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| Format: | Preprint |
| Publié: |
2025
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| Accès en ligne: | https://arxiv.org/abs/2508.12390 |
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| _version_ | 1866909739783290880 |
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| author | Karell, Justo |
| author_facet | Karell, Justo |
| contents | We calculate transport coefficients from the Chapman--Enskog expansion with BGK collision operators, obtaining exactly $κ= \frac{5nT}{2mν}$, and show that maximum entropy closure yields identical results when applied with the same collision operator. Through structural arguments, we suggest that this $1/ν$ divergence extends to other local collision operators of the form $\mathcal{L} = ν\hat{L}$, making the divergence fundamental to the Chapman--Enskog approach rather than a closure artifact. To address this limitation, we propose a phenomenological effective collision frequency $ν_{\eff} = ν\sqrt{1 + \Kn^2}$ motivated by gradient-driven decorrelation, where $\Kn$ is the Knudsen number. We verify that this regularization maintains conservation laws and thermodynamic consistency while yielding finite transport coefficients across all collisionality regimes. Comparison with exact solutions of a bounded kinetic model shows similar functional form, providing limited validation of our approach. This work provides explicit calculation of a known divergence problem in kinetic theory and offers one phenomenological regularization method with transparent treatment of mathematical assumptions versus physical approximations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_12390 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Chapman-Enskog Divergence Problem in Plasma Transport: Structural Limitations and a Practical Regularization Approach Karell, Justo Plasma Physics Mathematical Physics We calculate transport coefficients from the Chapman--Enskog expansion with BGK collision operators, obtaining exactly $κ= \frac{5nT}{2mν}$, and show that maximum entropy closure yields identical results when applied with the same collision operator. Through structural arguments, we suggest that this $1/ν$ divergence extends to other local collision operators of the form $\mathcal{L} = ν\hat{L}$, making the divergence fundamental to the Chapman--Enskog approach rather than a closure artifact. To address this limitation, we propose a phenomenological effective collision frequency $ν_{\eff} = ν\sqrt{1 + \Kn^2}$ motivated by gradient-driven decorrelation, where $\Kn$ is the Knudsen number. We verify that this regularization maintains conservation laws and thermodynamic consistency while yielding finite transport coefficients across all collisionality regimes. Comparison with exact solutions of a bounded kinetic model shows similar functional form, providing limited validation of our approach. This work provides explicit calculation of a known divergence problem in kinetic theory and offers one phenomenological regularization method with transparent treatment of mathematical assumptions versus physical approximations. |
| title | The Chapman-Enskog Divergence Problem in Plasma Transport: Structural Limitations and a Practical Regularization Approach |
| topic | Plasma Physics Mathematical Physics |
| url | https://arxiv.org/abs/2508.12390 |