SOLF1D and parallel transport in ESEL

1. SOLF1D and parallel transport in ESEL motivation of the project- improve calculation of parallel damping terms in ESEL with investigation of parallel transport by SOLF1D code, replace analytic model valid for steady-state simple SOL and couple both codes ESEL SOLF1D

2. SOLF1D model- Braginskii equations (continuity equation for ions, momentum equation for ions, energy equation for ions and electrons) solved along magnetic field boundary conditions - sheath boundary conditions neutrals- fluid model assumptions - ambipolarity, no net current cross-field transport - source of mass and energy

3. SOLF1D transport equation ion density ion momentum electron energy ion energy electron momentum assumptions quasineutrality ambipolarity

4. Outline steady state parallel transport - parallel damping in SOLF1D and ESEL compared for steady state transient parallel transport - application of SOLF1D to fluctuations calculated in ESEL • one peak only • series of fluctuations averaging - errors associated with averaging of plasma parameters estimated for data from ESEL • calculated at outer mid-plane • will be studied also along the SOL

5. Parallel losses in steady state parallel density loss time parallel energy loss time analytic model analytic model-parallel damping terms as a function of n, Te and L|| based on subsonic advection and Spitzer-Härm diffusion and L|| = Lc conclusions - approximation for temperature ok, density model too crude - neutrals important in steady state, not simple SOL, L|| Lc

6. Simple time-dependent case cross-field sources of particles and energy in time cross-field sources of particles and energy in parallel direction

7. Simple time-dependent case steady-state solution cross-field sources plasma parameters parallel losses

8. Simple time-dependent case temporal profiles cross-field sources mid-plane values target values parallel losses

9. Simple time-dependent case parallel losses parallel loss times parallel losses conduction and convection contribution

10. Simple time-dependent case parallel transport parallel profiles plasma velocity

11. Simple time-dependent case parallel transport plasma density

12. Time-dependent case with ESEL data case 1 - cross-field sources on input (initial condition is steady state for average values of sources) plasma parameters parallel losses cross-field sources

13. Time-dependent case with ESEL data case 1 ESEL SOLF1D

14. Time-dependent case with ESEL data case 2 - density and temperature on input (cross-field source adjusted to obtain specified density and temperature)

15. Time-dependent case with ESEL data case 2 ESEL SOLF1D

16. Time-dependent case with ESEL data case 2 ESEL SOLF1D

17. Time-dependent case with ESEL data case 2 parallel losses

18. Time-dependent case with ESEL data sources of particles and energy as input case 1 - density and temperature in SOLF1D can differ from ESEL - density and temperature must be limited in some range density and electron temperature as input case 2 - density and electron temperature copy ESEL values - ion temperature not stable, probably due to coarse grid - additional loop to find sources in each iteration conclusions - energy transport dominated by diffusion, T tends to flatten fast and assumption L|| = Lc more appropriate than for n - dominant source from the mid-plane in transient case, processes at target not as relevant as in steady state next step - parametrization ?

19. Averaging data results from ESEL at 4 radial positions results - errors associated with averaging of plasma parameters calculated as

20. Averaging next steps - effect in parallel direction - compare steady-state result taking average values and time-dependent case - effect on detachment