Comparison of Ion Thermal Transport From GLF23 and Weiland Models Under ITER Conditions A. H. Kritz 1 Christopher M. Wolfe 1 F. Halpern 1, G. Bateman 1, A.Y. Pankin 1 A. Eriksson 2 and J. Weiland 2 1 Lehigh University Physics Department, Bethlehem, PA, USA 2 Chalmers University, Göteborg, Sweden ITPA Meeting Lausanne, Switzerland May 2007

ITPA, Lausanne, May 2007 Introduction Comparison is made between the GLF23 transport model and two versions of the Weiland transport model –These models are widely used in integrated simulations of tokamaks It is difficult to carry out this comparison using integrated modeling simulations in which parameters are interrelated Consequently, useful to use a standalone test driver in which it is possible to control parameters in scans –Systematic scans are carried out by varying a single parameter, while holding all other parameters constant –Standalone code allows complete control over input received by the model –Allows the output to be expressed in a form that facilitates comparison of models Standalone test driver used to compare transport predicted by the GLF23 Model with that predicted by two versions of the Weiland model (Weiland14 and Weiland19)

ITPA, Lausanne, May 2007 Weiland Transport Models Computes anomalous transport driven by Ion Temperature Gradient (ITG) mode and Trapped Electron Modes (TEM) –Quasi-linear transport derived from linearization of fluid equations Weiland 14 [Physics of Plasmas 5, 1793 (1998) ] –Developed at Chalmers University of Technology in 1995 –Includes physics of finite beta, magnetic shear, electron-ion collisions, impurities and fast ions –Significant element in the Multi-Mode 95 model (MMM95) Weiland 19 –Developed at Chalmers University of Technology in 2007 –In addition to Weiland 14 physics, new model includes Improved finite beta effects More accurate model for effects of magnetic shear and elongation Varying correlation lengths Improved particle pinch effects Momentum transport [J. Weiland et al., P2.186, Proceedings of the 33rd EPS Conference 2006]

ITPA, Lausanne, May 2007 GLF23 Transport Model Includes anomalous transport driven by ITG modes, Electron Temperature Gradient (ETG) modes and TEMs 10 low-wavenumber (ITG/TEM) and 10 high-wavenumber (ETG) eigenmodes solved from a linear dispersion relation to compute quasi-linear fluxes Calibrated using scans carried out with the gyrokinetic (GKS) code –Flux originally compared to gyro-fluid simulations, –New model compared to non-linear gyro-kinetic GYRO simulations Fluxes follow from linear growth rates and quasi-linear mixing-length rule Model includes physics of: –Finite beta effects; magnetic shear; electron-ion collisions; particle pinch effects; impurities; fast ions; elongation effects; rotational flow shear stabilization (not considered here); Shafranov shift stabilization; [R.E. Waltz et al., Phys. Plasmas 4, 2482 (1997)]

ITPA, Lausanne, May 2007 Low Beta Limit Behavior of Models Ion thermal diffusivity plotted as a function of normalized temperature gradient for low  = 0.46% –ITER geometry q = 2, s = 1, R/L n = 0.1 Weiland 14 in MMM95 transport model: Effects of collisions and parallel momentum turned off –Collisions and parallel momentum turned on in Weiland 14 (Complete), used in all subsequent plots GLF23 is stiffer (steeper slope) and has a higher threshold than all of the Weiland models –At low beta and moderate shear, different Weiland models are similar Predictions using different models generally agree with experiment –Parameters tend to be in the region where the models overlap (R/L T = 6)

ITPA, Lausanne, May 2007 Baseline Parameters (Typical ITER H-mode) Background parameters for scans:Dimensionless plasma parameters:

ITPA, Lausanne, May 2007 Scan over Beta  is varied while holding  * and collisionality * fixed –T  B 2, n  B 4,   B 4 Transition from ITG mode to MHD ballooning mode for s = 1 –For Weiland 19, transition occurs at  = 3.6% –For Weiland 14, transition occurs for unrealistically low  = 1.9% Weiland 19 has more correct high  physics than Weiland 14 –For GLF23 transition does not occur GLF23 and Weiland models differ significantly at low shear –Low shear, high beta important for ITBs Shear = 1.0 Shear = 0.1

ITPA, Lausanne, May 2007 Magnetic Shear GLF23 threshold increases rapidly with increasing s Weiland 19 threshold increases with increasing s Weiland 14 threshold not sensitive to increase in s Shear = 0.1 Shear = 2.0 Shear = 1.0 Shear = 2.0

ITPA, Lausanne, May 2007 Scans over Magnetic Shear Low  limit shown in top panel and baseline ITER parameters in bottom panel –Results shown for R/L T = 6.0 Drift mode transport generally decreases at large shear Weiland 14 model has symmetric |s| dependence –GLF23 and Weiland 19 models have more complex behavior that is not a symmetric function of s  = 0.46%  = 1.8%

ITPA, Lausanne, May 2007 Scan over Collisionality Collisionality * is varied while holding  * and  fixed –T  B 2, n constant, *  B -4 Low  in top panel –Weiland models close while GLF23 is higher ITER baseline  results are shown in bottom panel –Note, * = 0.02 for ITER baseline  = 0.46%  = 1.8%

ITPA, Lausanne, May 2007 Summary of Results Magnetic Safety Factor (q) –As safety factor is increased: Threshold decreases for GLF23 and Weiland 14 Weiland 19 threshold increases Stiffness increases for Weiland 14, decreases for Weiland 19 –GLF23 stiffness is not affected by q Magnetic Shear (s) –As shear is increased: GLF23 and Weiland 19 threshold increases Weiland 14 threshold decreases GLF23 stiffness decreases –Weiland 14 and Weiland 19 stiffness near threshold is independent of shear –Weiland 19 is not symmetric with respect to magnetic shear Collisionality ( * ) –Increase in collisionality moderately reduces transport

ITPA, Lausanne, May 2007 Summary of Results Plasma Beta (β) –As beta increases: Weiland 14 threshold decreases, Weiland 19 threshold increases Weiland 14 and GLF stiffness increases –GLF23 threshold is not affected by changes in  –Weiland 19 stiffness near threshold is not affected by changes in  Normalized Ion Gyroradius (ρ * ) –GLF23, Weiland 14, and Weiland 19 models all follow gyro-Bohm scaling All three models are relatively independent of elongation (for baseline parameters) Inverse Aspect Ratio –Threshold decreases with increasing r/R; Stiffness is unaffected Temperature Ratio –Transport decrease with increasing T i /T e > 1 for all the models

ITPA, Lausanne, May 2007 GLF23 Wrapper Problem arose with the old GLF23 wrapper (callglf2d.f) packaged with GLF23 in the NTCC Module Library –Wrapper is the interface between the test driver and core GLF23 transport model Old wrapper required a radial profile of at least 3 points, in order to calculate normalized gradients internally This non-locality is not desirable, as we wish to carry out scans over a single variable, holding all others constant –Systematic scans are more cumbersome with a profile-based wrapper New wrapper was written to compute transport coefficients using plasma variables that are local to each flux surface Computation of flow shear rate was implemented in a separate module to be called before GLF23 as needed –Flow shear rate depends on second derivative with respect to radius, which is a non-local computation

ITPA, Lausanne, May 2007 Standalone Test Driver Written to compare two models side by side using the same data Written in Fortran 95 Takes in standardized input in the form of both scalar switches and array variables Outputs data in selected form for plots as specified in input file Gradients can be calculated internally or specified in the input file Imposes charge neutrality by calculating hydrogen/impurity ion densities and their gradients internally, given electron density, electron density gradient, Z eff, fast ion density and its gradient Designed with an intentional generality, so other models can be added besides the two Weiland models and GLF23 –Mixed-Bohm / gyro-Bohm model, for example, has been implemented