1. 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

2. Sawtooth behaviour depends on NBI sources
one beam only

3. 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)

4. Sawtooth behaviour for different NBI sources
two off-axis beams
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)

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

6. 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)

7. Sawtooth tailoring by ctr-ECCD

8. 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

9. 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

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

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

12. 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

13. 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

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

15. 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)

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

17. 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?

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

19. 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

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

21. Mitigation of ELM size possible

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

23. 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

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

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

26. 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

27. q-profile for two-beam discharge (q=1 surface)
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

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

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

30. Comparison to MSE measurements
ASTRA predictions

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

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

33. 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.

34. 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

35. 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

36. 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

37. 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
A
0.08
0.06
0.04
0.02
0.0

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

39. 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

40. 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 = m-3
ne = m-3
Second stable regime low density

41. 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

42. 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)
t [s]
10000
20000
15000
12000
f [kHz]
t [s]
1000
2000
5000
10000
20000
off-axis
beams
on-axis
beams
off-axis
beams
on-axis
beams

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

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

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

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

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

48. 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 ||

49. 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)

50. 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

51. 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

52. ||= 108 Convergence properties: single magnetic island
Still convergence only (r)2
But: absolute error reduced by factor of 10
Improvement increases for larger ||

53. Magnetic islands with two helicities

54. ||= 1010 Magnetic islands with two helicities
Magnetic islands seen in temperature contours, but still strong gradient in ergodic region

55. ||= 1012 Magnetic islands with two helicities
Temperature gradient vanishes in ergodic region due to increased radial transport along magnetic field lines

56. 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!

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

58. 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

59. 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!)