Gromov ground state in phase space engineering for fusion energy
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866917866406674432 |
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| author | Qin, Hong Kolmes, Elijah J. Updike, Michael Bohlsen, Nicholas Fisch, Nathaniel J. |
| author_facet | Qin, Hong Kolmes, Elijah J. Updike, Michael Bohlsen, Nicholas Fisch, Nathaniel J. |
| contents | Phase space engineering by RF waves plays important roles in both thermal D-T fusion and non-thermal advanced fuel fusion. But not all phase space manipulation is allowed, certain fundamental limits exist. In addition to Liouville's theorem, which requires the manipulation to be volume-preserving, Gromov's non-squeezing theorem imposes another constraint. The Gardner ground state is defined as the ground state accessible by smooth volume-preserving maps. However, the extra Gromov constraint should produce a higher-energy ground state. An example of a Gardner ground state forbidden by Gromov's non-squeezing theorem is given. The challenge question is: What is the Gromov ground state, i.e., the lowest energy state accessible by smooth symplectic maps? This is a difficult problem. As a simplification, we conjecture that the linear Gromov ground state problem is solvable. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_08494 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gromov ground state in phase space engineering for fusion energy Qin, Hong Kolmes, Elijah J. Updike, Michael Bohlsen, Nicholas Fisch, Nathaniel J. Plasma Physics Mathematical Physics Symplectic Geometry Computational Physics Phase space engineering by RF waves plays important roles in both thermal D-T fusion and non-thermal advanced fuel fusion. But not all phase space manipulation is allowed, certain fundamental limits exist. In addition to Liouville's theorem, which requires the manipulation to be volume-preserving, Gromov's non-squeezing theorem imposes another constraint. The Gardner ground state is defined as the ground state accessible by smooth volume-preserving maps. However, the extra Gromov constraint should produce a higher-energy ground state. An example of a Gardner ground state forbidden by Gromov's non-squeezing theorem is given. The challenge question is: What is the Gromov ground state, i.e., the lowest energy state accessible by smooth symplectic maps? This is a difficult problem. As a simplification, we conjecture that the linear Gromov ground state problem is solvable. |
| title | Gromov ground state in phase space engineering for fusion energy |
| topic | Plasma Physics Mathematical Physics Symplectic Geometry Computational Physics |
| url | https://arxiv.org/abs/2412.08494 |