Abstract
Here we address for the sake of completeness the modelling of the electron plasma waves, also called Langmuir waves. We recall how the coupling of these waves with the ion population leads to the system of Zakharov equations and the different approximations that are made for this derivation.
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Notes
- 1.
That is, the pressure P e is assumed to obey the law \(P_{e} = P_{\text{ref}}N_{\text{ref}}^{-3}N_{e}^{3}.\) Therefore, we get \(\nabla P_{e} = 3P_{\text{ref}}N_{\text{ref}}^{-3}N_{e}^{2}\nabla N_{e}\) ≃ 3T ref∇N e ).
- 2.
If one assumes that there is Neumann conditions on the boundary of the simulation domain, \(-{\Delta }^{-1}\) defines a function up to an additive constant.
- 3.
For an introduction to Galerkin methods, see the proof of Proposition 7 above.
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Sentis, R. (2014). Langmuir Waves and Zakharov Equations. In: Mathematical Models and Methods for Plasma Physics, Volume 1. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-03804-9_4
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DOI: https://doi.org/10.1007/978-3-319-03804-9_4
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