Kinetic simulations of the parallel transport in the JET Scrape-off Layer

1. Kinetic simulations of the parallel transport in the JET Scrape-off Layer D. Tskhakaya, R. A. Pitts, W. Fundamenski, T.Eich, S.kuhn and JET EFDA Contributors

2. OUTLINE Introduction Description of the kinetic model Discussion of simulations for JET Extrapolations to ITER conclusions

3. Introduction What is the aim of parallel transport study in the SOL? Separatrix SOL How does plasma propagate along B? What are the fluxes to the divertor? Classical model can fail. The reason: low collisionality, inelastic and short time scale processes Resulting uncertainties might be critical for next generation tokamaks Power loads to the JET divertor during the ELM

4. Introduction Kinetic factors characterizing parallel transport in the stationary SOL Boundary conditions at the divertor sheath Heat flux and viscosity limiters SOL Can we really apply these models to the SOL?

5. 1.5D kinetic model of the SOL BIT1: 1.5D PIC/MC code Maxwellian particle source mimicking cross field transport across separatrix SOL • Full resolution of particle motion, 1d3V plasma particles, 2d3V neutrals • Electric field is calculated self-consistently, magnetic field is fixed • Nonlinear collision model for arbitrary number of plasma and neutral particle species • Plasma recycling (nonlinear model). New • Electron radiation (linear model with fixed impurity profiles). New • Arbitrary diagnostics

6. Stationary SOL: boundary conditions the model including el. radiation 6 g e 5 g 4 i 3 j 2 1 n 0 1 2 10 10 10 Most boundary conditions weekly depend on the SOL parameters. jreduces by 40% with electron radiation the model including el. radiation and plasma recycling Boundary conditions versus SOL collisionality Electron VDF at the divertor sheath

7. Stationary SOL: flux and viscosity limiters f(v) Free streaming Maxwellian flux Ion parallel heat flux versus SOL collisionality

8. Stationary SOL: flux and viscosity limiters Including el. Radiation and recycling Including el. radiation a and b are strongly nonuniform, have “wrong” dependence on SOL collisionality and are too sensitive to inelastic processes! The solution for relatively high collisional SOL: no limiting at all! Heat flux and viscosity limiters versus SOL collisionality

9. ELMy SOL qdiv ELM tIR t SOL Previous model[Tskhakaya et al., EPS 07, CPP 08] No inelastic processes, stepwise ELM source S Particle source t 0 • Main findings • Power to the divertors is curried mainly by ions • 0.15 < WIR/WELM < 0.35 • We constructed fit functions describing BC and power loads to the divertor during the ELMs at JET • qdiv(t),ge,i(t) and j(t) WIR

10. ELMy SOL at JET Model dependence of power loads to the divertor Temporal shape of the ELM source Power loads and boundary conditions strongly depend on the ELM model. power loads to the divertor We need a reliable model for „reconnection“, or we can estimate it from measured power loads

11. ELMy SOL at JET Power flux to the outer divertor from IR measurements (shot 62221, T. Eich) and from PIC simulations (averaged over ~50 µs). Shot 62221 at JET WELM~ 0.4 MJ

12. Extrapolations to ITER Power loads to the ITER outer divertor for 4 MJ ELM Existing semi-analytic model well describes power loads [Eich/Funamenski]

13. CONCLUSIONS Most of boundary conditions at the divertor weekly depend on (attached) plasma parameters. The exception is j, reducing by ~ 40% with electron radiation. Heat flux and ion viscosity limiters are strongly nonuniform along the field lines and too sensitive to plasma conditions in the SOL All kinetic factors strongly depend on the choice of ELM model. Best agreement with the experiment at JET gives the complete PIC model with stepwise ELM “reconnection” Two parameters are model-independent: ions curry main part of power to the divertors and 0.15 < WIR/WELM < 0.35 No surprises from (simplified) ITER simulations: power loads to the divertor correspond to the energy propagation with Cs and can be described by existing analytic functions main power to the divertors is curried by ions, WIR~0.35 Inter-ELM SOL ELMy SOL

14. Energy loads to the divertors for different (ELM energy is fixed)

15. Choice of proper data Cross-sections for H2+ + H2 charge-exchange collision from different sources. Implementation Differential CS implemented in BIT1