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An original method is presented to solve the linearised heat transport equation for a general class of [Chi] models, of the form Chi=Chi(0)T{mu}G([anadelta]T/T), where Chi(0) is a constant and G an arbitrary function which depends only on [anadelta]T/T. These solutions allow one to address the propagation of heat and cold pulses in a tokamak plasma. By looking for solutions of the problem as functions of [anadelta]T/T instead of the usual radial coordinates, the linearised transport equation is reformulated into a much simpler second-order differential equation. In this new form, it may be solved directly, if an analytical solution of the problem exists. The calculations are carried out both in slab and cylindrical geometry, and can be generalised to other geometries. For slab geometry, the exact solutions of the linearised transport equation are found in the case G=(|[anadelta]T|/T){alpha}. An approximate solution is given in the case with critical gradient length G=(|[anadelta]T|/T){alpha}(|[anadelta]T|/T-[kappa]) {beta}, valid for strong profile stiffness ([anadelta]T/T~[kappa]). In cylindrical geometry, the Wentzel-Kramers-Brillouin solutions are found in the case G=(|[anadelta]T|/T){alpha}. These solutions are validated by comparison with numerical simulations. Their dependence on the modulation frequency and the model parameters is investigated. Finally, a method is proposed to identify the model parameters (e.g. Chi(0), alpha and mu which best fit given temperature modulation data, as an original application of these analytical calculations to experimental transport studies.

Additional information

Authors: IMBEAUX F, Association EURATOM-CEA, CEA Cadarache, Saint-Paul-Lez-Durance (FR);GARBET X, Association EURATOM-CEA, CEA Cadarache, Saint-Paul-Lez-Durance (FR)
Bibliographic Reference: An article published in: Plasma Physics and Controlled Fusion, 44 (August 2002), pp.1425-1447
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Record Number: 200215157 / Last updated on: 2002-08-26
Original language: en
Available languages: en