1. D. Tskhakaya et al. 1 (13) PSI 18, Toledo 26 - 30 July 2008 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. D. Tskhakaya et al. 2 (13) PSI 18, Toledo 26 - 30 July 2008 OUTLINE Introduction Description of the kinetic model Discussion of simulations for JET Extrapolations to ITER conclusions

3. D. Tskhakaya et al. 3 (13) PSI 18, Toledo 26 - 30 July 2008 Introduction What is the aim of parallel transport study in the SOL? What are the fluxes to the divertor? How does plasma propagate along B ? Classical model can fail. The reason: low collisionality, inelastic and short time scale processes Resulting uncertainties might be critical for next generation tokamaks Separatrix SOL Power loads to the JET divertor during the ELM

4. D. Tskhakaya et al. 4 (13) PSI 18, Toledo 26 - 30 July 2008 Kinetic factors characterizing parallel transport in the stationary SOL Introduction Heat flux and viscosity limiters Boundary conditions at the divertor sheath SOL Can we really apply these models to the SOL?

5. D. Tskhakaya et al. 5 (13) PSI 18, Toledo 26 - 30 July 2008 1.5D kinetic model of the 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 Maxwellian particle source mimicking cross field transport across separatrix SOL BIT1: 1.5D PIC/MC code

6. D. Tskhakaya et al. 6 (13) PSI 18, Toledo 26 - 30 July 2008 Stationary SOL: boundary conditions Boundary conditions versus SOL collisionality the model including el. radiation Electron VDF at the divertor sheath the model including el. radiation and plasma recycling Most boundary conditions weekly depend on the SOL parameters.  reduces by 40% with electron radiation

7. D. Tskhakaya et al. 7 (13) PSI 18, Toledo 26 - 30 July 2008 Stationary SOL: flux and viscosity limiters Ion parallel heat flux versus SOL collisionality Free streaming Maxwellian flux f(v)

8. D. Tskhakaya et al. 8 (13) PSI 18, Toledo 26 - 30 July 2008 Stationary SOL: flux and viscosity limiters Heat flux and viscosity limiters versus SOL collisionality Including el. radiation Including el. Radiation and recycling  and  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!

9. D. Tskhakaya et al. 9 (13) PSI 18, Toledo 26 - 30 July 2008 ELMy SOL Previous model [Tskhakaya et al., EPS 07, CPP 08] Main findings Power to the divertors is curried mainly by ions 0.15 < W IR /W ELM < 0.35 We constructed fit functions describing BC and power loads to the divertor during the ELMs at JET q div (t),  e,i (t) and  (t) SOL 0 ELM t S Particle source No inelastic processes, stepwise ELM source q div t  IR W IR

10. D. Tskhakaya et al. 10 (13) PSI 18, Toledo 26 - 30 July 2008 ELMy SOL at JET Model dependence of power loads to the divertor Temporal shape of the ELM source We need a reliable model for „reconnection“, or we can estimate it from measured power loads power loads to the divertor Power loads and boundary conditions strongly depend on the ELM model.

11. D. Tskhakaya et al. 11 (13) PSI 18, Toledo 26 - 30 July 2008 ELMy SOL at JET Shot 62221 at JET W ELM ~ 0.4 MJ Power flux to the outer divertor from IR measurements (shot 62221, T. Eich) and from PIC simulations (averaged over ~50 µs).

12. D. Tskhakaya et al. 12 (13) PSI 18, Toledo 26 - 30 July 2008 Extrapolations to ITER Existing semi-analytic model well describes power loads [Eich/Funamenski] Power loads to the ITER outer divertor for 4 MJ ELM

13. D. Tskhakaya et al. 13 (13) PSI 18, Toledo 26 - 30 July 2008 CONCLUSIONS Most of boundary conditions at the divertor weekly depend on (attached) plasma parameters. The exception is , 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 < W IR /W ELM < 0.35 No surprises from (simplified) ITER simulations: power loads to the divertor correspond to the energy propagation with C s and can be described by existing analytic functions main power to the divertors is curried by ions, W IR ~0.35 Inter-ELM SOL ELMy SOL

14. D. Tskhakaya et al. 14 (13) PSI 18, Toledo 26 - 30 July 2008 Energy loads to the divertors for different (ELM energy is fixed)

15. D. Tskhakaya et al. 15 (13) PSI 18, Toledo 26 - 30 July 2008 Differential CS implemented in BIT1 Choice of proper data Implementation Cross-sections for H 2 + + H 2 charge- exchange collision from different sources.