Development of a synthetic diagnostic for the non-linear MHD-code JOREK

1. Development of a synthetic diagnostic for the non-linear MHD-code JOREK R. Wenninger, H. Zohm and the ASDEX Upgrade Team Max-Planck-Institut für Plasmaphysik, EURATOM Association, Boltzmannstr. 2, 85748 Garching, Germany Many thanks to G. Huysmans, V. Igochine, S. Günter, W. C. Müller, M. Maraschek, O. Maj PhD Network – Advanced Course, Garching 05.10.2009

2. Objective Comparison Topic: Plasma edge phenomena (e.g. ELMs) Theory (JOREK) Experiment (AUG) Method: Synthetic Diagnostic R. Wenninger

3. Outline • Motivation: Edge Localised Modes • JOREK: A non-linear MHD Code • Synthetic diagnostics • Example: Synthetic Magnetics • Further diagnostics considered to synthesis R. Wenninger

4. Motivation: Edge Localised Modes I • “Edge Localised Modes” (ELMs): Cyclic MHD instabilities destabilised by pressure gradient in the H-mode edge pedestal • Losses of up to 10% plasma energy in several 100 s • One of the main concerns for operation of ITER and later devices • Control technology is essential  physics understanding required R. Wenninger

5. Motivation: Edge Localised Modes II Peeling-Ballooning model: • Evaluates linear ideal MHD stability boundary • Type I ELMs: Intermediate-n MHD boundary agrees with experiment at ELM-onset for various machines • Other scenarios (Type III, RMP ELM mitigated,…) operate below this boundary • Comments: • ELM crash is non-linear [Wilson 04]  Special code needed to account for this • Modelling of edge current? Snyder [NF 2009] R. Wenninger

6. Motivation: Edge Localised Modes III • Still considerable lack of basic understanding towards the ELM crash mechanism Some open questions: • What is the mechanism for the detachment of the filaments associated with ELMs? • What is the mechanism for the ELM energy loss? • Is current ejected during an ELM: what mechanism, and how fast? • What determines the size (energy / particle losses) of an ELM? • What are the mechanisms for ELM suppression (QH, RMP) and active/passive mitigation (RMP, Pellets, Vert. Kicks) R. Wenninger

7. JOREK: Code features I • JOREK has been developed with the specific aim to simulate ELMs by G. Huysmans (CEA) • It evolves MHD equations non-linearly • Reduced MHD  5 instead 8 evolved variables: • Density • Temperature • Electric potential (perp. Velocity) • Parallel velocity • Poloidal flux • Resistivity, viscosity and particle and temperature sources implemented • Time stepping fully implicit R. Wenninger

8. JOREK: Code features II • Geometric features: • X-point geometry: Closed and open field lines are included • Generalised finite elements in 3D (flux aligned) • Boundary of domain in the SOL (initially a flux surface) – treated as an ideal wall R. Wenninger

9. JOREK: Qualitative agreement with experimental results I • Edge density and temperature perturbations periodic in poloidal and toroidal direction > • Detaching of density-filament-like structures observed  Density Temperature Seen with fast visible cameras [Kirk 2006] R. Wenninger

10. JOREK: Qualitative agreement with experimental results II Good agreement of profile evolution • measured by Thompson Scattering • modeled by JOREK (midplane profiles): Density: Shows a minimum + erodes Temperature: Stays monotonic but erodes EXP.: MAST THEO.: JOREK 480A 700 A 1170 A R. Wenninger

11. Comparison Recon- struction Code Theo. Plasma Quantities Exp. Plasma Quantities Measured Signal Comparison Synthetic Diagnostic Code Theo. Plasma Quantities Synthetic Signal Measured Signal Synthetic diagnostics: Introduction A synthetic diagnostics models to a reasonable precision, what a corresponding real diagnostics would measure, if the plasma would be in the state as described by a modelling code. • Standard approach for Theory-Exp.-Comparison: • Approach with synthetic diagnostic: R. Wenninger

12. Comparison Recon- struction Code Theo. Plasma Quantities Exp. Plasma Quantities Measured Signal Comparison Synthetic Diagnostic Code Theo. Plasma Quantities Synthetic Signal Measured Signal Advantages of a synthetic diagnostics • For many measurements it is not possible to reconstruct associated local plasma quantities (e.g. magnetics) • Various diagnostics signals are functions of more than one plasma quantity • In general: Description in plasma quantities by codes is often higher dimensional than description in measurements  Synthetic diagnostic in contrary to calibration relation tends to be an injective transformation more often R. Wenninger

13. Synthetic Magnetics: Introduction • Objective • Simulate Bpol in the part of the AUG vessel containing the pickup coils for every time step • Extract from that synthetic signals for the real AUG coils • Guide lines • JOREK can only provide information on toroidal currents • Reduced MHD model currently does not account for plasma rotation, which significantly impacts coil signals  Add rotation (In first step non-differential) R. Wenninger

14. Synthetic Magnetics: Adjust JOREK to AUG • JOREK Boundary JOREK: • Boundary condition: =const. • AUG: Conducting structures • Vessel wall AUG and attached components • Passive Stabilization Loop (PSL) • All can be regarded as ideal conducting • Special treatment for PSL? JOREK AUG PSL R. Wenninger

15. Synthetic Magn.: Effects of conducting structures • Changing magnetic Field  Induced Voltage  Induced Current in conducting structures • Artificial distinction between effects of these currents in conducting structures: • T1: Induce eddy currents  B,IND=B,ORG • T2: Currents induced in macroscopic loops (e.g. PSL). (Can an ELM related current perturbation induce a significant macroscopic current?) • Dealing with T1: • Set =0 on AUG B=1/R(t)=0 • Additional dealing with T2: • INH (j  0, PSL = 0): Contribution from the plasma currents. PSL is modelled as an ideal conductor free of macroscopic currents. • HOM (j = 0, PSL = 1): Flux component from a macroscopic PSL current only. • The final solution:  = C HOM + INH R. Wenninger

16. Synthetic Magnetics: Obtaining  on AUG Solution 1: Disadvantage: The partial differential equation is solved on an area, which is much larger than the one we are interested in.  Efficiency can be improved • Solve on AUG • Get j from JOREK R. Wenninger

17. Synthetic Magnetics: Obtaining  on AUG\ JOREK Solution 2: • Extend JOREK Solution: • The solution on JOREK and further out is corresponding to a virtual ideal wall at JOREK  How can we get rid of it? • Decompose solution: JOREK JE Situation without plasma current but virtual ideal wall  Surface current on JOREK Situation with plasma current but without virtual ideal wall JE,I JE,H R. Wenninger

18. Synthetic Magnetics: Obtaining  on AUG\ JOREK • Calculate JE,H: Homogeneous PDE: Derivative at JOREK: Values at AUG:  Well posed problem • Calculate JE = c - JE,H R. Wenninger

19. Further diagnostics considered to synthesis • General Criteria: • Diagnostics for quantities calculated by JOREK • Measured in high temporal and spatial resolution in optimum dimensionality • Some candidates: • Electron Cyclotron Emission: • Now at AUG in 2D • Generic tool to synthesis any kind of line integrated diagnostics (e.g. Interferometry, Spectroscopy) • Thompson Scattering • Langmuir probe • … R. Wenninger

20. Summary • Gaining further understanding in Edge Localised Modes is vital for the development of tokamaks • JOREK is a non-linear MHD code that reproduces a number of ELM-features experimentally observed • A synthetic diagnostic offers a basis for an advanced theory-experiment-comparison • An accurate and efficient approach to synthesis magnetic signals for AUG has been developed R. Wenninger

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22. Poloidal flux Parallel momentum Poloidal momentum Temperature Density JOREK: Equations Formulation using electric and magnetic potentials:  Reduction from 8 to 5 variables R. Wenninger