2022
Constructing precisely quasi-isodynamic magnetic fields Goodman, A. G.; Camacho Mata, K.; Henneberg, S. A. Journal of Plasma Physics, Vol. 89, Issue 5 https://doi.org/10.1017/S002237782300065X	journal	September 2023
Three-dimensional effects on energetic particle confinement and stability Spong, D. A. Physics of Plasmas, Vol. 18, Issue 5 https://doi.org/10.1063/1.3575626	journal	May 2011
Collisionless high energy particle losses in optimized stellarators calculated in real-space coordinates Nemov, V. V.; Kasilov, S. V.; Kernbichler, W. Physics of Plasmas, Vol. 21, Issue 6 https://doi.org/10.1063/1.4876740	journal	June 2014
Steepest-descent moment method for three-dimensional magnetohydrodynamic equilibria Hirshman, S. P. Physics of Fluids, Vol. 26, Issue 12 https://doi.org/10.1063/1.864116	journal	January 1983
Optimization of quasi-symmetric stellarators with self-consistent bootstrap current and energetic particle confinement Landreman, M.; Buller, S.; Drevlak, M. Physics of Plasmas, Vol. 29, Issue 8 https://doi.org/10.1063/5.0098166	journal	August 2022
PM4Stell: A prototype permanent magnet stellarator structure Zhu, Caoxiang; Hammond, Kenneth; Rutkowski, Adam Physics of Plasmas, Vol. 29, Issue 11 https://doi.org/10.1063/5.0102754	journal	November 2022
Three-dimensional analysis of tokamaks and stellarators Garabedian, P. R. Proceedings of the National Academy of Sciences, Vol. 105, Issue 37 https://doi.org/10.1073/pnas.0806354105	journal	September 2008
Precise stellarator quasi-symmetry can be achieved with electromagnetic coils Wechsung, Florian; Landreman, Matt; Giuliani, Andrew Proceedings of the National Academy of Sciences, Vol. 119, Issue 13 https://doi.org/10.1073/pnas.2202084119	journal	March 2022
On a Theorem of Weyl Concerning Eigenvalues of Linear Transformations I Fan, Ky Proceedings of the National Academy of Sciences, Vol. 35, Issue 11 https://doi.org/10.1073/pnas.35.11.652	journal	November 1949
Use of the virtual-casing principle in calculating the containing magnetic field in toroidal plasma systems Shafranov, V. D.; Zakharov, L. E. Nuclear Fusion, Vol. 12, Issue 5 https://doi.org/10.1088/0029-5515/12/5/009	journal	September 1972
Solution of stellarator boundary value problems with external currents Merkel, P. Nuclear Fusion, Vol. 27, Issue 5 https://doi.org/10.1088/0029-5515/27/5/018	journal	May 1987
Overview of the Large Helical Device project Iiyoshi, A.; Komori, A.; Ejiri, A. Nuclear Fusion, Vol. 39, Issue 9Y https://doi.org/10.1088/0029-5515/39/9Y/313	journal	September 1999
PIES free boundary stellarator equilibria with improved initial conditions Drevlak, M.; Monticello, D.; Reiman, A. Nuclear Fusion, Vol. 45, Issue 7 https://doi.org/10.1088/0029-5515/45/7/022	journal	July 2005
New classes of quasi-helically symmetric stellarators Ku, L. P.; Boozer, A. H. Nuclear Fusion, Vol. 51, Issue 1 https://doi.org/10.1088/0029-5515/51/1/013004	journal	December 2010
Fast particle confinement with optimized coil currents in the W7-X stellarator Drevlak, M.; Geiger, J.; Helander, P. Nuclear Fusion, Vol. 54, Issue 7 https://doi.org/10.1088/0029-5515/54/7/073002	journal	April 2014
Error fields in the Wendelstein 7-X stellarator Lazerson, Samuel A.; Bozhenkov, Sergey; Israeli, Ben Plasma Physics and Controlled Fusion, Vol. 60, Issue 12 https://doi.org/10.1088/1361-6587/aae96b	journal	November 2018
Efficient high-order singular quadrature schemes in magnetic fusion Malhotra, Dhairya; Cerfon, Antoine J.; O’Neil, Michael Plasma Physics and Controlled Fusion, Vol. 62, Issue 2 https://doi.org/10.1088/1361-6587/ab57f4	journal	December 2019
Single-stage stellarator optimization: combining coils with fixed boundary equilibria Jorge, R.; Goodman, A.; Landreman, M. Plasma Physics and Controlled Fusion, Vol. 65, Issue 7 https://doi.org/10.1088/1361-6587/acd957	journal	June 2023
An improved current potential method for fast computation of stellarator coil shapes Landreman, Matt Nuclear Fusion, Vol. 57, Issue 4 https://doi.org/10.1088/1741-4326/aa57d4	journal	February 2017
New method to design stellarator coils without the winding surface Zhu, Caoxiang; Hudson, Stuart R.; Song, Yuntao Nuclear Fusion, Vol. 58, Issue 1 https://doi.org/10.1088/1741-4326/aa8e0a	journal	November 2017
An adjoint method for gradient-based optimization of stellarator coil shapes Paul, E. J.; Landreman, M.; Bader, A. Nuclear Fusion, Vol. 58, Issue 7 https://doi.org/10.1088/1741-4326/aac1c7	journal	May 2018
Optimisation of stellarator equilibria with ROSE Drevlak, M.; Beidler, C. D.; Geiger, J. Nuclear Fusion, Vol. 59, Issue 1 https://doi.org/10.1088/1741-4326/aaed50	journal	November 2018
Properties of a new quasi-axisymmetric configuration Henneberg, S. A.; Drevlak, M.; Nührenberg, C. Nuclear Fusion, Vol. 59, Issue 2 https://doi.org/10.1088/1741-4326/aaf604	journal	January 2019
Modeling of energetic particle transport in optimized stellarators Bader, A.; Anderson, D. T.; Drevlak, M. Nuclear Fusion, Vol. 61, Issue 11 https://doi.org/10.1088/1741-4326/ac2991	journal	October 2021
A general stellarator version of the systems code PROCESS Lion, J.; Warmer, F.; Wang, H. Nuclear Fusion, Vol. 61, Issue 12 https://doi.org/10.1088/1741-4326/ac2dbf	journal	October 2021
A quasi-isodynamic configuration with good confinement of fast ions at low plasma β Sánchez, E.; Velasco, J. L.; Calvo, I. Nuclear Fusion, Vol. 63, Issue 6 https://doi.org/10.1088/1741-4326/accd82	journal	May 2023
Magnetic Fields with Precise Quasisymmetry for Plasma Confinement Landreman, Matt; Paul, Elizabeth Physical Review Letters, Vol. 128, Issue 3 https://doi.org/10.1103/PhysRevLett.128.035001	journal	January 2022
Confinement of Nonneutral Plasmas on Magnetic Surfaces Pedersen, Thomas Sunn; Boozer, Allen H. Physical Review Letters, Vol. 88, Issue 20 https://doi.org/10.1103/PhysRevLett.88.205002	journal	May 2002
A Closed-Form Formula for Magnetic Dipole Localization by Measurement of Its Magnetic Field and Spatial Gradients Nara, T.; Suzuki, S.; Ando, S. IEEE Transactions on Magnetics, Vol. 42, Issue 10 https://doi.org/10.1109/TMAG.2006.879151	journal	October 2006
Complete Set of Partial Differential Equations for Direct Localization of a Magnetic Dipole Higuchi, Yusuke; Nara, Takaaki; Ando, Shigeru IEEE Transactions on Magnetics, Vol. 52, Issue 5 https://doi.org/10.1109/TMAG.2015.2512536	journal	May 2016
Magnetic dipole localization based on magnetic gradient tensor data at a single point Gang, Yin; Yingtang, Zhang; Hongbo, Fan Journal of Applied Remote Sensing, Vol. 8, Issue 1 https://doi.org/10.1117/1.JRS.8.083596	journal	July 2014
The gradient tensor of potential field anomalies: Some implications on data collection and data processing of maps Pedersen, L. B.; Rasmussen, T. M. GEOPHYSICS, Vol. 55, Issue 12 https://doi.org/10.1190/1.1442807	journal	December 1990
The magnetic gradient tensor: Its properties and uses in source characterization Schmidt, P. W.; Clark, D. A. The Leading Edge, Vol. 25, Issue 1 https://doi.org/10.1190/1.2164759	journal	January 2006
TJ-II Project: A Flexible Heliac Stellarator Alejaldre, Carlos; Gozalo, Jose Javier Alonso; Perez, Jose Botija Fusion Technology, Vol. 17, Issue 1 https://doi.org/10.13182/FST17-131-139	journal	January 1990
The ARIES-CS Compact Stellarator Fusion Power Plant Najmabadi, F.; Raffray, A. R.; Abdel-Khalik, S. I. Fusion Science and Technology, Vol. 54, Issue 3 https://doi.org/10.13182/FST54-655	journal	October 2008
The Advanced Toroidal Facility (ATF) Fusion Technology, Vol. 8, Issue 1P2A https://doi.org/10.13182/FST85-A40084	journal	July 1985
Physics and Engineering Design for Wendelstein VII-X Beidler, Craig; Grieger, Günter; Herrnegger, Franz Fusion Technology, Vol. 17, Issue 1 https://doi.org/10.13182/FST90-A29178	journal	January 1990
The Helically Symmetric Experiment, (HSX) Goals, Design and Status Anderson, F. Simon B.; Almagri, Abdulgader F.; Anderson, David T. Fusion Technology, Vol. 27, Issue 3T https://doi.org/10.13182/FST95-A11947086	journal	April 1995
Magnetic Configuration and Modular Coil Design for the Chinese First Quasi-Axisymmetric Stellarator Liu, Haifeng; Shimizu, Akihiro; Isobe, Mitsutaka Plasma and Fusion Research, Vol. 13, Issue 0 https://doi.org/10.1585/pfr.13.3405067	journal	January 2018
SIMSOPT: A flexible framework for stellarator optimization Landreman, Matt; Medasani, Bharat; Wechsung, Florian Journal of Open Source Software, Vol. 6, Issue 65 https://doi.org/10.21105/joss.03525	journal	September 2021

Similar Records

Effects of drifts on scrape-off layer transport in W7-X

Journal Article · 2023 · Nuclear Fusion · OSTI ID:1908274

Kriete, D. M.; Pandey, A.; Perseo, V.; +17 more

Deciphering the sensitivity of urban canopy air temperature to anthropogenic heat flux with a forcing-feedback framework

Journal Article · 2023 · Environmental Research Letters · OSTI ID:1995029

Wang, Linying; Sun, Ting; Zhou, Wenyu; +2 more

Resonant mode effects on rotation braking induced by n = 1 resonant magnetic perturbations in the EAST tokamak

Journal Article · 2023 · Nuclear Fusion · OSTI ID:1974281

Sheng, H.; Sun, Y. W.; Li, X. Y.; +13 more

Related Subjects

Physics

Title: The magnetic gradient scale length explains why certain plasmas require close external magnetic coils

Citation Formats

References (52)

Similar Records

Related Subjects