Asymptotic scaling laws for the stagnation conditions of Z-pinch implosions
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| Format: | Preprint |
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2025
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| _version_ | 1866915113708027904 |
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| author | Ruiz, D. E. Williams, C. A. Vesey, R. A. |
| author_facet | Ruiz, D. E. Williams, C. A. Vesey, R. A. |
| contents | Implosions of magnetically-driven annular shells (Z pinches) are studied in the laboratory to produce high-energy-density plasmas. Such plasmas have a wide-range of applications including x-ray generation, controlled thermonuclear fusion, and astrophysics studies. In this work, we theoretically investigate the in-flight dynamics of a magnetically-driven, imploding cylindrical shell that stagnates onto itself upon collision on axis. The converging flow of the Z-pinch is analyzed by considering the implosion trajectory in the $(A, M)$ parametric plane, where $A$ is the in-flight aspect ratio and $M$ is the implosion Mach number. For an ideal implosion in the absence of instabilities and in the limit of $A\gg1$, we derive asymptotic scaling laws for hydrodynamic quantities evaluated at stagnation (e.g., density, temperature, and pressure) and for performance metrics (e.g., soft x-ray emission, K-shell x-ray emission, and neutron yield) as functions of target-design parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_12284 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotic scaling laws for the stagnation conditions of Z-pinch implosions Ruiz, D. E. Williams, C. A. Vesey, R. A. Plasma Physics Implosions of magnetically-driven annular shells (Z pinches) are studied in the laboratory to produce high-energy-density plasmas. Such plasmas have a wide-range of applications including x-ray generation, controlled thermonuclear fusion, and astrophysics studies. In this work, we theoretically investigate the in-flight dynamics of a magnetically-driven, imploding cylindrical shell that stagnates onto itself upon collision on axis. The converging flow of the Z-pinch is analyzed by considering the implosion trajectory in the $(A, M)$ parametric plane, where $A$ is the in-flight aspect ratio and $M$ is the implosion Mach number. For an ideal implosion in the absence of instabilities and in the limit of $A\gg1$, we derive asymptotic scaling laws for hydrodynamic quantities evaluated at stagnation (e.g., density, temperature, and pressure) and for performance metrics (e.g., soft x-ray emission, K-shell x-ray emission, and neutron yield) as functions of target-design parameters. |
| title | Asymptotic scaling laws for the stagnation conditions of Z-pinch implosions |
| topic | Plasma Physics |
| url | https://arxiv.org/abs/2501.12284 |