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Generalized n-dimensional Effective Temperature for Cryogenic Systems in Accelerator Physics
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Version 1
: Received: 2 July 2024 / Approved: 2 July 2024 / Online: 2 July 2024 (14:03:02 CEST)
How to cite: Kim, H.; Park, C.-S. Generalized n-dimensional Effective Temperature for Cryogenic Systems in Accelerator Physics. Preprints 2024, 2024070251. https://doi.org/10.20944/preprints202407.0251.v1 Kim, H.; Park, C.-S. Generalized n-dimensional Effective Temperature for Cryogenic Systems in Accelerator Physics. Preprints 2024, 2024070251. https://doi.org/10.20944/preprints202407.0251.v1
Abstract
Investigations into the properties of generalized effective temperature are conducted across arbitrary dimensions. Maxwell-Boltzmann distribution is displayed for one, two, and three dimensions, with effective temperatures expressed for each dimension. The energy density of blackbody radiation is examined as a function of dimensionality. Effective temperatures for non-uniform temperature distributions in one, two, three, and higher dimensions are presented, with generalizations extended to arbitrary dimensions. Furthermore, the application of generalized effective temperature is explored not only for linearly non-uniform temperature distributions but also for scenarios involving the volume fraction of two distinct temperature distributions. Finally, the effective temperature is determined for a cryogenic system supplied with both liquid nitrogen and liquid helium.
Keywords
effective temperature; fractional dimension; thermal radiation; cryogenic system; accelerator physics
Subject
Physical Sciences, Quantum Science and Technology
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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