1. PIC simulations of the propagation of type-1 ELM-produced energetic particles on the SOL of JET D. Tskhakaya 1, *, A. Loarte 2, S. Kuhn 1, and W. Fundamenski 3 1 Plasma and Energy Physics Group, Association Euratom – ÖAW, Department of Theoretical Physics, University of Innsbruck, Innsbruck, Austria 2 EFDA, Close Support Unit Garching, Max-Planck-Institut fuer Plasmaphysik, D-85748 Garching bei Muenchen, Germany 3 UKAEA Fusion, Association Euratom-UKAEA, Culham Science Center, Abingdon, United Kingdom *Permanent address: Institute of Physics, Georgian Academy of Sciences, Tbilisi, Georgia

2. Outline of the Talk Introduction Characteristics of the codes EDGE2D-NIMBUS and BIT1 Results of test simulations Results of ELM-free and ELMy SOL simulations Conclusions D. Tskhakaya et. al., 9 th EU-US Transport Task Force Workshop Córdoba, Spain, (2002)

3. Introduction Investigation of the energy and particle transport inside the SOL during ELM activity is an extremely important topic, especially for predicting the heat loads on the divertor plates of next-generation fusion devices [Loarte et al., 2000, 2001]. The short time scale of the process and the low collisionality of the ELM-produced highly energetic particles define the kinetic nature of ELMy transport. Despite its importance, kinetic simulations of the ELMy SOL are rare. Simulations done up to now use either simplified linear profiles for neutrals [Tskhakaya, et al., 2001], or do not consider them at all [Bergmann, 2002]. Hence, they correspond to very simplified SOL models with low recycling.

4. 2 D Modelling of the Plasma Edge of Fusion Devices (EDGE2D, B2-Eirene) The plasma edge is modelled with 2-D Fluid (plasma) + 2-D Monte Carlo Codes (neutrals) 2-D Fluid equations A : Density, Momentum and Energy (e-, D+, Z+). Particle, momentum, energy of the neutrals computed with Monte Carlo Codes (Nimbus, Eirene) Fluid + Monte Carlo are iterated to convergence

5. Advantages of 2-D Modelling of EDGE Plasmas Realistic 2-D geometry Fully time-dependent & consistent plasma solution with sources and sinks Disadvantages of 2-D Modelling of EDGE Plasmas Fluid approximation is not fulfilled in many interesting edge plasma conditions (ELMs, hot ions in SOL, etc.)

6. ELMs are modelled by increasing  ELM, D ELM ~ (10 - 1000) x  0, D 0 during  ELM in pedestal & SOL Experiments  p@ELM ~ (1 - 2) p@between ELMs ELM simulation for ITER with B2-Eirene [Loarte, 2000] Pedestal only Pedestal + SOL

7. TeTe @ ELM Radiation Radiation @ EL

8. PIC code BIT1  The 1d3v (one space and three velocity dimensions) code BIT1 was developed on the basis of the XPDP1 code from Berkeley.  During the simulation the motion of a large number (up to some 10 6 ) of ions and electrons is followed: Nonlinear Coulomb and charged- neutral particle collisions  Coulomb collisions and charged-neutral particle collisions are modelled via a binary collision model, so that the total momentum and the energy is conserved during a collision : Choosing random pairs Colliding particles

9.  At present the code does not follow neutrals, and assumes fixed neutral density and temperature profiles.  All (relevant to the SOL) charged-neutral particle collisions between hydrogen isotopes are implemented: Elastic A + e - A + e Excitation A + e - A* + e Ionization A + e - A + + 2e Elastic A + A + - A + A + Charge-exchange A + A + - A + + A A = H, D, T Charged-neutral particle collision cross-sections

10.  Secondary electron emission is implemented in the code. Secondary electron emission due to electron impact For graphite Secondary electron emission due to ion impact [Diem, 2001]

11. Simulation geometry  During the simulation, the Maxwell-distributed electrons and ions are injected into the source region. Particles reaching the divertor plates are absorbed.  In the PIC simulation neutral density and temperature profiles are used from the corresponding fluid simulations. Fluid simulation Neutral density and temperature PIC simulation

12. Test simulations Source effect Electron heat flux profile from PIC, and corresponding Spitzer- Härm and the Spitzer-Härm + “sheath” heat fluxes. e =130. Sheath effects play an important role not only in the ELMy but also in the ELM-free SOL

13. ELM-free and ELMy SOL simulations Mismatch between fluid and kinetic (PIC) simulations  It is necessary to shorten the simulated SOL (scaling has to be conserved).  During the PIC simulation the plasma density and temperature at the source cannot be controlled directly. Input parameters are the particle source intensity and the temperature of injected particles.  Source effect: There are peaks in the density and the temperature profile.

14. the absence of sheath in the fluid simulation results in a higher plasma density at the wall than in the PIC simulation. Hence, in order to have a similar charged- neutral collisionality in the PIC simulation it is necessary to shift the neutral density (obtained from the fluid model).

15. Two sets of simulations have been made for low and high recycling SOL Low recycling ELM-free SOL High recycling ELM-free SOL

16. ELMy SOL for JET-like conditions P e EDGE = 2.5 MW, P i EDGE = 6.5 MW n sep before ELM = 0.8 10 19 m -3 (low recycling) = 1.7 10 19 m -3 (high recycling)  e,i before ELM = 0.75 m 2 /s, D before ELMe = 0.10 m 2 /s n sep ELM = 5 10 19 m -3 (low recycling) = 10 20 m -3 (high recycling) T e,i ELM = 1.5 keV (low recycling) = 0.75 keV (high recycling)  ELM /  before ELM = D ELM /D before ELM = 100  ELM = 200  s,  W ELM ~ 100 kJ

17. Low recycling case The secondary electrons (SE) do not play any significant role Potentil and electron temperature profiles in the SOL, as parameters most „sensitive“ to the SE.

19. From PIC simulation

21. High recycling case The secondary electrons (SE) do not play any significant role Potential and electron temperature profiles in the SOL, as parameters most „sensitive“ to the SE.

23. From PIC simulation

24. Sheath effects play an extremely important role in both the ELM-free and the ELMy SOL: i. The electron heat flux due to the “cut-off” effect can exceed the Spitzer-Härm heat flux even in a highly collisional regime. ii. the potential drop in the sheath affects the time scale of heat loads on the divertor plates during the ELM. The secondary electrons do not play any significant role in the ELMy SOL Conclusions

25. During ELM activity the time evolution of the heat load on the divertor plates exhibits two peaks: i. The first (small) one appears in an electron time scale after ELM set-on and corresponds to highly energetic ELM electrons arriving at the divertor. ii. The second peak corresponds to the main ELM burst propagating through the SOL with a high-energy ion speed. For more realistic modelling of the ELMy SOL it is necessary to consider the neutrals self-consistently Conclusions