Numerical computation of the modified plasma dispersion function with curvature

A particular generalization of the plasma dispersion function, which is linked to the regular plasma dispersion function via recurrence relations is discussed. The generalization allows a fast numerical implementation of a certain two-dimensional integral that appears in the description of the plasma dispersion in curved geometry, by reducing it to a single integral over a function involving the generalized plasma dispersion function. The local dielectric function of the toroidal ion temperature gradient driven mode can be written in terms of these integral functions. A matrix method is proposed to combine the consecutive integrals as a single 1D integral over a single integrand. The method allows two orders of magnitude speed up over the 2D integral implementation. Using various optimizations and an efficient implementation of the regular plasma dispersion function, further speed up is obtained.