Multiple species extensions to the Weiland model and the Semi-predictive DEA code

1. 9th Meeting of the ITPA Confinement Database & Modeling Topical Group, 3-6 October, 2005, St. Petersburg, Multiple species extensions to the Weiland model and the Semi-predictive DEA code P.I. Strand, With contributions/support from W.A. Houlberg (ORNL), H. Nordman (CTH), A. Eriksson (CTH), J. Weiland(CTH), G. Bateman(Lehigh), A. Kritz (Lehigh)

2. Multiple Ion Species Drift Wave Transport Straightforward extension of the Weiland drift wave model for ITG/TEM (Extended Drift Wave Model or ExtendeDWeiland Model): • Arbitrary number of Ion Species • Each charge state treated as a single fluid species • Separate descriptions of H, D and T transport • Differs only through mass dependence in (first order) FLR term and k// dynamics • FLR stabilisation gives different peak locations for growth rates in kqrsH. • Transport is summed over extended kqrsH range to cover maximum growth rate for each hydrogenic species • Modular, self-contained code distribution • Strict adherence to F95 standard • Strongly typed through automatic module features • Parametric kinds (all system supported precisions ) • Data encapsulation with no global dependencies • Fully compatible with and tested against original disp9t description (Weiland) • Weak Ballooning problematic in multiple species setting Model can be used in different settings and allows for physical effects to be turned on/off to study impact on transport/stability. • Two versions used here: • Simple Baseline model (Electrostatic, no • k// effects, strong ballooning • Full physics (incl, collisions and • electromagnetic effects,…)

3. Density Evolution Assessor – DEA* *DEA – Latin for ‘Goddess’ A semi-predictive particle transport code • Evolves arbitrary number of ion species assuming fixed temperatures. • Linked to the international profile database (Using MDSplus server). • Targeted “read” from WDB being implemented. • Flexible geometry acces: • Eqdsk files (EFIT, CHEASE, etc…) • Inverse coordinate solvers (VMEC output) • Simple 3-moment approximation available • NCLASS for comprehensive neoclassical transport description. • EDWM for anomalous transport (ITG/TE) • Currently only prescribed source terms fully available • Modular structure, simple adaptive grid method(s) • Planned extensions (Summer and fall 05) • Source terms (neutrals,…) • Frantic (implementation being tested), PELLET (ORNL code) being processed • Improved access for experimental data • Input system is being changed to a more flexible/adaptable system • Transport models (GLF23, …., ?) link to JET/ITM-TF Code integration effort • Explicit thermo-diffusion coupling (longer term) AJAX

4. Effects of impurities on drift wave based D and T particle transportExample studies with EDWM

5. Comparison of anom. D and T fluxes R/LTi = R/LTe = 3.75, Te/Ti = 1, (all species), R/LnC = 2, ft =0.4, fC = 0.01 R/Lne ambipolar Slight asymmetry in fluxes enters through first order FLR effects in the baseline version of Weilands fluid model. ITG driven mode only is excited for these parameters.

6. Tritium gradient scans Impurity content (clockwise 1%, 3% and 5%) R/LT = 3.75, all species R/Ln = 2, Te/Ti = 1, ft = 0.4 R/Lne by ambipolarity Tendency to equilibrate the density scale-lengths between species remain

7. Impact of an impurity species A • DT particle transport is reduced through stabilising carbon dilution. • However • Less peaked or inverted Carbon profiles tend to enhance both D and T transport • Impurity Driven ITG mode does not alter but rather increase these effects. A B B 1 2

8. Comparison of DW particle transport with neoclassical estimates DIII-D like base case derived from Neon seeded shot #98775

9. Trace impurity scans for Ne, Ar and W r/a = 0.52 r/a = 0.7 Strong Z- dependence of the neoclassical flux as expected, shift of W pinch may be explained through detailed balance of the thermodiffusion terms. Weak and inverted Z-dependence of anomalous transport as expected but comparatively weak D contrib.

10. Full response to non trace species Full response when a non-trace species is perturbed is much more complex and would require more careful analysis. We note that D has a outward flux for hollow profile leading to an even stronger depletion and that it provides a pinch flow for already peaked profile whereas Ne has the opposite trend. (Nominal values R/LnD = 1.12 and R/LnNe (2.07))

11. Simple predictive example case JET 37718 @ 53.8s NB fuelled ELMy H-mode Taken from the PR98 International Profile Tokamak Initial condition for simulation shown: Beam particle contribution turned off Flat Te profile => reduced TEM drive no anomalous inner core pinch.

12. Interpretative analysis: 37718 Deuterium transport in high coll. JET Anomalous contribution: ITG mode and TE modes excited at r =0.25 • ITG modes drives an outward • flux in inner core region • TE mode dominate transport in • outer core defining a net pinch. Neoclassical contributions • Ware pinch provides an inner • core pinch contribution • Pinch not fully balanced by • diffusive term • Other off-diagonal contributions • are weaker except closer to edge

13. Time evolution: Peaking of nD Only Wall source available Beam sources artificially turned off The strong TEM driven pinch weaken as density peaks up. At 53.9s pinch has vanished and A weak outward flux persist for remainder of simulation Neoclassical transport dominated by Ware pinch => peaking of nD(0). Axial peaking off-set by kinetic Ballooning mode as density increases. Density profile determined by Balance between different neoclassical and anomalous terms.

14. Summary Two new code developments • EDWM (Extended Drift Wave Model) • Closely linked to Weiland’s disp9t model • Arbitrary number of ion species • Extended wave-length spectra • Separate description for H, D and T, etc • Modular, Self-contained F95 coding • DEA (Density Evolution Assessor) • Semi-predictive transport code for core particle transport • First test implementation with adaptive grids • NCLASS/EDWM models • MDSplus link to ITPA databases • Flexible geometry data access and processing • Eqdsks (EFIT, CHEASE,…) • Inverse equilibrium solvers (VMEC) • Uses AJAX interface for moment solutions. • Intended to fill gap between interpretative analysis and fully pred. codes Users welcome! Complimentary exploration tool To large scale transport codes

15. Summary Initial results Effect of impurities on D and T transport in core plasmas • Deuterium and tritium transport coefficients may separate when their corresponding scale lengths differ for ITG dominated transport. • Asymmetry in D and T fluxes due to (first order) FLR effects. • The presence of impurities does not appear to affect previous results to any larger extent • Less peaked or inverted impurity (Carbon) profiles tend to increase both T and D transport • D and T particle transport is reduced through stabilising (Carbon) dilution • Impurity driven ITG modes does not alter but rather enhance the trends Comparison with neoclassical fluxes • Dynamic coupling of Neoclassical and anomalous effects may be needed to explain density peaking at least for high collisionality. • Trace impurity analysis shows anomalous and neoclassical particle flows of similar magnitude • Profile effects enters in both components Neoclassical elements (thermo-diffusion and off-diagonal elements) depends sensitively on gradient scalelengths of different species changing sign and magnitude of effective pinch flow relative to Ware pinch. • Small changes in ITG/TEM drive terms may drastically change anomalous estimates • Non-trace analysis is much more complex but may still have anomalous and neoclassical pinch velocities of similar magnitude. Diffusivities however dominated by anomalous contributions

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17. References Physics background: J. Weiland, IoP Publ., Bristol, 2000, "Collectives Modes in Inhomogeneous Plasma”, and references therein Numerical Techniques: G. Bateman, J. Weiland, H. Nordman, J. Kinsey. C. Singer, Phys. Scripta, 51, (1995) Implementation: P. Strand, H. Nordman, J. Weiland, J.P. Christiansen, Nucl. Fusion, 38 (1998) NCLASS: W.A.Houlberg et al., Phys. Plasmas 4 (1997), 3230 IPD databases: "The International Multi-Tokamak Profile Database", Nucl. Fus 40 (2000), 1955 And ITER Physics Basis, Chapter 2, Nucl. Fus, 39 (1999), 2175

18. Sensitivity to background gradients 0.75 * Grad Ti 1.25* grad Ti Effect of changing the background temperature gradients: Major change in anomalous transport as expected. Higher Z neoclassical estimates more strongly affected than lower Z. Results of analysis method strongly dependent on resolution of background profiles and their gradients..

19. Perturbative trace transport analysis • Particle transport is generally described trough a diffusivity D and a pinch velocity V. • To avoid using a full transport matrix off-diagonal terms are lumped into the pinch term. • D and V cannot simultaneously be determined through steady state analysis. • Perturbative, timedependent analysis needed where: • A Background close to SS • High resolution diagnostics • Assumption of time constant transport coeffs during analysis • are all needed.