Generalized curvature modified plasma dispersion functions and Dupree renormalization of toroidal ITG
Abstract
A new generalization of curvature modified plasma dispersion functions is introduced in order to express Dupree renormalized dispersion relations used in quasi-linear theory. For instance the Dupree renormalized dispersion relation for gyrokinetic, toroidal ion temperature gradient driven (ITG) modes, where the Dupree's diffusion coefficient is assumed to be a low order polynomial of the velocity, can be written entirely using generalized curvature modified plasma dispersion functions: Knm's. Using those, Dupree's formulation of renormalized quasi-linear theory is revisited for the toroidal ITG mode. The Dupree diffusion coefficient has been obtained as a function of velocity using an iteration scheme, first by assuming that the diffusion coefficient is constant at each v (i.e. applicable for slow dependence), and then substituting the resulting v dependence in the form of complex polynomial coefficients into the Knm's for verification. The algorithm generally converges rapidly after only a few iterations. Since the quasi-linear calculation relies on an assumed form for the wave-number spectrum, especially around its peak, practical usefullness of the method is to be determined in actual applications.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2017
- DOI:
- 10.48550/arXiv.1711.11498
- arXiv:
- arXiv:1711.11498
- Bibcode:
- 2017arXiv171111498G
- Keywords:
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- Physics - Plasma Physics