A perturbative correction for electron-inertia in magnetized sheath structures
We propose a hydrodynamic model to study the equilibrium properties of planar plasma sheaths in two-component quasi-neutral magnetized plasmas. It includes weak but finite electron-inertia incorporated via a regular perturbation of the electronic fluid dynamics only relative to a new smallness parameter, δ, assessing the weak inertial-to-electromagnetic strengths. The zeroth-order perturbation around δ leads to the usual Boltzmann distribution law, which describes inertialess thermalized electrons. The forthwith next higher-order yields the modified Boltzmann law describing the putative lowest-order electron-inertial correction, which is applied meticulously to derive the local Bohm criterion for sheath formation. It is found to be influenced jointly by electron-inertial corrective effects, magnetic field and field orientation relative to the bulk plasma flow. We establish that the mutualistic action of electron-inertia amid gyro-kinetic effects slightly enhances the ion-flow Mach threshold value (typically, M i0 ⩾ 1.140), against the normal value of unity, confrontationally towards the sheath entrance. A numerical illustrative scheme is methodically constructed to see the parametric dependence of the new sheath properties on diverse problem arguments. The merits and demerits are highlighted in the light of the existing results conjointly with clear indication to future ameliorations.
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