TY - JOUR

T1 - Generalization of Solovev's approach to finding equilibrium solutions for axisymmetric plasmas with flow

AU - Chu, M. S.

AU - Hu, Yemin

AU - Guo, Wenfeng

N1 - Funding Information:
This work was supported by the program of Fusion Reactor Physics and Digital Tokamak with the CAS ‘One-Three-Five’ Strategic Planning, National Natural Science Foundation of China under Grant Nos. 11375234, 11105175 and 11475219 and also partly by National Magnetic Confinement Fusion Science Program of China under Contract Nos. 2015GB101003 and 2015GB110001. The authors would also like to acknowledge the ShenMa High Performance Computing Cluster at the Institute of Plasma Physics, Chinese Academy of Sciences. Part of the present work is revised from a previous unpublished manuscript sent to another journal. We would like to thank the referee of this other journal for pointing out to us the works of Zheng-Wootton-Solano [2] and Cerfon and Freiberg [7]. This led us to improve our presentation.
Publisher Copyright:
© 2018 Hefei Institutes of Physical Science, Chinese Academy of Sciences and IOP Publishing.

PY - 2018/3

Y1 - 2018/3

N2 - Solovev's approach of finding equilibrium solutions was found to be extremely useful for generating a library of linear-superposable equilibria for the purpose of shaping studies. This set of solutions was subsequently expanded to include the vacuum solutions of Zheng, Wootton and Solano, resulting in a set of functions {SOLOVEV-ZWS} that were usually used for all toroidally symmetric plasmas, commonly recognized as being able to accommodate any desired plasma shapes (complete-shaping capability). The possibility of extending the Solovev approach to toroidal equilibria with a general plasma flow is examined theoretically. We found that the only meaningful extension is to plasmas with a pure toroidal rotation and with a constant Mach number. We also show that the simplification ansatz made to the current profiles, which was the basis of the Solovev approach, should be applied more systematically to include an internal boundary condition at the magnetic axis; resulting in a modified and more useful set {SOLOVEV-ZWSm}. Explicit expressions of functions in this set are given for equilibria with a quasi-constant current density profile, with a toroidal flow at a constant Mach number and with specific heat capacity 1. The properties of {SOLOVEV-ZWSm} are studied analytically. Numerical examples of achievable equilibria are demonstrated. Although the shaping capability of the set {SOLOVE-ZWSm} is quite extensive, it nevertheless still does not have complete shaping capability, particularly for plasmas with negative curvature points on the plasma boundary such as the doublets or indented bean shaped tokamaks.

AB - Solovev's approach of finding equilibrium solutions was found to be extremely useful for generating a library of linear-superposable equilibria for the purpose of shaping studies. This set of solutions was subsequently expanded to include the vacuum solutions of Zheng, Wootton and Solano, resulting in a set of functions {SOLOVEV-ZWS} that were usually used for all toroidally symmetric plasmas, commonly recognized as being able to accommodate any desired plasma shapes (complete-shaping capability). The possibility of extending the Solovev approach to toroidal equilibria with a general plasma flow is examined theoretically. We found that the only meaningful extension is to plasmas with a pure toroidal rotation and with a constant Mach number. We also show that the simplification ansatz made to the current profiles, which was the basis of the Solovev approach, should be applied more systematically to include an internal boundary condition at the magnetic axis; resulting in a modified and more useful set {SOLOVEV-ZWSm}. Explicit expressions of functions in this set are given for equilibria with a quasi-constant current density profile, with a toroidal flow at a constant Mach number and with specific heat capacity 1. The properties of {SOLOVEV-ZWSm} are studied analytically. Numerical examples of achievable equilibria are demonstrated. Although the shaping capability of the set {SOLOVE-ZWSm} is quite extensive, it nevertheless still does not have complete shaping capability, particularly for plasmas with negative curvature points on the plasma boundary such as the doublets or indented bean shaped tokamaks.

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U2 - 10.1088/2058-6272/aa9841

DO - 10.1088/2058-6272/aa9841

M3 - Article

AN - SCOPUS:85041422640

VL - 20

JO - Plasma Science and Technology

JF - Plasma Science and Technology

SN - 1009-0630

IS - 3

M1 - 035101

ER -