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)

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

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

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

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

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

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

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

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

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

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

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

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.

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

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