Transverse instability of electron phase-space holes in multi-dimensional Maxwellian plasmas
The stability of an initially one-dimensional electron hole to perturbations varying sinusoidally transverse to its trapping direction is analysed in detail. It is shown that the expected low-frequency eigenmode of the linearized Vlasov-Poisson system consists of a shift mode, proportional to the gr...
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| Format: | Article |
| Language: | English |
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Cambridge University Press (CUP)
2020
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| Online Access: | https://hdl.handle.net/1721.1/124399 |
| _version_ | 1811085413979258880 |
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| author | Hutchinson, Ian Horner |
| author2 | Massachusetts Institute of Technology. Plasma Science and Fusion Center |
| author_facet | Massachusetts Institute of Technology. Plasma Science and Fusion Center Hutchinson, Ian Horner |
| author_sort | Hutchinson, Ian Horner |
| collection | MIT |
| description | The stability of an initially one-dimensional electron hole to perturbations varying sinusoidally transverse to its trapping direction is analysed in detail. It is shown that the expected low-frequency eigenmode of the linearized Vlasov-Poisson system consists of a shift mode, proportional to the gradient of the equilibrium potential. The resulting dispersion relation is that the total jetting force exerted by a perturbed hole on the particles balances the electric restoring tension of the hole. The tension is quantitatively small and can often be ignored. The particle force is expressed as integrals of equilibrium parameters over the hole and is shown at low frequency to be exactly equal to what has recently been found (by different analysis) to express 'kinematic' hole momentum conservation. The mechanism of instability has nothing to do with the previously hypothesized transverse electron focusing. The unmagnetized growth rate γ (k) is found numerically and is in excellent agreement with recent kinematic estimates. Magnetic field stabilization of the transverse mode is also evaluated. The resulting stability boundary for Maxwellian holes is in reasonable agreement with previously published criteria based on particle simulation. It arises from a change of trapped force sign across the resonance between bounce and cyclotron frequencies. ©2018 |
| first_indexed | 2024-09-23T13:09:12Z |
| format | Article |
| id | mit-1721.1/124399 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T13:09:12Z |
| publishDate | 2020 |
| publisher | Cambridge University Press (CUP) |
| record_format | dspace |
| spelling | mit-1721.1/1243992022-09-28T12:17:41Z Transverse instability of electron phase-space holes in multi-dimensional Maxwellian plasmas Hutchinson, Ian Horner Massachusetts Institute of Technology. Plasma Science and Fusion Center The stability of an initially one-dimensional electron hole to perturbations varying sinusoidally transverse to its trapping direction is analysed in detail. It is shown that the expected low-frequency eigenmode of the linearized Vlasov-Poisson system consists of a shift mode, proportional to the gradient of the equilibrium potential. The resulting dispersion relation is that the total jetting force exerted by a perturbed hole on the particles balances the electric restoring tension of the hole. The tension is quantitatively small and can often be ignored. The particle force is expressed as integrals of equilibrium parameters over the hole and is shown at low frequency to be exactly equal to what has recently been found (by different analysis) to express 'kinematic' hole momentum conservation. The mechanism of instability has nothing to do with the previously hypothesized transverse electron focusing. The unmagnetized growth rate γ (k) is found numerically and is in excellent agreement with recent kinematic estimates. Magnetic field stabilization of the transverse mode is also evaluated. The resulting stability boundary for Maxwellian holes is in reasonable agreement with previously published criteria based on particle simulation. It arises from a change of trapped force sign across the resonance between bounce and cyclotron frequencies. ©2018 NASA (Grant NNX16AG82G) 2020-03-27T20:41:37Z 2020-03-27T20:41:37Z 2018-11 2018-04 2020-02-27T15:17:57Z Article http://purl.org/eprint/type/JournalArticle 1469-7807 0022-3778 https://hdl.handle.net/1721.1/124399 Hutchinson, I.H., "Transverse instability of electron phase-space holes in multi-dimensional Maxwellian plasmas." Journal of Plasma Physics 84, 4 (November 2018): no. 905840411 doi 10.1017/S0022377818000909 ©2018 Author en 10.1017/S0022377818000909 Journal of Plasma Physics Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Cambridge University Press (CUP) arXiv |
| spellingShingle | Hutchinson, Ian Horner Transverse instability of electron phase-space holes in multi-dimensional Maxwellian plasmas |
| title | Transverse instability of electron phase-space holes in multi-dimensional Maxwellian plasmas |
| title_full | Transverse instability of electron phase-space holes in multi-dimensional Maxwellian plasmas |
| title_fullStr | Transverse instability of electron phase-space holes in multi-dimensional Maxwellian plasmas |
| title_full_unstemmed | Transverse instability of electron phase-space holes in multi-dimensional Maxwellian plasmas |
| title_short | Transverse instability of electron phase-space holes in multi-dimensional Maxwellian plasmas |
| title_sort | transverse instability of electron phase space holes in multi dimensional maxwellian plasmas |
| url | https://hdl.handle.net/1721.1/124399 |
| work_keys_str_mv | AT hutchinsonianhorner transverseinstabilityofelectronphasespaceholesinmultidimensionalmaxwellianplasmas |