On Minimizing Phase Space Energies
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866913729873969152 |
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| author | Updike, Michael Bohlsen, Nicholas Qin, Hong Fisch, Nathaniel |
| author_facet | Updike, Michael Bohlsen, Nicholas Qin, Hong Fisch, Nathaniel |
| contents | A primary technical challenge for harnessing fusion energy is to control and extract energy from a non-thermal distribution of charged particles. The fact that phase space evolves by symplectomorphisms fundamentally limits how a distribution may be manipulated. While the constraint of phase-space volume preservation is well understood, other constraints remain to be fully appreciated. To better understand these constraints, we study the problem of extracting energy from a distribution of particles using area-preserving and symplectic linear maps. When a quadratic potential is imposed, we find that the maximal extractable energy can be computed as trace minimization problems. We solve these problems and show that the extractable energy under linear symplectomorphisms may be much smaller than the extractable energy under special linear maps. The method introduced in the present study enables an energy-based proof of the linear Gromov non-squeezing theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_07965 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Minimizing Phase Space Energies Updike, Michael Bohlsen, Nicholas Qin, Hong Fisch, Nathaniel Mathematical Physics Optimization and Control Classical Physics Plasma Physics A primary technical challenge for harnessing fusion energy is to control and extract energy from a non-thermal distribution of charged particles. The fact that phase space evolves by symplectomorphisms fundamentally limits how a distribution may be manipulated. While the constraint of phase-space volume preservation is well understood, other constraints remain to be fully appreciated. To better understand these constraints, we study the problem of extracting energy from a distribution of particles using area-preserving and symplectic linear maps. When a quadratic potential is imposed, we find that the maximal extractable energy can be computed as trace minimization problems. We solve these problems and show that the extractable energy under linear symplectomorphisms may be much smaller than the extractable energy under special linear maps. The method introduced in the present study enables an energy-based proof of the linear Gromov non-squeezing theorem. |
| title | On Minimizing Phase Space Energies |
| topic | Mathematical Physics Optimization and Control Classical Physics Plasma Physics |
| url | https://arxiv.org/abs/2503.07965 |