Unperturbed-orbit integration and the 3D kinetic dispersion relation of the electron cyclotron drift instability
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866909989864472576 |
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| author | Zhao, Yinjian |
| author_facet | Zhao, Yinjian |
| contents | High-frequency instabilities in crossed-field ($\bm E\times\bm B$) plasmas are widely implicated in anomalous cross-field electron transport in Hall thrusters and related devices. Building on the fully kinetic 3D electrostatic dispersion relations reported by Ducrocq \emph{et al.} and later by Lafleur \emph{et al.}, we provide a concise, self-contained derivation of the key missing step: the magnetized-electron density perturbation $n_{e1}$ obtained from the linearized Vlasov equation via a retarded integration along unperturbed orbits, including finite-Larmor-radius effects and cyclotron harmonics. We collect the required mathematical identities in appendices and clarify the mapping between the Ducrocq Poisson-form and the Lafleur dielectric-form representations, including ion closures (cold-fluid versus kinetic Landau response). We conclude with a brief discussion of the assumptions and possible extensions toward more realistic configurations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_09047 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Unperturbed-orbit integration and the 3D kinetic dispersion relation of the electron cyclotron drift instability Zhao, Yinjian Plasma Physics High-frequency instabilities in crossed-field ($\bm E\times\bm B$) plasmas are widely implicated in anomalous cross-field electron transport in Hall thrusters and related devices. Building on the fully kinetic 3D electrostatic dispersion relations reported by Ducrocq \emph{et al.} and later by Lafleur \emph{et al.}, we provide a concise, self-contained derivation of the key missing step: the magnetized-electron density perturbation $n_{e1}$ obtained from the linearized Vlasov equation via a retarded integration along unperturbed orbits, including finite-Larmor-radius effects and cyclotron harmonics. We collect the required mathematical identities in appendices and clarify the mapping between the Ducrocq Poisson-form and the Lafleur dielectric-form representations, including ion closures (cold-fluid versus kinetic Landau response). We conclude with a brief discussion of the assumptions and possible extensions toward more realistic configurations. |
| title | Unperturbed-orbit integration and the 3D kinetic dispersion relation of the electron cyclotron drift instability |
| topic | Plasma Physics |
| url | https://arxiv.org/abs/2601.09047 |