High fidelity simulations of the multi-species Vlasov-Maxwell system with the Numerical Flow Iteration
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918222592212992 |
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| author | Wilhelm, Rostislav-Paul Bacchini, Fabio |
| author_facet | Wilhelm, Rostislav-Paul Bacchini, Fabio |
| contents | Validity of fluid models breaks down for non-thermal or weakly collisional plasmas which often occur e.g. in the solar wind. In these regimes one has to resort to modelling through the first-principle Vlasov-Maxwell system, but its six-dimensional phase-space dynamics, strong filamentation, and multi-scale structure make direct numerical simulation extremely demanding. Particle-In-Cell (PIC) methods remain the standard for ion-scale studies, yet their memory cost and intrinsic noise hinder accurate electron-scale simulations. In this paper, we introduce an alternative method based on an iterative-in-time approximation of characteristics. The approach reconstructs the phase-space dynamics from the time history of the electromagnetic fields and the initial distribution functions, enabling extremely high effective resolution far below the phase-space grid scale without storing or advecting high-dimensional data. Earlier work demonstrated this capability for the multi-species electrostatic Vlasov system. Here we discuss an extension of the method to the full Vlasov-Maxwell equations using a Hamiltonian splitting to advance the solution in a structure-preserving way while retaining the reduced memory footprint. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_23286 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | High fidelity simulations of the multi-species Vlasov-Maxwell system with the Numerical Flow Iteration Wilhelm, Rostislav-Paul Bacchini, Fabio Plasma Physics Numerical Analysis Computational Physics Validity of fluid models breaks down for non-thermal or weakly collisional plasmas which often occur e.g. in the solar wind. In these regimes one has to resort to modelling through the first-principle Vlasov-Maxwell system, but its six-dimensional phase-space dynamics, strong filamentation, and multi-scale structure make direct numerical simulation extremely demanding. Particle-In-Cell (PIC) methods remain the standard for ion-scale studies, yet their memory cost and intrinsic noise hinder accurate electron-scale simulations. In this paper, we introduce an alternative method based on an iterative-in-time approximation of characteristics. The approach reconstructs the phase-space dynamics from the time history of the electromagnetic fields and the initial distribution functions, enabling extremely high effective resolution far below the phase-space grid scale without storing or advecting high-dimensional data. Earlier work demonstrated this capability for the multi-species electrostatic Vlasov system. Here we discuss an extension of the method to the full Vlasov-Maxwell equations using a Hamiltonian splitting to advance the solution in a structure-preserving way while retaining the reduced memory footprint. |
| title | High fidelity simulations of the multi-species Vlasov-Maxwell system with the Numerical Flow Iteration |
| topic | Plasma Physics Numerical Analysis Computational Physics |
| url | https://arxiv.org/abs/2511.23286 |