Generalized curvature modified plasma dispersion functions and Dupree renormalization of toroidal ITG

Gultekin O., Gurcan O. D.

PLASMA PHYSICS AND CONTROLLED FUSION, vol.62, no.2, 2020 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 62 Issue: 2
  • Publication Date: 2020
  • Doi Number: 10.1088/1361-6587/ab56a7


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: K-nm'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 K-nm'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 usefulness of the method is to be determined in actual applications. A parameter scan of eta(i) shows that the form of the diffusion coefficient is better represented by the polynomial form as eta(i) is increased.