Abstract
In this paper, a number of new approximations are introduced to estimate the perturbative diffusivity (χ), convectivity (V), and damping (τ) in cylindrical geometry. For this purpose, the harmonic components of heat waves induced by localized deposition of modulated power are used. The approximations are based on semi-infinite slab approximations of the heat equation. The main result is the approximation of χ under the influence of V and τ based on the phase of two harmonics making the estimate less sensitive to calibration errors. To understand why the slab approximations can estimate χ well in cylindrical geometry, the relationships between heat transport models in slab and cylindrical geometry are studied. In addition, the relationship between amplitude and phase with respect to their derivatives, used to estimate χ, is discussed. The results are presented in terms of the relative error for the different derived approximations for different values of frequency, transport coefficients, and dimensionless radius. The approximations show a significant region in which χ, V, and τ can be estimated well, but also regions in which the error is large. Also, it is shown that some compensation is necessary to estimate V and τ in a cylindrical geometry. On the other hand, errors resulting from the simplified assumptions are also discussed showing that estimating realistic values for V and τ based on infinite domains will be difficult in practice. This paper is the first part (Part I) of a series of three papers. In Part II and Part III, cylindrical approximations based directly on semi-infinite cylindrical domain (outward propagating heat pulses) and inward propagating heat pulses in a cylindrical domain, respectively, will be treated.
Highlights
TO PART 1This paper, Part 1 of a series of three papers, deals with semi-innite slab approximations
Part 3 will deal with approximations for inward propagating heat pulses in cylindrical geometry
In this case were almost exactly the same in terms of their error. This comparison is based on a cylindrical geometry using an innite domain boundary condition assuming
Summary
The eciency of future thermo-nuclear fusion reactors will be largely determined by the level of transport of heat and particles in the magnetically conned plasma. In this paper a large number of new approximations is derived, which estimate the diusivity, the convectivity, and the damping in regions with strong cylindrical eects. These approximations can be used in any frequency range and as such χ, V , and τ can be estimated with much more precision than for instance the method presented in [1, 14], where the limit of high frequency, resulting in noisy measurements, is necessary to determine χ rst after which V and τ can be studied. Part 3 will deal with approximations for inward propagating heat pulses in cylindrical geometry
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