Magnetic Ripple as a Tool for ELMs Mitigation

1. Magnetic Ripple as a Tool for ELMs Mitigation V. Parail,T. Johnson, J. Lonnroth, T. Kiviniemi, P. de Vries, G. Saibene,Y. Kamada, N. Oyama, K. Shinohara, S. Konovalov, D. Howell

2. Outlook • Evolution of plasma profiles between ELMs; • Ways to maximise top-of-the-barrier plasma pressure; • Ways to avoid (mitigate) ELMs; • Analytical theory of ripple transport; • Predictive transport modelling of JET plasmas with ripple transport; • OFMC code ASCOT and simulation of thermal ion ripple losses in plasmas with JET and JT-60U magnetic coils; • Summary.

3. Evolution of plasma profiles between ELMs (1) • Since transport within the ETB is quite small, plasma develops strong pressure gradient to transmit heat flux through the ETB:

4. Evolution of plasma profiles between ELMs (2) • As soon as edge parameters hit one or the other stability limit, an ELM develops, which throws away excessive pressure or current;

5. Evolution of plasma profiles between ELMs (3) • How can we mitigate ELMs or remove them entirely (without sacrificing performance, which means keeping )? • Reduce the heat flux, which enters ETB (up to but not beyond the limit, which triggers transition to type-III ELMs): • Increase radiated power (extra impurities at the edge); • Increase CX losses (gas puffing?); • Increase the heat flux through the ETB between ELMs by increasing thermal conductivity: • Increase ion density ( ); • Increase transport by magnetic ripples or ergodic magnetic limiter; • Induce quasi-continuous benign MHD (EDA, type-II ELMs, washboard modes, pellets ???)

6. Evolution of plasma profiles between ELMs (4) • Reduce the heat flux, which enters ETB (up to but not beyond the limit, which triggers transition to type-III ELMs): • Increase radiated power (extra impurities at the edge); impurity accumulation in plasma core; does not affect ions; difficult to optimise pressure within ETB; • Increase CX losses (gas puffing?); it simultaneously increase losses between ELMs but it’s difficult to do it in a controlled way; • Increase the heat flux through the ETB between ELMs by increasing thermal conductivity: • Increase ion density ( ); difficult to control , often triggers transition to type-III ELMs; pressure and current profiles might be far from optimum; • Induce quasi-continuous benign MHD (EDA, type-II ELMs, washboard modes, pellets ???) We need much better understanding of these modes before we could reliably use them in a controllable way;

7. Follow B. Then |B|~B0[1+ecos(q)+dsin(Nf)] oscillate due to Toridicity Ripple Particles can be toroidally trapped in magnetic wells caused by the ripple. The ripple well depth: • Increase transport by ergodic magnetic limiter(controllable, but increases electron transport only)or bymagnetic ripples; Magnetic ripple as ELM mitigation tool • Ripple well trapping Bmax Bmin

8. Ripple well trapping (2) • Toroidal symmetry is broken, so orbits arenot confined. • The motion is a sum of: • Oscillationbetween turning points; • Vertical drift • Detrapped by: • Collisions; • Moving towards smaller ; • Collisionalityregimes: • High: (these particles oscillate between banana and ripple trapped state in a diffusive way) • Low: non-diffusive losses

9. Ripple Perturbations of Banana Orbits • Ripples perturb banana orbits at their “banana tips”, moving itacross flux surfaces. [A.N. Boozer, Physics of Fluids23, 2283 (1980)] • If the “unperturbed tip” appear at a ripple maximum, then the reflection appear earlier and vice versa. • This is a diffusive process

10. Total ripple-induced transport Total ripple-induced transport is a combination of: • convective/diffusive ripple losses (depending on collisionality), which are toroidally localised and • stochastic ripple-banana diffusion, which is toroidally uniform; N. Oyama, K. Shinohara 2005

11. We use analytical formula for additional ion thermal transport due to ripple-induced thermal ion losses in our predictive simulations with JETTO • P. Yushmanov, Review of Plasma Physics, v. 16, New York, Consultants Bureau (1991). • Flux surface averaged additional ion thermal transport. • Implemented into the JETTO transport code. has to be satisfied for the extent of the region inside local mirrors on the outboard side of the torus with locally trapped particles. Please note that this inequality is actually NOT satisfied for most JT-60U plasmas!

12. Narrow edge-localised ripple: reduces performance and increases ELM frequency: • JETTO transport simulation. • The ripple-affected region is assumed to be significantly narrower than the pedestal width. • Bohm / gyro-Bohm transport model. • The density is low in this case. no ripple-induced transportripple-induced transport

13. Narrow edge-localised ripple: reduces performance and increases ELM frequency (2) Ripple-induced edge-localised transport Flattening of the pressure gradient near the separatrix, effective narrowing of the pedestal. Lowering of the pedestal height. Lowering of the core pressure due to profile stiffness. no ripple-induced transportripple-induced transport Non-optimum pressure gradient

14. Narrow edge-localised ripple reduces performance and increases ELM frequency (3) • The ELM frequency increases with the introduction of ripple-induced transport because of: • profile stiffness, which leads to increased transport inside the top of the pedestal in the case of lower pedestal height and faster replenishment of ETB; • less energy loss during the ELM; • Might explain the higher ELM frequency at JT-60U. •  Smaller, more benign ELMs. • Ripple losses can be an important tool used for ELM mitigation. no ripple-induced transport With ripple

15. Wide ripple at the edge: improved performance • JETTO transport simulation. • The ripple-affected region is assumed to be significantly wider than the pedestal width. • Bohm / gyro-Bohm transport model. • The density is high in this case. no ripple-induced transportwith ripple-induced transport

16. Wide ripple at the edge: improved performance (2) • The ELM frequency decreases due to larger edge losses between ELMs with increased ripple transport. no ripple-induced transportripple-induced transport

17. Wide ripple at the edge: improved performance (3) Decreasing ELM frequency:  The time-average pressure at the top of the pedestal increases (even if max. pressure stays the same).  The time-average core pressure increases due to profile stiffness. more ripple less ripple No ripple

18. Wide ripple at the edge: improved performance (4) • A reduction in the ELM frequency was occasionally seen in JET ripple experiments in 1995. • Resembles the improved performance obtained with a stochastic magnetic boundary in DIII-D [T. Evans, 2004 IAEA Fusion Energy Conference]. • This mechanism is most pronounced in high density plasmas, which have the highest level of transport within the pedestal because of the temperature and density dependency of neo-classical transport.

19. Numerical simulation of ripple losses in realistic geometry (1) • #60856 belongs to JET/JT-60U identity plasma. • Ripple-induced transport in plasma with JET coils is outboard midplane localised. • Same plasma with JT-60U coils should have much larger ripple transport near x-point; After drawing general conclusions on what might be expected from magnetic ripples we decide to perform a detailed analysis of realistic plasmas JT-60U coils JET coils I2/I1=0.5

21. Numerical simulation of ripple losses in realistic geometry (2) • Orbit Following Monte Carlo code ASCOT was used for the simulations; • Code follows guiding centre orbits of thermal particles ensemble in a torus; • 3D JET and JT-60U ripple model has been included as B=B0 + B1cosN + B2cos2N , where Bn=Bn(R,Z), N- number of toroidal coils; • Only collisions with a fixed background are considered; • Ensemble of particles can be initialised as: • delta-function in radius or • according to assumed ne(r) and Ti(r);

22. Numerical simulation of ripple losses in realistic geometry (3) • To speed up the simulations, c can be calculated from the spreading of a “pulse” (with the radial electric field turned off): f(t=0,r, v)=d(r-r0)fMaxwell(v) • If the process is diffusive the variance will grow at a constant rate <(r (t,v)-<r (t,v)>)2> =V (t,v)=2Dv(v)t • Since the flow G~Dv, the transport coefficients are given by: c0 - relates pressure gradients and particles transport, c2 - relates temperature gradients and energy transport, and c1 - is the off-diagonal coefficient. • Accuracy ~ [Ntpd-1/2 e-E/T Nmeasurements]-1/2 ~ 20%

23. Numerical simulation of ripple losses in realistic geometry (4) Rho=0.98, JET I2/I1=0.5 Rho=0.98, JT-60U coils

24. JT-60U coils JET coils, I2/I1=0.5 JET coils, I2/I1=1.0 neo-classical CHI-I

25. Numerical simulation of ripple losses in realistic geometry (5) Rho=0.98, JETcoils, I2/I1=0.5 Rho=0.98, JT-60U coils

26. Numerical simulation of ripple losses in JET geometry (1) • Four level of current imbalance between odd and even JET coils is being considered: I1/I2= 1.0; 0.66; 0.33 and 0.0 • JAERI OFMC code is being used for the modelling of fast ion losses 2 2 2 I1/I2= 0.66 I1/I2= 0.33 I1/I2= 0.0

27. 2 FULL ripple 66% ripple 2 Pmax~3.6MW/m2 33% ripple

28. Numerical simulation of ripple losses in JET geometry (2) • ASCOT code is being used to evaluate the role of magnetic ripple in thermal ion transport; • “Pulse propagation” technique is being used for first level of analysis; • Three levels of current imbalance are used: I1/I2= 0.0; 0.5 and 1.0; • JET shot #60856 (JET/JT-60U identity plasma with Ip=1.15 MA) is used as an example; Full ripple Half ripple No ripple

29. Numerical simulation of ripple losses in JET geometry (3)

30. SUMMARY • Magnetic ripple, if carefully controlled, might serve as a valuable tool for ELM mitigation; • Magnetic ripple losses increase thermal ion transport only and it might be better to use it in combination with stochastic magnetic limiter; • Experiments on JET and JT-60U are under preparation to elucidate the role of controlled magnetic ripple in ELMy H-mode performance;