Non-Perturbative Solutions to the Vlasov-Boltzmann Equation for Weakly Ionized Plasmas
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916843625644032 |
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| author | Saucedo, Joel Lamba, Uday Mahabaduge, Hasitha |
| author_facet | Saucedo, Joel Lamba, Uday Mahabaduge, Hasitha |
| contents | The electron energy distribution function (EEDF) in low-temperature plasmas exhibits features not fully captured by classical collisional models, particularly across the transition from kinetic to hydrodynamic regimes. This work attributes these phenomena to a dynamically broken scale invariance within the Vlasov-Boltzmann equation. By applying renormalization group (RG) techniques directly to the kinetic operator, we derive non-perturbative EEDF solutions valid across a range of collisionality. The formalism yields analytic scaling relations for electron heating and predicts the emergence of distinct EEDF forms - bimodal in the kinetic limit and generalized exponential in the hydrodynamic limit - separated by a critical pressure. It is shown that the stable RG fixed point governing the system's long-time behavior corresponds to a state of minimum entropy production, establishing a thermodynamic basis for plasma self-organization. The theory provides a quantitative explanation for the experimentally observed universal data collapse of rescaled EEDFs and resolves standing issues like Godyak's EEDF metamorphosis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_10565 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-Perturbative Solutions to the Vlasov-Boltzmann Equation for Weakly Ionized Plasmas Saucedo, Joel Lamba, Uday Mahabaduge, Hasitha Plasma Physics The electron energy distribution function (EEDF) in low-temperature plasmas exhibits features not fully captured by classical collisional models, particularly across the transition from kinetic to hydrodynamic regimes. This work attributes these phenomena to a dynamically broken scale invariance within the Vlasov-Boltzmann equation. By applying renormalization group (RG) techniques directly to the kinetic operator, we derive non-perturbative EEDF solutions valid across a range of collisionality. The formalism yields analytic scaling relations for electron heating and predicts the emergence of distinct EEDF forms - bimodal in the kinetic limit and generalized exponential in the hydrodynamic limit - separated by a critical pressure. It is shown that the stable RG fixed point governing the system's long-time behavior corresponds to a state of minimum entropy production, establishing a thermodynamic basis for plasma self-organization. The theory provides a quantitative explanation for the experimentally observed universal data collapse of rescaled EEDFs and resolves standing issues like Godyak's EEDF metamorphosis. |
| title | Non-Perturbative Solutions to the Vlasov-Boltzmann Equation for Weakly Ionized Plasmas |
| topic | Plasma Physics |
| url | https://arxiv.org/abs/2507.10565 |