next up previous
Next: Coordinate System for the Up: No Title Previous: No Title


This program is intended to serve as a stand-alone code for testing the GLF23 model for Ion Temperature Gradient (ITG) and Trapped Electron Mode (TEM) modes. The GLF23 model was formulated by approximating the linear growth rates of the 3D ballooning mode gyrokinetic (GKS) code whereby the transport coefficients were taken from simulations of a 3D nonlinear gyro-Landau-fluid (GLF) code [1]. The model contains magnetic shear and Shafranov shift (tex2html_wrap_inline273) stabilization in addition to tex2html_wrap_inline275 rotational shear stabilization. It is a comprehensive transport model that predicts particle, electron and ion thermal, toroidal momentum flows as well as turbulent electron-ion energy exchange.

It is a dispersion type transport model similar in construction to the fluid based Weiland ITG/TEM model where the diffusivities are found by solving the complex eigenvalue problem
for a reduced set of perturbed equations of motion. Here, tex2html_wrap_inline277 is the eigenvalue and v is the corresponding eigenvector. The current version of the model uses eight equations (nroot = 8) and is electrostatic. The user has the option to include impurity dynamics by setting nroot = 12, but this is usually a small effect at low to moderate values of tex2html_wrap_inline281. An internal eigenvalue solver (cgg) is incorporated inside the main subroutine glf2d.f utilizing a sequence of routines from the eispack package. The user has the option of using the cgg solver (default) by setting leigen = 0 or using the more modern tomsqz solver (leigen = 1). The tomsqz routine has proven to be robust but solves the generalized eigenvalue problem which makes it more computationally intensive than the cgg eispack based solver. In our experience, the cgg solver has proven reliable on a number of platforms.

The eigenvalues yield the frequency and growth rates of the modes while the eigenvectors give the phase of the perturbed variables relative to one another. A nonlinear saturation rule is used to compute the transport for a spectrum of eigenmodes with 10 wavenumbers for the ion temperature gradient (ITG) and trapped electron modes (TEM) and 10 wavenumbers for the short wavelength electron temperature gradient (ETG) modes. A mixing length formula is used to give the heat diffusivity such that
where tex2html_wrap_inline283 is the mode frequency, tex2html_wrap_inline285 is radial mode damping rate, and tex2html_wrap_inline287 with tex2html_wrap_inline289 denoting the mode growth rate in the absence of rotational shear and with tex2html_wrap_inline291 and tex2html_wrap_inline293 denoting the tex2html_wrap_inline275 and diamagnetic rotational shear rates, respectively.

next up previous
Next: Coordinate System for the Up: No Title Previous: No Title

Thu Feb 20 11:20:39 EST 2003