Probabilistic transport model for transitions to improved confinement regimes in fusion plasmas

SEBASTIÁN BOUZAT; RICARDO FARENGO

University of York. York. Inglaterra.

Workshop; 3rd IAEA Technical Meeting on Theory of Plasma Instabilities; 2007

IAEA y University of York

Nota: El trabajo de siete páginas, cuyo archivo se adjunta tal como apareció publicado, no incluye resumen. El siguiente resumen -largo y con referencias- aparece en el libro de resúmenes del congreso y, por separado, en el CD.///// In recent years, several one dimensional models based on concepts such as self organized criticality, superdiffusivity, and continuous time random walk, have been developed to study anomalous phenomena observed in fusion plasmas. Recently, the probabilistic transport model introduced in [1] was shown to provide a consistent description of transitions to improved confinement regimes when appropriate particle step probability distributions are considered [2]. In this contribution we summarize and extend the results in [2] by providing additional information on the spatial structure of the density profiles, and its relation to the enhancement of fluctuations and confinement time observed when the source intensity is increased. We also analyze the use of different functional forms for the psd. The model is formulated in terms of a generalized master equation for a field n(x,t) representing the particle or energy density of the plasma: Here, x represents a Cartesian coordinate along a minor diameter of a toroidal reactor, S(x) the distribution of the fuelling, and tD the waiting time for the particles jumps. The function P is the psd. In the present proposal P includes two critical mechanisms, acting respectively on the first and second spatial derivatives of the density. These mechanisms allow switching between three different transport channels: one, corresponding to classical diffusion and the other two to different faster transport mechanisms (possibly scale free). The dependence of the transport properties on the second derivative models the appearance of a sheared radial electric field that causes a reduction of transport. The results of the model reproduce the enhancement of confinement time and the appearance of fluctuations (associated to edge localized modes) that take place during transitions, when the fuelling rate is increased. The main conclusions refer to the relevance of introducing the dependence of the psd on the second spatial derivative of n(x,t), and to results being qualitatively independent of the particular functional forms considered for the psd on the three different transport channels. [1] B.Ph. van Milligen, R. Sánchez. and B.A. Carreras, Phys. of Plasma 11 2272 (2004). [2] S. Bouzat and R. Farengo, Phys. Rev. Lett. 97 205008 (2006).