1. E3D: status report and application to DIII-D
Max-Planck-Institut für Plasmaphysik, EURATOM Association
E3D: status report and application to DIII-D
A. Runov
Max-Planck Institut für Plasmaphysik, Teilinstitut Greifswald
- Motivation: DIII-D experiments with I&C-coils
Results of modelling
Code improvements
- Conclusions and future work
In collaboration with:
S.V. Kasilov (IPP NSC Kharkov, Ukraine)
R. Moyer, T. Evans, I. Joseph (DIII-D)
R. Schneider, A. Kalentyev (IPP HGW)
D. Reiter (FZ Juelich)

2. Hydrodynamic set of equations, all of this same generic type:
Max-Planck-Institut für Plasmaphysik, EURATOM Association
E3D Features
Hydrodynamic set of equations,
all of this same generic type:
Local magnetic coordinate system:
- contribution from D|| in D33 only
x1=const
x2=const x3
reference cut
- scope of a single system restricted
- metric tensor determined by field line tracing
Fluid Monte-Carlo and
Interpolated Cell Mapping
- numerical diffusion is negligible
Arbitrary magnetic configuration calculable

3. Motivation: DIII-D experiments with additional coils
Max-Planck-Institut für Plasmaphysik, EURATOM Association
Motivation: DIII-D experiments with additional coils
The C-coil (error field Correction coil) is wrapped around the outboard midplane outside the vacuum vessel (perturbs core and boundary, n=1)
The I-coil (Internal MHD mode coil) has 12 segments above and below the outboard midplane inside the vacuum vessel

5. Magnetic configurations of DIII-D
Max-Planck-Institut für Plasmaphysik, EURATOM Association
Magnetic configurations of DIII-D
Idealized (symmetric)
with additional coils (asymmetric)

6. E3D calculations for DIII-D
Max-Planck-Institut für Plasmaphysik, EURATOM Association
E3D calculations for DIII-D
Te, eV
Ti, eV

9. E3D calculations for DIII-D: divertor region
Max-Planck-Institut für Plasmaphysik, EURATOM Association
E3D calculations for DIII-D: divertor region

10. I-coil pulse quickly establishes a bifurcated power deposition profile in the divertor
C.J. Lasnier

11. Heat load on the divertor plate
Max-Planck-Institut für Plasmaphysik, EURATOM Association
Heat load on the divertor plate
Outer strike point bifurcates

12. Code Improvements: Momentum Equation
Max-Planck-Institut für Plasmaphysik, EURATOM Association
Code Improvements: Momentum Equation

13. 2D results with full fluid model
Max-Planck-Institut für Plasmaphysik, EURATOM Association
2D results with full fluid model
Te, eV
Ti, eV
n, cm-3
v, cm/s

14. 3D results with full fluid model
Max-Planck-Institut für Plasmaphysik, EURATOM Association
3D results with full fluid model
Te, eV
Ti, eV
n, cm-3
v, cm/s

15. Alternative approach: finite differences
Max-Planck-Institut für Plasmaphysik, EURATOM Association
Alternative approach: finite differences
Mesh optimization
Fieldline tracing
Magnetic field
Triangulation
Metric coefficients
Grid
Neighborhoods
Transport code
(N. McTaggart, A. Kalentyev et al)
Temperature solution
Linearization matrix

16. Max-Planck-Institut für Plasmaphysik, EURATOM Association
Conclusions
E3D is being successfully applied to ergodic configuration of DIII-D:
the behaviour of pedestal plasma can not be described with E3D physics model;
splitting of the outer strike point in divertor reproduced;
no essential redistribution of heat load between the surface elements observed
Improved theory and simulation are needed to understand the plasma response during high performance tokamak operation.
Momentum equation is being successfully implemented to E3D :
benchmark needed
Finite difference approach (A.Kalentyev):
semi-implicit scheme is tested.

17. Max-Planck-Institut für Plasmaphysik, EURATOM Association
Code E3D - Physics Model

18. Improvement: semi-implicit scheme
Max-Planck-Institut für Plasmaphysik, EURATOM Association
Improvement: semi-implicit scheme
Implicit scheme
Semi-implicit scheme