The theory of early nonlinear stage of m=1 instability with locally flattened q-profile
In this paper, we analyze the modification of fast particles on the nonlinear radial displacement of m = 1 internal kink mode with a shoulder-like equilibrium current theoretically. Using the matching method on the solutions of the outer and inner regions, we derive the analytical form of nonlinear...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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AIP Publishing LLC
2018-09-01
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| Series: | Matter and Radiation at Extremes |
| Online Access: | http://dx.doi.org/10.1016/j.mre.2018.04.002 |
| _version_ | 1818136570846248960 |
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| author | Kai-Qi Cao Xian-Qu Wang |
| author_facet | Kai-Qi Cao Xian-Qu Wang |
| author_sort | Kai-Qi Cao |
| collection | DOAJ |
| description | In this paper, we analyze the modification of fast particles on the nonlinear radial displacement of m = 1 internal kink mode with a shoulder-like equilibrium current theoretically. Using the matching method on the solutions of the outer and inner regions, we derive the analytical form of nonlinear radial displacement in the limit of q' = q" = 0, which is valid to the cases of weak shear due to a slight flattening of the q(r) profile around q = 1. We have taken into consideration the effects of the circulating and trapped fast particles on the nonlinear state of the mode. It is found that a fast particle can modify the nonlinear saturation level by the change of potential energy, depending on the fast particle properties. By the matching of linear dispersion relation to early nonlinear result, we also obtain the relations of radial displacement to the mode frequency and linear growth rate, and discuss the scaling for different stabilities of the MHD modes. |
| first_indexed | 2024-12-11T09:42:31Z |
| format | Article |
| id | doaj.art-a24ea61f94f8415db70ef5d8088f73c1 |
| institution | Directory Open Access Journal |
| issn | 2468-080X |
| language | English |
| last_indexed | 2024-12-11T09:42:31Z |
| publishDate | 2018-09-01 |
| publisher | AIP Publishing LLC |
| record_format | Article |
| series | Matter and Radiation at Extremes |
| spelling | doaj.art-a24ea61f94f8415db70ef5d8088f73c12022-12-22T01:12:38ZengAIP Publishing LLCMatter and Radiation at Extremes2468-080X2018-09-013524324710.1016/j.mre.2018.04.002002805JCPThe theory of early nonlinear stage of m=1 instability with locally flattened q-profileKai-Qi Cao0Xian-Qu Wang1Institute of Fusion Science, School of Physical Science and Technology, Southwest Jiaotong University, Chengdu, Sichuan 610031, ChinaInstitute of Fusion Science, School of Physical Science and Technology, Southwest Jiaotong University, Chengdu, Sichuan 610031, ChinaIn this paper, we analyze the modification of fast particles on the nonlinear radial displacement of m = 1 internal kink mode with a shoulder-like equilibrium current theoretically. Using the matching method on the solutions of the outer and inner regions, we derive the analytical form of nonlinear radial displacement in the limit of q' = q" = 0, which is valid to the cases of weak shear due to a slight flattening of the q(r) profile around q = 1. We have taken into consideration the effects of the circulating and trapped fast particles on the nonlinear state of the mode. It is found that a fast particle can modify the nonlinear saturation level by the change of potential energy, depending on the fast particle properties. By the matching of linear dispersion relation to early nonlinear result, we also obtain the relations of radial displacement to the mode frequency and linear growth rate, and discuss the scaling for different stabilities of the MHD modes.http://dx.doi.org/10.1016/j.mre.2018.04.002 |
| spellingShingle | Kai-Qi Cao Xian-Qu Wang The theory of early nonlinear stage of m=1 instability with locally flattened q-profile Matter and Radiation at Extremes |
| title | The theory of early nonlinear stage of m=1 instability with locally flattened q-profile |
| title_full | The theory of early nonlinear stage of m=1 instability with locally flattened q-profile |
| title_fullStr | The theory of early nonlinear stage of m=1 instability with locally flattened q-profile |
| title_full_unstemmed | The theory of early nonlinear stage of m=1 instability with locally flattened q-profile |
| title_short | The theory of early nonlinear stage of m=1 instability with locally flattened q-profile |
| title_sort | theory of early nonlinear stage of m 1 instability with locally flattened q profile |
| url | http://dx.doi.org/10.1016/j.mre.2018.04.002 |
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