Abstract
A nonlinear version of the CPTM is presented in this chapter. This version can be applied to tokamak regimes with improved confinement in the presence of External and/or Internal Transport Barriers (ETB, ITB). To describe these ETB or ITB in the expressions for the fluxes as presented in Chap. 5 some multipliers are included which nonlinearly (exponentially) depend on the pressure gradients. The appearance of barriers corresponds to a bifurcation of the solution of the transport equations which is localized in space. The appearance of an ETB is described by a bifurcation parameter. The appearance of an ITB is described by a bifurcation function with radial dependence. Both the bifurcation parameter and bifurcation function are determined by comparing with experimental data. Examples are given for several tokamaks. Asymptotic expressions are derived which allow to calculate the L–H transition threshold and to estimate the pedestal temperature values. The radial dependence of the ion temperature profile stiffness and its dependence on toroidal rotation velocity are discussed.
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Dnestrovskij, Y. (2015). Nonlinear Version of the Canonical Profiles Transport Model (CPTM) for Improved Confinement Regimes. In: Self-Organization of Hot Plasmas. Springer, Cham. https://doi.org/10.1007/978-3-319-06802-2_6
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DOI: https://doi.org/10.1007/978-3-319-06802-2_6
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