Multiple species extensions to the weiland model and the semi predictive dea code
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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

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Multiple species extensions to the weiland model and the semi predictive dea code

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)

Multiple ion species drift wave transport
Multiple Ion Species Drift Wave Transport Topical Group, 3-6 October, 2005, St. Petersburg,

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,…)

Density evolution assessor dea
Density Evolution Assessor – DEA* Topical Group, 3-6 October, 2005, St. Petersburg,

*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)


Comparison of anom d and t fluxes
Comparison of anom. D and T fluxes transport

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.

Tritium gradient scans
Tritium gradient scans transport

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

Impact of an impurity species
Impact of an impurity species transport


  • 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.






Comparison of dw particle transport with neoclassical estimates

Comparison of DW particle transport with neoclassical estimates

DIII-D like base case derived from Neon seeded shot #98775

Trace impurity scans for ne ar and w
Trace impurity scans for Ne, Ar and W estimates

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.

Full response to non trace species
Full response to non trace species estimates

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))

Simple predictive example case
Simple predictive example case estimates

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.

Interpretative analysis 37718 deuterium transport in high coll jet
Interpretative analysis: 37718 estimatesDeuterium 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

Time evolution peaking of n d
Time evolution: Peaking of n estimatesD

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.

Summary estimates

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

Summary initial results
Summary Initial results estimates

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

References estimates

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

Sensitivity to background gradients
Sensitivity to background gradients estimates

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..

Perturbative trace transport analysis
Perturbative trace transport analysis estimates

  • 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.