1. Introduction to Plasma-Surface Interactions Lecture 6 Divertors

2. Divertor functions 1. Removes plasma surface interactions from the confined plasma: hence reduces the impurity flux back into the plasma 2. Removes deposited power to a region where it is easier to remove using a heat transfer fluid 3. Reduces the flux of fast CX neutrals to the main chamber walls by reducing the flux of neutrals which can reach the main plasma 4. Impurities ionized in the SOL will flow into the divertor 5. Pumps helium. The divertor maintains a higher neutral pressure than the SOL and therefore it is easier to pump the helium out. (Important in DT burning devices)

3. Potted history of divertors A form of divertor was part of the early stellerators designed by Spitzer in the 1950’s Much later, divertors were designed for tokamaks, DIVA (1974), DITE (1976), T12, PDX and ASDEX Early divertors used a separate chamber but in D- III it was discovered that they worked well with the target in the same chamber ASDEX discovered the H-mode during divertor operation

4. Typical poloidal divertor Poloidal cross-section of tokamak with typical field lines. The poloidal fields are used to produce a null which causes the field lines to diverge and flow out into a separate chamber remote from the confined plasma The null is known as the X-point

5. Simple analytical modelling of the divertor Consider only region between X-point and the target Energy flow comes across the LCFS from the confined plasma Assume a 1-dimensional model no energy or momentum sinks in SOL specifically, no radiation

6. Geometry of the 1-D 2-point fluid model Poloidal cross-section Geometry along the field line Upstream density and temp n u and T u are assumed to be at the X- point. Downstream density and temp n t and T t are at the target

7. Modelling the divertor - 1 Model using the following assumptions Momentum conservation along the field line requires constant Heat transfer along field line is by conduction where Heat transmitted across the sheath is given by Where is the sheath transmission factor and c s is the ion sound speed Taking q II to be known we can solve the 3 equations for T t. T u and n t in terms of n u

8. Modelling the divertor - 2 The solutions are messy but when we have a sufficiently high temperature gradient so that T u 7/2 >> T t 7/2 then we can obtain the simple forms m -3 And keV Note the n u 3 and n u -2 dependence of target density and temperature respectively

9. Target temperature and density vs upstream density q II =1000MW m - 2 L=50m A=2 Note the n u 3 dependence of n t And the n u -2 dependence of T t At low n u target density n t is linear with n u Calculated with the simple analytical 1-D model described

10. High density limit When T u 7/2 >> T t 7/2 the ratio of the upstream to down stream temperatures can be calculated From which it can be noted that a large temperature gradient requires low power, a long connection length or a high density

11. Effect of recycling at the target Assumed plasma source function due to recycling T i = T e nene Mach number Plasma due to recycling enhances the flow back to the target At high densities when flow across the separatrix is small this is the dominant source Ionization and density peak near the target plate and T falls Flow accelerates near the target due to the source

12. Radial power distribution in the SOL Divergence of heat flux must be zero Where qs are heat flux vectors. From this an expression for the parallel heat flux at the target and the power scrape off thickness can be derived For q II =0.5 MWm -2, L=150m,  =1 m 2 s -1 and n u =1x10 m -3 we obtain p =0.01 m and q II =7 GW m -2

13. Dispersal of divertor power The SOL is very thin, determined by the relative rates of parallel and cross field transport Upstream widths are  p ~3 mm in present devices, C-Mod, AUG, JET - estimated to be  p ~ 100mm in ITER  leading to q u ~ 2000 MW/m 2 Divertor plates have a limit of ~ 10 MW /m 2 requiring a factor of 200 reduction Methods of reducing power flux 1.Mid-plane pitch angle (~x7) 2.Flux surface expansion (~x3) 3.Tilted divertor plate (~x3) 4.Divertor/SOL radiation requires a further factor of 3

14. Volume losses of power in the divertor by impurity radiation, simple calculation Impurity radiation can be written Where n m is the impurity concentration an R(T e ) is the radiation parameter which depends on species. Maximum values of R are ~10 31 Wm 3 Considering average values, to radiate 1GW requires n m n e V> 10 40 m -3 For V= 10 3 m 3 and n e =~10 20 m -3, the impurity fraction n m/ /n e ~10%

15. Power loss mechanisms Radiation: Such high concentrations could lead to impurities flowing back into the confined plasma. It may also cause an unacceptable sputter rate of the target Charge exchange: The ratio of charge exchange to ionization rate coefficients indicate that the temperature must be already low (<10 eV) to obtain a significant energy loss by charge exchange The answer appears to be to have radiating mantle in the main plasma. Up to 70% of the plasma power has been radiated in experimental tokamaks but it is still uncertain whether this much power can be radiated in ITER

16. Removal of helium ash Pressure is very low at the boundary of the plasma and would require an enormous pumping speed to remove it The gas pressure in the divertor has to be optimized by operating at high density and improving the baffle geometry He pressure tends to be proportional to H pressure, experimentally the enrichment factor  is Experimentally the effect of baffles tends to be small (<2 in JET and C-Mod )

17. 2D effects: schematic of particle flow in the divertor While the region near the separatrix tends to be at high density and in the recycle mode, further out it is low density with low tempoerature and little recycle

18. General design considerations Tile geometry needs to be very carefully controlled. Because of the very high parallel power density any surface not at grazing incidence will suffer serious damage. Flat plate geometry has the advantage of simplicity, good diagnostic access and a simple rigid structure can be used Because of the high powers there is significant thermal expansion and non-uniform heating To minimize stress in the tiles they are normally small ~20-30 mm The angle of the tiles wrt field lines has to be as small as possible to increase the effective area At very low angles the tile edge can become exposed. This is overcome displacing each tile wrt its neighbour

19. Example of target tile geometry With this geometry, in order to prevent tile edges being exposed, the tile accuracy has to be high (~0.1 mm)

20. Divertor analysis Divertors are very complicated and still not fully understood Although these 1-D analytical models are helpful in understanding the important parameters it is necessary to use 2-D codes These have analytical sections for the plasma fluid and Monte Carlo codes for the neutrals. The two parts have to be coupled which is complex. Examples of these B2-Eirene Braams and Reiter (Julich)and EDGE2D-Nimbus (JET)