|Title||Explicit approximations to estimate the perturbative diffusivity in the presence of convectivity and damping. II. Semi-infinite cylindrical approximations|
|Publication Type||Journal Article|
|Year of Publication||2014|
|Authors||M. van Berkel, G.MD Hogeweij, N. Tamura, H.J Zwart, S. Inagaki, MR de Baar, K. Ida|
|Journal||Physics of Plasmas|
|Keywords||approximation theory, convection, damping, diffusion, heat transfer, plasma transport processes|
In this paper, a number of new explicit approximations are introduced to estimate the perturbative diffusivity (χ), convectivity (V), and damping (τ) in a cylindrical geometry. For this purpose, the harmonic components of heat waves induced by localized deposition of modulated power are used. The approximations are based upon the heat equation in a semi-infinite cylindrical domain. The approximations are based upon continued fractions, asymptotic expansions, and multiple harmonics. The relative error for the different derived approximations is presented for different values of frequency, transport coefficients, and dimensionless radius. Moreover, it is shown how combinations of different explicit formulas can yield good approximations over a wide parameter space for different cases, such as no convection and damping, only damping, and both convection and damping. This paper is the second part (Part II) of a series of three papers. In Part I, the semi-infinite slab approximations have been treated. In Part III, cylindrical approximations are treated for heat waves traveling towards the center of the plasma.
|Alternate Title||Phys. Plasmas|
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