Topology Shape and Parametric Design Optimization of Hall Effect Thrusters

Rtimi, Youness; Bonnet, Marie‐Paule; Messine, Frédéric; Hénaux, Carole

doi:10.1007/978-3-030-44101-2_24

Cited by 1 publication

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References 4 publications

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“…The quadratic nonlinearity ∇ × ((∇ × B) × B) is referred to as the Hall current term after the discovery of Hall [35], and makes (E-MHD) a quasilinear dispersive equation. While the Hall current term is omitted in the usual ideal MHD model, it is known to be directly responsible for various situations including plasma confinement, collisionless magnetic reconnection featuring X-configuration ( [6,67,38,27]), Hall-effect thrusters ( [76,68,62]), planetary magnetospheres including that of the Earth's ( [26,57]) and magnetic field dynamics in neutron stars ( [33,46,34,74]). In all of these situations, the effect of magnetic resistivity is considered negligible with respect to that of the Hall current term.…”

Section: Introductionmentioning

confidence: 99%

On the Cauchy Problem for the Hall and Electron Magnetohydrodynamic Equations Without Resistivity I: Illposedness Near Degenerate Stationary Solutions

Jeong

2022

Ann. PDE

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We prove the local wellposedness of the Cauchy problems for the electron magnetohydrodynamics equations (E-MHD) without resistivity for possibly large perturbations of nonzero uniform magnetic fields. While the local wellposedness problem for (E-MHD) has been extensively studied in the presence of resistivity (which provides dissipative effects), this seems to be the first such result without resistivity. (E-MHD) is a fluid description of plasma in small scales where the motion of electrons relative to ions is significant. Mathematically, it is a quasilinear dispersive equation with nondegenerate but nonelliptic second-order principal term. Our result significantly improves upon the straightforward adaptation of the classical work of Kenig-Ponce-Rolvung-Vega on the quasilinear ultrahyperbolic Schrödinger equations, as the regularity and decay assumptions on the initial data are greatly weakened to the level analogous to the recent work of Marzuola-Metcalfe-Tataru in the case of elliptic principal term.A key ingredient of our proof is a simple observation about the relationship between the size of a symbol and the operator norm of its quantization as a pseudodifferential operator when restricted to high frequencies. This allows us to localize the (non-classical) pseudodifferential renormalization operator considered by Kenig-Ponce-Rolvung-Vega, and produce instead a classical pseudodifferential renormalization operator. We furthermore incorporate the function space framework of Marzuola-Metcalfe-Tataru to the present case of nonelliptic principal term.4 Although, pedantically, Section 7.5 considers the paralinearized system, which is more difficult than the simplified problem discussed here.5 This was done without having uniqueness corresponding to the initial data, which is still an open problem.

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Section: Introductionmentioning

confidence: 99%

On the Cauchy Problem for the Hall and Electron Magnetohydrodynamic Equations Without Resistivity I: Illposedness Near Degenerate Stationary Solutions

Jeong

2022

Ann. PDE

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Topology Shape and Parametric Design Optimization of Hall Effect Thrusters

Cited by 1 publication

References 4 publications

On the Cauchy Problem for the Hall and Electron Magnetohydrodynamic Equations Without Resistivity I: Illposedness Near Degenerate Stationary Solutions

On the Cauchy Problem for the Hall and Electron Magnetohydrodynamic Equations Without Resistivity I: Illposedness Near Degenerate Stationary Solutions

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