Recent work on the control of MHD instabilities at ASDEX Upgrade S. Günter, J. Hobirk, P. Lang, P. Merkel, A. Mück, G. Pereverzev, ASDEX Upgrade Team Max-Planck-Institut für Plasmaphysik Garching, Germany Sawtooth control by ECCD ELM control by plasma shaping and pellets Current profile control by off-axis NBI? RWM physics on ASDEX Upgrade? NTM control, see next talk

Sawtooth behaviour depends on NBI sources one beam only

Sawtooth behaviour for different NBI sources one beam only Off-axis heating only, leads to density peaking j’ decreased (increased off-axis BS current) diagmagnetic stabilization (* increased)

Sawtooth behaviour for different NBI sources two off-axis beams 2.0 3.0 4.0 5.0 6.0 t [s] 10000 20000 15000 12000 f [kHz] Sawteeth/ fishbones (q=1)=0.2 (q=1)=0.1 two q=1 surfaces no sawteeth, but continous (1,1) activity two q=1 surfaces in the plasma (off-axis NBI-CD)

Sawtooth tailoring by co- ECCD Experiments with slow Bt-ramp, 0.8 MW co-ECCD and 5.1 MW NBI

Influencing (1,1) mode activity by co-ECCD co-ECCD at pol = 0.4 no sawteeth, only fishbones FB amplitude also decreases (SXR amplitude reduced by factor of 3)

Sawtooth tailoring by ctr-ECCD

Destabilisation of (1,1) activity by on-axis ctr-ECCD For ctr-ECCD deposition close to plasma center (here pol = 0.1)  reversed q-profile  destabilization of (1,1) mode No sawteeth or fishbones, but continous (1,1) activity

NTM control by sawtooth mitigation (off-axis-ECCD) Co –ECCD: no sawteeth as expected Reduced fishbone amplitude NTM triggered after ECCD (by ST) Counter-ECCD: NTM triggered by FB during ECCD

ELM mitigation: type II ELMs Inner divertor Outer divertor power density

Type I Type II Consider two discharges with different plasma shape #15865 #15863 Type I Type II

but with similar edge temperature and density profiles 0.0 0.2 0.4 0.6 0.8 1.0 1.2 2 4 6 8 10 12 Electron density [10 19 m -3 ] r poloidal 15863 15865 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.5 1.5 2.0 2.5 Electron temperature [keV] r poloidal 15863 15865

Influence of closeness to Double Null Ballooning Stability unchanged Low-n modes become more stable (broad mode structure) Stability of medium-n modes unchanged, but eigenfunctions more localised at plasma edge n=8 peeling mode

Operational regime for type II ELMs closeness to DN/high  q95 > 3.5 high n/nGW

Why do we need high density/high q95? Hypothesis: type II ELMs only if low-n modes are stable JET, ELM precursors low n modes only for high density (Perez, Koslowski et al., IAEA 2002)

Influence of edge collisionality Theory: low mode number MHD activity destabilised by current gradient jBS  since n  jBS  since * 

Is type II ELM regime accessible for ITER? Higher density increases edge collisionality  BS current density reduced  reduced drive for low-n modes If not n/nGW, but collisionality counts, type II ELMs would not occur in ITER  Other means for ELM control?

ELM mitigation: by pellets Control of ELM frequency possible (each pellet triggers an ELM)

Control of ELM frequency by pellets small pellets (2 … 3x1019 D atoms, not strong fuelling) Confinement degradation ~ f-0.16 (less than for frequency change by, e.g., heating power, density puff) ~ f-0.6

Mitigation of ELM size possible same plasma parameters natural ELM frequency 52 Hz

Mitigation of ELM size possible

Energy loss per pellet triggered ELM as for type I ELMs at same frequency

Current profile control by off-axis NBI? Redirected NBI box provides off axis deposition of 93 keV ions: NB driven current clearly seen by reduced OH flux consumption current profile changes seem much smaller than expected

Two off-axis beams, an example (#14513) Plasma current pol dia li S3+S5 S6+S7 NBI gas Raus ne,0

One off-axis beam (Te change compensated by ICRH) #18091 Plasma current pol dia li NBI ICRH S3 S6 gas ne,0 Raus

Strong change in li only for one-beam discharge Very small change in li, much smaller than predicted (ASTRA li shifted up) two-beam discharge ASTRA experiment Change in li for one-beam case in agreement with ASTRA code ASTRA experiment on- off-axis beams one-beam discharge

q-profile for two-beam discharge (q=1 surface) 2.0 3.0 4.0 5.0 6.0 t [s] 10000 20000 15000 12000 f [kHz] Sawteeth/ fishbones (q=1)=0.2 (q=1)=0.1 two q=1 surfaces ASTRA predicts observable change of q-profile, but no change measured (MSE, q=1 radius) But: in the plasma centre (tor < 0.15) q-profile changes as two q=1 surfaces at tor < 0.10 and tor = 0.2 observed

Current profile modifications due to one off-axis beam Change in radius of q=1 surface is significant and agrees with ASTRA predictions

Current profile modifications due to one off-axis beam Current profile modifications mainly caused by off-axis beam (ASTRA)

Comparison to MSE measurements ASTRA predictions

Non-stiff electron temperature profiles for one-beam discharge one beam (without additional heating) two beams (#14513)

Non-stiff ion temperature profile for one beam case Ion temperature during off-axis NBI modeled by MMM95, agreement with measured pressures

To explain unchanged current profile one needs a particle pinch! Anomalous particle pinches are well-known in theory (density peaking) Simple picture: strong turbulence of background plasma redistributes particles while maintaining the two adiabatic invariants  and with the density follows from const.

Does theory predict such a particle pinch? Need: full non-linear turbulence simulation with marker particles, in progress (B. Scott) So far: quasi-linear GS2-calculations (G. Tardini, A. Peeters) G. Tardini First results: particle pinch exists, but too small To be done: realistic density profile of fast particles, parameter scan

Simulations for realistic wall structures (as planned for AUG) low triang. Wall structures only relevant on low field side (ballooning mode structure) high triang. Plasma separatrix + 3 cm in midplane Realistic model for AUG wall structures

3D MHD code with 3d wall structures 3d MHD code CAS3D extended for 3d ideally conducting walls MHD eigenfunctions fully self-consistent Benchmark with 2d MHD code CASTOR successful

A Simulation results for realistic wall structures closed wall Without wall: ßmarg = 1 % Efficiency of realistic wall compared to closed wall <ß> = 4.5 % closed wall rw/rpl 1.2 1.4 1.6 1.8 2.0 A 0.08 0.06 0.04 0.02 0.0

Wall resistivity causes mode growth on wall time (RWMs) Further plans: - Resistive 3d walls (already started) - Feedback system (active coils to stabilise RWM)

Summary Sawtooth mitigation by localized ECCD demonstrated Seed island control allows to control NTM onset type II-ELMs achieved by plasma shaping compatible with required plasma parameters: N, q95, H, n/nGW open question: does collisionality count? (BS current) ELM mitigation by pellets demonstrated smaller pellets at higher frequency needed off-axis NBI current for current profile control only for non-stiff ion temperature profiles? RWM physics: 3D ideal MHD code with 3D ideally conducting wall structures, finite wall resistivity being implemented

Influence of edge density (BS current): ballooning modes Higher density increases edge collisionality  BS current density reduced  Increased magnetic shear prevents access to second stable regime Experiment Ideal ballooning limit: ne = 9 1019 m-3 ne = 1.1 1020 m-3 Second stable regime low density

Non-stiff ion temperature profiles for one-off-axis beam two beam discharge diamagnetic pressure nearly constant, pol increases for off axis beams (fast increases, mainly ||) electron temperature and density constant, but diamagnetic pressure decreases  hint to non-stiff ion temperature profiles one beam discharge

Non-stiff rotation profiles? (mode frequency also dependent on diamagnetic drift) Strong reduction in (1,1) mode frequency for one-beam discharge two beams (#14513) one beam (#18091) 2.0 3.0 4.0 5.0 6.0 t [s] 10000 20000 15000 12000 f [kHz] t [s] 2.0 3.0 4.0 5.0 1000 2000 5000 10000 20000 off-axis beams on-axis beams off-axis beams on-axis beams

Good match of electron temperature profiles ... … by additional central ICRH for the one-beam discharge to adjust Inductive current profiles

Two-beam discharges: so far non-symmetric beam deposition Q5, Q6, Q7, Q8 A. Stäbler

Future two-beam experiments: try to match symmetric deposition (closeness to DN) Z = 0 z = 9.5 cm Q5, Q6, Q7, Q8 A. Stäbler

CASTOR with antenna: calculate torque Torque on the plasma due to external error fields: Re P   jant B cos  ~ tor Maximum torque 1/ ~

An example: Interaction of NTMs with perturbation fields No simultaneous large NTMs of different helicities observed in experiments

An example: Interaction of NTMs with perturbation fields Analytic theory: for NTMs stabilising effect of additional helical field can be proven for small values of || effect vanishes for ||  Is there an effect remaining for realistic values of || ? If so: new stabilisation method for NTMs can be propsed: stabilisation by external helical perturbation fields Many other problems, but: so far no non-linear MHD code can deal with realistic ||

Proposal for a solution in non-aligned coordinate system In the following, for simplicity (not in the code): Cartesian coordinates with one perturbation field component Heat conduction equation for different Fourier components of temperature: … … To close the equations one should not truncate the Fourier series in T, but in q  heat flux along perturbed magnetic field line remains finite (nearly vanishing temperature gradients)

Fourier decomposition for perturbation In the following, for simplicity (not in the code): Cartesian coordinates with one perturbation field component Heat conduction equation for different Fourier components of temperature: To lowest order (for explanation): include only terms up to first order in q  T2 adjusts itself such that q||1 becomes small

What about the radial derivatives? perturbation field: simplest discretisation at i’s grid point new scheme Introduces an additional error or order (r)2 , but equations for each grid point ensure vanishing temperature gradients along perturbed field lines

||= 108 Convergence properties: single magnetic island Still convergence only (r)2 But: absolute error reduced by factor of 10 Improvement increases for larger ||

Magnetic islands with two helicities

||= 1010 Magnetic islands with two helicities Magnetic islands seen in temperature contours, but still strong gradient in ergodic region

||= 1012 Magnetic islands with two helicities Temperature gradient vanishes in ergodic region due to increased radial transport along magnetic field lines

An example: Interaction of NTMs with perturbation fields Is there an effect remaining for realistic values of || ? If so: new stabilisation method for NTMs can be propsed: stabilisation by external helical perturbation fields (next talk) YES!

Improved Diagnostics at the edge Comparison with theory possible ...

Plasma shape is important for ELM losses higher upper triangularity leads to bigger ELM losses can be explained by wider ELM affected region at higher triangularity

Our understanding of transition type I  type II ELMs Strong plasma shaping (high , closeness to DN) - stabilises low-n modes - reduces width of medium-n eigenfunctions High edge density (reduced BS current density) - reduces drive for low-n modes - closes access to second stable regime for ballooning modes (limits achievable pressure gradient) Can we expect type II ELMs in ITER ? (low collisionality!)