Asymptotic quasisymmetric high-beta three-dimensional magnetohydrodynamic equilibria near axisymmetry

Sengupta, Wrick; Nikulsin, Nikita; Gaur, Rahul; Bhattacharjee, Amitava

doi:10.1017/S0022377824000357

Title: Asymptotic quasisymmetric high-beta three-dimensional magnetohydrodynamic equilibria near axisymmetry

Journal Article · 05 April 2024 · Journal of Plasma Physics

DOI: https://doi.org/10.1017/S0022377824000357 · OSTI ID:2335376

;

Quasisymmetry (QS), a hidden symmetry of the magnetic field strength, is known to support nested flux surfaces and provide superior particle confinement in stellarators. In this work, we study the ideal magnetohydrodynamic (MHD) equilibrium and stability of high-beta plasma in a large-aspect-ratio stellarator. In particular, we show that the lowest-order description of a near-axisymmetric equilibrium vastly simplifies the problem of three-dimensional quasisymmetric MHD equilibria, which can be reduced to a standard elliptic Grad–Shafranov equation for the flux function. We show that any large-aspect-ratio tokamak, deformed periodically in the vertical direction, is a stellarator with approximate volumetric QS. We discuss exact analytical solutions and numerical benchmarks. Finally, we discuss the ideal ballooning and interchange stability of some of our equilibrium configurations.

View Journal Article

Cite

Export

Save

Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0024548

OSTI ID:: 2335376

Journal Information:: Journal of Plasma Physics, Journal Name: Journal of Plasma Physics Journal Issue: 2 Vol. 90; ISSN 0022-3778

Publisher:: Cambridge University Press (CUP)Copyright Statement

Country of Publication:: United Kingdom

Language:: English

References (49)

Ideal MHD Freidberg, Jeffrey P. https://doi.org/10.1017/CBO9780511795046	book	July 2014
Equilibrium 𝛽-limits in classical stellarators Loizu, J.; Hudson, S. R.; Nührenberg, C. Journal of Plasma Physics, Vol. 83, Issue 6 https://doi.org/10.1017/S0022377817000861	journal	November 2017
Quasi-axisymmetric magnetic fields: weakly non-axisymmetric case in a vacuum Plunk, G. G.; Helander, Per Journal of Plasma Physics, Vol. 84, Issue 2 https://doi.org/10.1017/S0022377818000259	journal	April 2018
Direct construction of optimized stellarator shapes. Part 1. Theory in cylindrical coordinates Landreman, Matt; Sengupta, Wrick Journal of Plasma Physics, Vol. 84, Issue 6 https://doi.org/10.1017/S0022377818001289	journal	December 2018
Direct construction of optimized stellarator shapes. Part 3. Omnigenity near the magnetic axis Plunk, Gabriel G.; Landreman, Matt; Helander, Per Journal of Plasma Physics, Vol. 85, Issue 6 https://doi.org/10.1017/S002237781900062X	journal	November 2019
Stellarator equilibria with reactor relevant energetic particle losses Bader, Aaron; Drevlak, M.; Anderson, D. T. Journal of Plasma Physics, Vol. 85, Issue 5 https://doi.org/10.1017/S0022377819000680	journal	October 2019
Constructing stellarators with quasisymmetry to high order Landreman, Matt; Sengupta, Wrick Journal of Plasma Physics, Vol. 85, Issue 6 https://doi.org/10.1017/S0022377819000783	journal	November 2019
Perturbing an axisymmetric magnetic equilibrium to obtain a quasi-axisymmetric stellarator Plunk, G. G. Journal of Plasma Physics, Vol. 86, Issue 4 https://doi.org/10.1017/S0022377820000902	journal	August 2020
On quasisymmetric plasma equilibria sustained by small force Constantin, Peter; Drivas, Theodore D.; Ginsberg, Daniel Journal of Plasma Physics, Vol. 87, Issue 1 https://doi.org/10.1017/S0022377820001610	journal	February 2021
Equilibriumβ-limits dependence on bootstrap current in classical stellarators Baillod, A.; Loizu, J.; Qu, Z. S. Journal of Plasma Physics, Vol. 89, Issue 5 https://doi.org/10.1017/S0022377823000910	journal	September 2023
An adjoint-based method for optimising MHD equilibria against the infinite-n, ideal ballooning mode Gaur, Rahul; Buller, Stefan; Ruth, Maximilian E. Journal of Plasma Physics, Vol. 89, Issue 5 https://doi.org/10.1017/S0022377823000995	journal	October 2023
Reduced MHD in nearly potential magnetic fields Strauss, H. R. Journal of Plasma Physics, Vol. 57, Issue 1 https://doi.org/10.1017/S0022377896005296	journal	January 1997
3D field phase-space control in tokamak plasmas Park, Jong-Kyu; Jeon, YoungMu; In, Yongkyoon Nature Physics, Vol. 14, Issue 12 https://doi.org/10.1038/s41567-018-0268-8	journal	September 2018
Anderson localization of ballooning modes, quantum chaos and the stability of compact quasiaxially symmetric stellarators Redi, M. H.; Johnson, J. L.; Klasky, S. Physics of Plasmas, Vol. 9, Issue 5 https://doi.org/10.1063/1.1448344	journal	May 2002
Local equilibrium of nonrotating plasmas Boozer, Allen H. Physics of Plasmas, Vol. 9, Issue 9 https://doi.org/10.1063/1.1501474	journal	September 2002
Determination of Hydromagnetic Equilibria Greene, John M.; Johnson, John L. Physics of Fluids, Vol. 4, Issue 7 https://doi.org/10.1063/1.1706420	journal	January 1961
Generation and damping of neoclassical plasma flows in stellarators Spong, D. A. Physics of Plasmas, Vol. 12, Issue 5 https://doi.org/10.1063/1.1887172	journal	May 2005
Computation of three-dimensional tokamak and spherical torus equilibria Park, Jong-kyu; Boozer, Allen H.; Glasser, Alan H. Physics of Plasmas, Vol. 14, Issue 5 https://doi.org/10.1063/1.2732170	journal	May 2007
Importance of plasma response to nonaxisymmetric perturbations in tokamaks Park, Jong-kyu; Boozer, Allen H.; Menard, Jonathan E. Physics of Plasmas, Vol. 16, Issue 5 https://doi.org/10.1063/1.3122862	journal	May 2009
Existence of three-dimensional ideal-magnetohydrodynamic equilibria with current sheets Loizu, J.; Hudson, S. R.; Bhattacharjee, A. Physics of Plasmas, Vol. 22, Issue 9 https://doi.org/10.1063/1.4931094	journal	September 2015
Some mathematics for quasi-symmetry Burby, J. W.; Kallinikos, N.; MacKay, R. S. Journal of Mathematical Physics, Vol. 61, Issue 9 https://doi.org/10.1063/1.5142487	journal	September 2020
Magnetic field strength of toroidal plasma equilibria Garren, D. A.; Boozer, A. H. Physics of Fluids B: Plasma Physics, Vol. 3, Issue 10 https://doi.org/10.1063/1.859915	journal	October 1991
Existence of quasihelically symmetric stellarators Garren, D. A.; Boozer, A. H. Physics of Fluids B: Plasma Physics, Vol. 3, Issue 10 https://doi.org/10.1063/1.859916	journal	October 1991
Limiting beta of stellarators with no net current Strauss, H. R. Physics of Fluids, Vol. 24, Issue 6 https://doi.org/10.1063/1.863504	journal	January 1981
Ballooning mode spectrum in general toroidal systems Dewar, R. L. Physics of Fluids, Vol. 26, Issue 10 https://doi.org/10.1063/1.864028	journal	January 1983
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
Noncircular, finite aspect ratio, local equilibrium model Miller, R. L.; Chu, M. S.; Greene, J. M. Physics of Plasmas, Vol. 5, Issue 4 https://doi.org/10.1063/1.872666	journal	April 1998
Necessary and sufficient conditions for quasisymmetry Rodríguez, E.; Helander, P.; Bhattacharjee, A. Physics of Plasmas, Vol. 27, Issue 6 https://doi.org/10.1063/5.0008551	journal	June 2020
Integrability, normal forms, and magnetic axis coordinates Burby, J. W.; Duignan, N.; Meiss, J. D. Journal of Mathematical Physics, Vol. 62, Issue 12 https://doi.org/10.1063/5.0049361	journal	December 2021
Islands and current singularities in quasisymmetric toroidal plasmas Rodríguez, E.; Bhattacharjee, A. Physics of Plasmas, Vol. 28, Issue 9 https://doi.org/10.1063/5.0057186	journal	September 2021
Numerical study of δ -function current sheets arising from resonant magnetic perturbations Huang, Yi-Min; Hudson, Stuart R.; Loizu, Joaquim Physics of Plasmas, Vol. 29, Issue 3 https://doi.org/10.1063/5.0067898	journal	March 2022
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
Stellarator equations of motion Strauss, H. R. Plasma Physics, Vol. 22, Issue 7 https://doi.org/10.1088/0032-1028/22/7/010	journal	July 1980
Theory of plasma confinement in non-axisymmetric magnetic fields Helander, Per Reports on Progress in Physics, Vol. 77, Issue 8 https://doi.org/10.1088/0034-4885/77/8/087001	journal	July 2014
Physics of the compact advanced stellarator NCSX Zarnstorff, M. C.; Berry, L. A.; Brooks, A. Plasma Physics and Controlled Fusion, Vol. 43, Issue 12A https://doi.org/10.1088/0741-3335/43/12A/318	journal	November 2001
Effects of the radial electric field in a quasisymmetric stellarator Landreman, Matt; Catto, Peter J. Plasma Physics and Controlled Fusion, Vol. 53, Issue 1 https://doi.org/10.1088/0741-3335/53/1/015004	journal	November 2010
Structure of pressure-gradient-driven current singularity in ideal magnetohydrodynamic equilibrium Huang, Yi-Min; Zhou, Yao; Loizu, Joaquim Plasma Physics and Controlled Fusion, Vol. 65, Issue 3 https://doi.org/10.1088/1361-6587/acb382	journal	February 2023
Constructing the space of quasisymmetric stellarators through near-axis expansion Rodríguez, E.; Sengupta, W.; Bhattacharjee, A. Plasma Physics and Controlled Fusion, Vol. 65, Issue 9 https://doi.org/10.1088/1361-6587/ace739	journal	July 2023
Construction of quasisymmetric stellarators using a direct coordinate approach Jorge, R.; Sengupta, W.; Landreman, M. Nuclear Fusion, Vol. 60, Issue 7 https://doi.org/10.1088/1741-4326/ab90ca	journal	June 2020
Stellarator and Heliotron Devices Wakatani, Masahiro https://doi.org/10.1093/oso/9780195078312.001.0001	book	May 1998
Absence of Diffusion in Certain Random Lattices Anderson, P. W. Physical Review, Vol. 109, Issue 5 https://doi.org/10.1103/PhysRev.109.1492	journal	March 1958
Quasisymmetric Optimization of Nonaxisymmetry in Tokamaks Park, J. -K.; Yang, S. M.; Logan, N. C. Physical Review Letters, Vol. 126, Issue 12 https://doi.org/10.1103/PhysRevLett.126.125001	journal	March 2021
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
Shear, Periodicity, and Plasma Ballooning Modes Connor, J. W.; Hastie, R. J.; Taylor, J. B. Physical Review Letters, Vol. 40, Issue 6 https://doi.org/10.1103/PhysRevLett.40.396	journal	February 1978
Experimental Evidence of Reduced Plasma Flow Damping with Quasisymmetry Gerhardt, S. P.; Talmadge, J. N.; Canik, J. M. Physical Review Letters, Vol. 94, Issue 1 https://doi.org/10.1103/PhysRevLett.94.015002	journal	January 2005
Control of Asymmetric Magnetic Perturbations in Tokamaks Park, Jong-kyu; Schaffer, Michael J.; Menard, Jonathan E. Physical Review Letters, Vol. 99, Issue 19 https://doi.org/10.1103/PhysRevLett.99.195003	journal	November 2007
Relationship between the shape of equilibrium magnetic surfaces and the magnetic field strength Skovoroda, A. A. Plasma Physics Reports, Vol. 33, Issue 7 https://doi.org/10.1134/S1063780X0707001X	journal	July 2007
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 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

Similar Records

An asymptotic Grad–Shafranov equation for quasisymmetric stellarators

Journal Article · 2024 · Journal of Plasma Physics · OSTI ID:2479661

Nikulsin, Nikita; Sengupta, Wrick; Jorge, Rogerio; +1 more

Lyapunov stability analysis of magnetohydrodynamic plasma equilibria with axisymmetric toroidal flow

Journal Article · 1988 · Phys. Fluids; (United States) · OSTI ID:7231350

Almaguer, J A; Hameiri, E; Herrera, J; +1 more

Connection between quasisymmetric magnetic fields and anisotropic pressure equilibria in fusion plasmas

Journal Article · 2021 · Physical Review. E · OSTI ID:1814020

Rodríguez, E.; Bhattacharjee, A.

Title: Asymptotic quasisymmetric high-beta three-dimensional magnetohydrodynamic equilibria near axisymmetry

Citation Formats

References (49)

Similar Records

Related Subjects