1. International Spherical Tori Workshop 2009, Madison, WI1 Modelling plasma scenarios for MAST-Upgrade Neutral beam requirements, sensitivity studies and stability D. Keeling R. Akers, I. Chapman, G. Cunningham, H. Meyer, S. Pinches, S. Saarelma, O. Zolotukhin and the MAST team EURATOM/UKAEA Fusion Association Culham Centre for Fusion Energy Culham Science Centre, Abingdon, Oxon, OX14 3DB, UK.

2. International Spherical Tori Workshop 2009, Madison, WI2 Outline Overview of the MAST-U project Baseline scenarios modelling methodology Scenario sensitivity studies –Example 1 - PINI position and tangency radius –Example 2 - T e /n e profiles ASTRA studies MHD stability studies

3. International Spherical Tori Workshop 2009, Madison, WI3 MAST Upgrade principal features Long pulse (  t ~ 5  R), fully non-inductive to prove current drive physics on and off-axis. High B t and off-axis NBI (5 MW) to access q(r) > 2 avoiding low n MHD  test CTF-like q(r). Cryo pumped closed divertor density control EBW (~ 1 MW) to test heating and current drive and start-up On axis co- and counter current NBI (each 2.5 MW) for q-profile control, rotation and fast particle physics Closed divertor More flux, higher TF Cryo-pumps 12.5 MW NBI

4. International Spherical Tori Workshop 2009, Madison, WI4 MAST Upgrade principal features Long pulse (  t ~ 5  R), fully non-inductive to prove current drive physics on and off-axis. High B t and off-axis NBI (5 MW) to access q(r) > 2 avoiding low n MHD  test CTF-like q(r). EBW (~ 1 MW) to test heating and current drive and start-up On axis co- and counter current NBI (each 2.5 MW) for q-profile control, rotation and fast particle physics Advanced divertor concepts can be tested  DEMO, ST Increased connection length and flux expansion reduces heat loads Expanded flux divertor Low poloidal field

5. International Spherical Tori Workshop 2009, Madison, WI5 MAST-U plasma modelling

6. International Spherical Tori Workshop 2009, Madison, WI6 Plasma scenario modelling methodology – step 1 SCENE equilibrium

7. International Spherical Tori Workshop 2009, Madison, WI7 Plasma scenario modelling methodology – step 1 The initial scenario was produced using the SCENE code to create a “CTF-like” plasma:- –Input boundary and n e, T e /T i profiles produced from analytical expressions (using e.g. elongation/triangularity values for boundary and T 0 /T ped in temperature expression) informed by appropriate MAST/NSTX experimental pulses. –Other parameters (I p, Z eff, I rod etc) prescribed. I p = 1.2MA I rod =2.2MA Z eff =1.781 T i =T e

8. International Spherical Tori Workshop 2009, Madison, WI8 Plasma scenario modelling methodology – step 2 SCENE equilibrium FIESTA equilibrium guided by SCENE

9. International Spherical Tori Workshop 2009, Madison, WI9 Plasma scenario modelling methodology – step 2 SCENE equilibrium then used to guide FIESTA modelling. Pressure profile used as input and a realistic coil set is used to attempt to match SCENE boundary and global parameters (kappa, li,  p etc) as closely as possible. SCENE FIESTA

10. International Spherical Tori Workshop 2009, Madison, WI10 Plasma scenario modelling methodology – step 3 SCENE equilibrium FIESTA equilibrium guided by SCENE TRANSP run from FIESTA eqm.

11. International Spherical Tori Workshop 2009, Madison, WI11 Plasma scenario modelling methodology – step 3 FIESTA equilibrium then used to derive inputs to TRANSP code TRANSP used to investigate Neutral Beam requirements to produce a fully relaxed simulation with global parameters matching the SCENE and FIESTA equilibria. TRANSP considered useful for NB investigation due to integrated plasma equilibrium solver and Monte-Carlo NUBEAM package. By specifying various NB layouts and tweaking input profiles to match SCENE/FIESTA global parameters, the NB requirements could be assessed. TRANSP run for a sufficient time (>5s) to reach a fully relaxed state.

12. International Spherical Tori Workshop 2009, Madison, WI12 TRANSP Neutral Beam investigation 2 double PINI boxes (1 on-axis, 2 off-axis PINIs. 1 unpopulated on- axis position) 1 on-axis counter-current PINI 4 beam system: 1×on-axis, 1×on-axis counter, 2×off-axis

13. International Spherical Tori Workshop 2009, Madison, WI13 Plasma scenario modelling methodology – step 4 SCENE equilibrium FIESTA equilibrium guided by SCENE TRANSP run from FIESTA eqm. TRANSP Scenario A TRANSP Scenario B TRANSP Scenario C TRANSP Scenario D TRANSP Scenario E TRANSP Scenario F TRANSP Scenario G Common parameters: Ip=1.2MA κ=2.5 A=1.6 li(3)=0.5 (except where stated otherwise) A1,A2 : baseline, CTF-like q profile, 2 density variants B : high fast particle content - confinement, f NI =0.9, β N =6, C1, C2 : long pulse, f NI >1, β N =6.7, reduced TF, 2 I p variants D : high β T, I p =2MA, q0~1, test fast particle β limit E : 'touch-base', high l i, low β F : high  =0.6, β limit and confinement scaling G : high thermal β T (β N up to 7), I p =2MA, n g =1, β limit testing TRANSP Scenario A TRANSP Scenario B TRANSP Scenario C TRANSP Scenario D TRANSP Scenario E TRANSP Scenario F TRANSP Scenario G Each scenario demonstrates a different aspect of CTF/ITER/DEMO physics.

14. International Spherical Tori Workshop 2009, Madison, WI14 Plasma scenario modelling methodology – step 4 TRANSP pressure and current profiles then passed back to guide further FIESTA modelling using a modified coil set (engineering design evolved since last modelling round!). New boundary passed to TRANSP model. In principle this iteration could continue but it was considered that no significant improvements to the boundary or pressure profile would result.

15. International Spherical Tori Workshop 2009, Madison, WI15 Plasma scenario modelling methodology SCENE equilibrium FIESTA equilibrium guided by SCENE TRANSP run from FIESTA eqm. TRANSP Scenario A TRANSP Scenario B TRANSP Scenario C TRANSP Scenario D TRANSP Scenario E TRANSP Scenario F TRANSP Scenario G Pressure Profile + updated coil set Sensitivity studiesTime evolution studiesStability studies

16. International Spherical Tori Workshop 2009, Madison, WI16 Sensitivity studies

17. International Spherical Tori Workshop 2009, Madison, WI17 Sensitivity studies Equilibria presented are based on carefully chosen assumptions. –Necessary to test how scenarios react to changes in these assumptions. NB layout based on engineering considerations –Necessary to test that layout chosen is sufficiently close to optimum for physics.

18. International Spherical Tori Workshop 2009, Madison, WI18 Sensitivity studies Ex 1 – T e /n e profile peaking T e /n e profiles are assumed to be achievable based on observation of MAST/NSTX plasmas. In practice there is a risk of the profiles being more peaked. What is the effect on the baseline scenarios? Simple peaking algorithm applied to n e profile, scaling applied to keep line average n e constant and T e adjusted to maintain H 98 ~1. Simple peaking algorithm applied, T e scaled to maintain H 98 ~1.

19. International Spherical Tori Workshop 2009, Madison, WI19 Sensitivity studies Ex 1 – n e profile peaking Scenario Parameter Sc Awith very peaked density IPIP 1.2MA B0B0 0.78T n e (0)/ 1.131.78 H 98 1.030.92 q 0 q min q 95 2.32 2.12 8.71 2.23 1.74 8.35  95 0.370.33  95 2.48 tt 11% pp 1.481.66  N thermal 3.162.90 f bs 0.290.31 f NBCD 0.150.21 Some risk to scenario as q min drops below 2 but is still above 3/2 Non-inductive current drive increases q-profile with flat and peaked density profiles

20. International Spherical Tori Workshop 2009, Madison, WI20 Sensitivity studies Ex 1 – T e profile peaking Scenario Parameter Sc A With very peaked temperature IPIP 1.2MA B0B0 0.78T T e (0)/ 1.532.88 H 98 1.031.00 q 0 q min q 95 2.32 2.12 8.71 1.12 0.94 7.53  95 0.370.27  95 2.48 tt 11%12% pp 1.482.11  N thermal 3.163.22 f bs 0.290.27 f NBCD 0.150.13 Catastrophic drop in q-profile, q min <1 Reduction in non-inductive current Such highly peaked T e unlikely due to H-mode profile shape (generally much flatter in H-mode) and off-axis heating from off-axis NBI.

21. International Spherical Tori Workshop 2009, Madison, WI21 Sensitivity studies Ex 2 - PINI position and Tangency radius A single PINI is defined for the TRANSP run. Vertical position and tangency radius (using horizontal LOS) varied to obtain total I beam and electron/ion heating from a PINI in a wide range of positions. Equilibrium shape differs only a little from the baseline scenario so, although most of the parameters from the run are unrealistic ( , H 98 etc), the beam driven current, shine-through and heating power is reasonably reliable.

22. International Spherical Tori Workshop 2009, Madison, WI22 Sensitivity studies Ex 2- PINI position and Tangency radius Scenario A beam driven current presented. (Other parameters such as heating power, shine-through etc can also be determined.) Contours show total I beam for a PINI in a particular Z/R Tan position. This is NOT a map of I beam contours in the plasma! Simulation indicates more efficient beam current drive may be realised with beams at higher R Tan Total I beam /PINI R Tan (m) Z (m)

23. International Spherical Tori Workshop 2009, Madison, WI23 Sensitivity studies Ex 2 - PINI position and Tangency radius Studies on all Baseline scenarios showed a clear advantage to increasing R Tan for some PINIs. New configuration specified as: Different PINI positions produce an NB system with greater flexibility. Z (cm)R Tan (cm) Off-axis 16590 Off-axis 26580 On-axis090 On-axis (cntr.) 0-70

24. International Spherical Tori Workshop 2009, Madison, WI24 Other sensitivity studies A number of other sensitivity studies have been carried out including: –Plasma rotation (eqm. assumption test) –T i scaling (eqm. assumption test) –PINI power scaling (q-profile control) –Anomalous Fast Ion diffusivity (MHD sensitivity) –Reduced number of PINIs (project staging approach) –Increased number of PINIs (project staging approach) Whereas assumptions used to set up the TRANSP model, particularly T e and n e shape, introduce uncertainties into the results… Uncertainties can be mitigated by carrying out sensitivity studies allowing optimum engineering decisions to be made.

25. International Spherical Tori Workshop 2009, Madison, WI25 ASTRA studies O. Zolotukhin

26. International Spherical Tori Workshop 2009, Madison, WI26 ASTRA studies ASTRA is a 1.5D transport code –Core transport properties determined by turbulence-driven transport coefficients from GLF23 –Pedestal zone described by critical pressure gradient from empirical MAST scaling and width ~ –For this study it has been coupled with the ESC 2D equilibrium code and the NUBEAM Monte-Carlo neutral beam code Parameters taken from appropriate TRANSP run to set-up ASTRA model: –n e profile –I p, Z eff, boundary etc –Temperature edge value set to 0.175 - 0.4keV to simulate H-mode, T e profile calculated Studies –Scenario D: time evolution during I p ramp-up and to stationary state. –Scenario A: sensitivity to temperature boundary conditions –Scenario A: Calculated plasma density profile

27. International Spherical Tori Workshop 2009, Madison, WI27 ASTRA studies – scenario D time evolution I p and n e ramp to flat-top values by 300ms Core temperature and stored thermal energy equilibrate by 800ms Current profile equilibrates after 2.5s Flux consumption reaches limit after 2.5s Run to fully relaxed state should be possible for high-current scenario

28. International Spherical Tori Workshop 2009, Madison, WI28 ASTRA studies – Scenario A boundary conditions Pedestal temperature varied in model (ref: 175eV) to determine scenario sensitivity Change of T e0 and T e0 /T ea with T ea define boundary between L and H mode Change in current drive efficiency less sensitive to boundary values in H-mode With scenario in H-mode, lower than expected boundary temperature does not result in catastrophic loss of non-inductive current drive.

29. International Spherical Tori Workshop 2009, Madison, WI29 ASTRA studies – Scenario A density profile calculation Previous studies have used prescribed density profile. Addition of particle flux term allows density to be calculated along with temperature using specified pressure parameters. Stationary state density profile more peaked than prescribed T e profile agrees well More peaked density profile may occur than is presently accepted in the baseline model Earlier sensitivity study indicated moderate density peaking can easily be tolerated

30. International Spherical Tori Workshop 2009, Madison, WI30 MHD stability studies I. Chapman, S. Pinches, S. Saarelma

31. International Spherical Tori Workshop 2009, Madison, WI31 MHD Stability Studies have been carried out using the MISHKA MHD code to test stability of the scenarios to all MHD modes Stability of the Baseline scenarios has been investigated It has been found in all cases the most problematic instability is an n=1 internal kink mode (so called “infernal” mode) Stabilisation effects of rotation, conducting wall structures and triangularity variation have been investigated.

32. International Spherical Tori Workshop 2009, Madison, WI32 MHD Stability – Rotational stabilisation Example: Scenario C is most challenging with a calculated  N limit of 4.0 and a target  N of 6.7 TRANSP rotation model and prescribed rotation profile used: Rotation stabilises the n=1 mode but, for Scenario C, it is unlikely rotation alone will be sufficient to reach the target  N.

33. International Spherical Tori Workshop 2009, Madison, WI33 MHD stability – stabilisation plates Conducting 1 st wall and structures in the vessel can have a stabilising influence. MAST vessel is large ⇒ wall is far from plasma Stabilisation plates can be included in the design Stabilisation plates significantly improve  limit of n=1-3 modes (“plates 3” is the realistically achievable preferred option)

34. International Spherical Tori Workshop 2009, Madison, WI34 Tests carried out on Scenario C, triangularity varied between  =0.3 and  =0.72 (reference  =0.52)  N is varied and the limit taken to be the value where growth rate of the n=1 mode becomes positive. Significant increase in the  limit is seen with increased triangularity Divertor upgrade (more divertor coils) should assist in exploiting this mechanism MHD stability - triangularity

35. International Spherical Tori Workshop 2009, Madison, WI35 Conclusions

36. International Spherical Tori Workshop 2009, Madison, WI36 Conclusions A set of baseline scenario models have been produced in support of the MAST-U physics case. Testing neutral beam layouts has optimised the MAST-U design for non-inductive current drive and heating. A series of sensitivity studies has demonstrated the scenarios are robust with respect to initial assumptions and temperature pedestal height. Transport modelling of the startup phase has shown the increased flux available is sufficient to reach a fully relaxed state in the demanding high I p scenario. Modelling of density profile broadly agrees with assumed densities with the possibility of moderate profile peaking MHD stability has been assessed and mitigating effects of plasma rotation, stabilisation plates and plasma shaping have been investigated.

37. International Spherical Tori Workshop 2009, Madison, WI37 END