Generalization of the Stability Condition for the Semi–Implicit Formulation of the Radial Impurity Transport Equation in Tokamak Plasma in Terms ... View Full Text


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Article Info

DATE

2021-08-20

AUTHORS

Amrita Bhattacharya, Joydeep Ghosh, M. B. Chowdhuri, Ashoke De

ABSTRACT

The present study details the generalization of a stability condition for the semi-implicit formulation of the one-dimensional impurity transport equation for tokamak plasmas in terms of the magnetic flux surface coordinate system (ρ). The radial impurity transport equation for tokamak plasmas is a set of non-linear, parabolic, partial differential equations, solving which generates the radial distributions of all impurity charge states (Z) within the plasma. The present study illustrates the application of a semi-implicit method over the ρ-based impurity transport equation, generated by applying a transformation of the coordinate for the poloidal cross-section of the torus-shaped plasma confinement system, from its geometric radius (r) to the magnetic flux surface coordinate system (ρ). The study further discusses the von Neumann stability analysis of the numerical scheme applied to this transformed (ρ-based) impurity transport equation. The von Neumann stability analysis of the semi-implicit formulation of the radial impurity transport equation has been reported earlier. The stability condition derived in this study is, therefore, a generalization to the earlier reported stability condition now applicable to all ρ(r) including the specific case ρ = r considered in the earlier study. The effects of the impurity transport coefficient (D and v) profiles and the plasma and impurity parameter profiles on the derived ρ-based stability condition are analysed in this study. The impurity element considered is oxygen (1 ≤ Z ≤ 8) and the geometry and plasma parameters of the ADITYA tokamak are applied to the cases studied for consistency. More... »

PAGES

20

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URI

http://scigraph.springernature.com/pub.10.1007/s10894-021-00308-2

DOI

http://dx.doi.org/10.1007/s10894-021-00308-2

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https://app.dimensions.ai/details/publication/pub.1140551385


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