On the linearity and stability of electrostatic structures based on the Schamel equation
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929594693582848 |
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| author | Schamel, Hans Pelinovsky, Efim Flamarion, Marcelo V |
| author_facet | Schamel, Hans Pelinovsky, Efim Flamarion, Marcelo V |
| contents | This paper contributes in the first part to the correct understanding of the linear limit in the Schamel equation (S-equation) from the perspective of structure formation in collisionless plasmas. The corresponding modes near equilibrium turn out to be nonlinear modes of the underlying microscopic Vlasov-Poisson (VP) system for which particle trapping is responsible. A simple shift of the electrostatic potential to a new pedestal leads to non-negativity and thus mitigates the positivity problem of the S-equation. The stability of a solitary electron hole (bright soliton), based on both the S-equation and an earlier transverse but limited VP instability analysis, exhibits marginal stability and linear perturbations in the form of the asymmetric shift eigenmode of a solvable Schrödinger problem. This finding of a dominant shift mode perturbation also seems to have been observed in a numerical PIC simulation, thus providing some confirmation for both theories. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_17923 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the linearity and stability of electrostatic structures based on the Schamel equation Schamel, Hans Pelinovsky, Efim Flamarion, Marcelo V Plasma Physics This paper contributes in the first part to the correct understanding of the linear limit in the Schamel equation (S-equation) from the perspective of structure formation in collisionless plasmas. The corresponding modes near equilibrium turn out to be nonlinear modes of the underlying microscopic Vlasov-Poisson (VP) system for which particle trapping is responsible. A simple shift of the electrostatic potential to a new pedestal leads to non-negativity and thus mitigates the positivity problem of the S-equation. The stability of a solitary electron hole (bright soliton), based on both the S-equation and an earlier transverse but limited VP instability analysis, exhibits marginal stability and linear perturbations in the form of the asymmetric shift eigenmode of a solvable Schrödinger problem. This finding of a dominant shift mode perturbation also seems to have been observed in a numerical PIC simulation, thus providing some confirmation for both theories. |
| title | On the linearity and stability of electrostatic structures based on the Schamel equation |
| topic | Plasma Physics |
| url | https://arxiv.org/abs/2410.17923 |