1. Anomalous Transport Models Glenn Bateman Lehigh University Physics Department Bethlehem, PA SWIM Workshop Toward an Integrated Fusion Simulation Bloomington, Indiana 25 September 2006

2. SWIM, 25-27 September 2006 Anomalous Transport Models The most widely used anomalous transport models are –GLF23 (Gyro Landau Fluid) –MMM95 (Multi-Mode Model) –JETTO (Mixed-Bohm/gyro-Bohm) These models are available in the NTCC Module Library at http://w3.pppl.gov/NTCC Each module satisfies NTCC Module Library standards –All input/output variables passed through documented argument list –A driver program, together with the input and output of test cases, illustrate how the module works and enable the user to test the module with different compilers on different computers –A makefile is provided to build the module and test program –A README file and other supporting documentation are provided –About half of the NTCC Modules have been reviewed –These models have been widely tested in integrated simulations of tokamak experimental data

3. SWIM, 25-27 September 2006 Improvements to the NTCC Modules A graduate student at Lehigh, Chris Wolfe, made improvements to the GLF23, MMM95 and JETTO modules –These improvements leave the results essentially unchanged while fixing logical problems and parallelism –Wolfe wrote a test program for comparing module results under uniform controlled conditions. Models compared in many scans. The GLF23 interface routine (callglf2d) was rewritten –Internal computations of the gradients were removed Now, all of normalized gradients are passed through the argument list –As a result, the improved GLF23 model is now completely local to each magnetic flux surface, as it should be Transport can be evaluated one flux surface at a time or in any order This change should facilitate parallelization of the GLF23 module –Unfortunately, there are still internal common blocks in GLF23 –The changes are being reviewed by Jon Kinsey before being submitted to the NTCC Module Library

4. SWIM, 25-27 September 2006 Improvements to the NTCC Modules - 2 Wolfe fixed an error in the growth rates and frequencies returned as arrays by the MMM95 module –This error had no effect on the transport computed using MMM95 –The growth rates and frequencies were used only as a diagnostic The logic used within the JETTO (Mixed-Bohm/gyro-Bohm) module was fixed –Non-local, edge conditions are now passed as separate scalar variables, rather than being computed internally –Transport can now be computed one flux surface at a time or using flux surfaces given in any order –This change should improve parallelism The improved modules have not yet been installed in the NTCC Module Library

5. SWIM, 25-27 September 2006 New Multi-Mode Model being Developed The MMM95 Multi-Mode Model has been held fixed since 1995 because many people asked for a fixed model –The normalization of the GLF23 model was changed in 2003 During the last decade, new versions of the Multi-Mode Model have been developed and partially tested –Weiland’s group in Sweden has developed new versions of their ion drift mode model with improved dependence on beta, geometry, magnetic shear and multiple ion species –Quasi-linear models for Electron-Temperature-Gradient (ETG) mode electron thermal transport have been implemented –Drift Alfvén mode transport model based on nonlinear gyrokinetic simulations by Bruce Scott –Kinetic ballooning mode transport model replaced Lehigh graduate student, Federico Halpern, is assembling and testing a new Multi-Mode transport model

6. J. Kinsey - EU/US TTF06 The TGLF Trapped Gyro-Landau-Fluid Transport Model TGLF is the next generation GLF model – Model valid continuously from low-k ITG/TEM to high-k ETG (GLF23 contained a limited ITG/TEM spectrum w/ max k   s =0.5) – Extended validity to NCS and pedestal relevant parameters – Valid for shaped geometry via Miller equilibrium model (GLF23 is an shifted circle model) TGLF solves for the eigenvalues using a new set of 6-moment gyro-fluid equations for linear drift-wave instabilities in tokamaks using a Hermite basis function approach TGLF has been systematically tested against a database of about 1800 linear growth rates and frequencies created using the GKS gyrokinetic code (Staebler, Kinsey, Waltz, PoP 12, 102508 (2005))  Avg  (  ) = 0.11 for TGLF model  Avg  (  ) = 0.38 for 1997 GLF23 model Mixing length rule for saturation levels being finalized

7. J. Kinsey - EU/US TTF06 TGLF Mixing Length Rule With Quasilinear Weights Fit to GYRO Nonlinear Simulations Transport computed w/ fluxes of the form Quasilinear fit to be of the form where F  is a combination of growth rate and curvature drift frequency (  d0 =k y /R 0 ) Coefficients & exponents in mixing length formula found be minimizing error (w/ zero offset) between TGLF and GYRO diffusivity spectrum for 87 nonlinear simulations (1305 spectral pts) –Used same spectrum for TGLF as used for GYRO (16 modes) Fit confirms QL theory ! –c i,c e,c d about equal and c15-17 about equal (QL constraint) –c7,c8 near 4 and c5,c6 near 2 ^ ^

8. J. Kinsey - EU/US TTF06 TGLF Saturation Rule Fits the Energy and Particle Transport Spectrums from 87 Nonlinear GYRO Simulations Very Well Comparisons for: Shifted circle geometry, electrostatic, collisionless A low-k spectral cutoff is applied to each branch –Cutoff acts like a Dimits shift; constant value times (1/q) applied at all ky’s seems to suffice Best fit yields RMS errors of 19%, 21%, 35% for ion, electron, particle fluxes

9. J. Kinsey - EU/US TTF06 RMS Errors in Electron Energy Diffusivity Significantly Smaller for TGLF Model in Comparison With GLF23 Model RMS errors computed between model and GYRO for scans in shat, q, a/Lt, a/Ln, Ti/Te, ei, r/a, R/a, ,  ExB shear  x =[ ∑ i (X i GYRO -X i TGLF ) 2 / ∑ i (X i GYRO ) 2 ] 1/2 where X =  or D ii ee D #16=  E -scan, #17=  -scan, #18=  -scan, #19=A-scan, #20 = shat-scan w/ pedestal parameters

10. J. Kinsey - EU/US TTF06 TGLF Model Valid for Real Geometry & Reproduces Stabilizing Effect of Elongation Seen in GYRO Simulations TGLF compared to GYRO for STD case w/ kinetic electrons varying  and s  using Miller geometry,  =0, =0,  =0 Used same QL formula found in fitting s-  simulations Electron energy transport increases from 3.0 to 5.3  e /  GB in GYRO going from s-  to Miller geometry w/  =1.0

11. J. Kinsey - EU/US TTF06 TGLF Shows Good Agreement With GKS Growth Rates for DIII-D ITB Discharge Including Real Geometry, Collisions TGLF compared to GKS for #84736 for the case w/  =0 and =0 and for the case w/ full physics (except for parallel velocity shear) Reduction in growth rates w/ full physics due to finite  in the inner plasma and collision in the outer plasma