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

Off-axis heating only, leads to density peaking j’ decreased (increased off-axis BS current) diagmagnetic stabilization (* increased)

one beam only

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)=0.2

(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)

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

Sawtooth tailoring by co- ECCD

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

#15865 #15863

Consider two discharges with different plasma shape

Type I Type II

0.0 0.2 0.4 0.6 0.8 1.0 1.20

2

4

6

8

10

12

Ele

ctro

n de

nsity

[1019

m-3]

poloidal

15863 15865

0.0 0.2 0.4 0.6 0.8 1.0 1.20.0

0.5

1.0

1.5

2.0

2.5

Ele

ctro

n te

mpe

ratu

re [k

eV]

poloidal

15863 15865

but with similar edge temperature and density profiles

Influence of closeness to Double Null

n=8 peeling mode

• 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

Operational regime for type II ELMs

• closeness to DN/high • q95 > 3.5 • high n/nGW

Why do we need high density/high q95?

JET, ELM precursorslow n modes only for high density(Perez, Koslowski et al., IAEA 2002)

Hypothesis: type II ELMs only if low-n modes are stable

Influence of edge collisionality

jBS since * jBS since n

Theory: low mode number MHD activity destabilised by current gradient

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 ELMsat 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)

S3+S5 S6+S7

Plasma current

ne,0

pol dia

NBI

li

gas

Raus

One off-axis beam (Te change compensated by ICRH)

S3 S6

ICRH

Plasma current

ne,0

pol dia

NBI

li

gas

Raus

#18091

Strong change in li only for one-beam discharge

Change in li for one-beam casein agreement with ASTRA code

ASTRA

experiment

on- off-axis beams one-beam discharge

Very small change in li,much smaller than predicted(ASTRA li shifted up)

two-beam dischargeASTRA

experiment

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

ASTRA predicts observable changeof q-profile, but no change measured(MSE, q=1 radius)

But: in the plasma centre (tor < 0.15) q-profile changes as two q=1surfaces at tor < 0.10 and tor = 0.2 observed

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)=0.2

(q=1)=0.1

two q=1 surfaces

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)

First results: particle pinch exists, but too smallTo be done: realistic density profile of fast particles, parameter scan

G. Tardini

Simulations for realistic wall structures (as planned for AUG)

low triang.

high triang.

Plasmaseparatrix+ 3 cm in midplane

Wall structures only relevant onlow field side (ballooning mode structure)

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

Simulation results for realistic wall structures

Efficiency of realistic wallcompared to closed wall

Without wall: ßmarg = 1 %

<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

Experiment

Ideal ballooning limit:

ne = 9 1019 m-3

ne = 1.1 1020 m-3

Second stable regime low density

• Higher density increases edge collisionality BS current density reduced

Increased magnetic shear prevents access to second stable regime

Non-stiff ion temperature profiles for one-off-axis beam

electron temperature and density constant, but diamagneticpressure decreases hint to non-stiff ion temperature profiles

one beam discharge

two beam discharge

diamagnetic pressure nearly constant,pol increases for off axis beams(fast increases, mainly ||)

Non-stiff rotation profiles? (mode frequency also dependent on diamagnetic drift)

Strong reduction in (1,1) mode frequency for one-beam discharge

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

20000two beams (#14513) one beam (#18091)

on-axis beams

off-axisbeams

on-axis beams

off-axisbeams

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

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.0 0.2 0.4 0.6 0.8 1.0

Q1 /+60 /z=+9.5Q2 /+70 /z=+9.5

Q3 /–70 /z=+9.5Q4 /–60 /z=+9.5

Q5, Q6, Q7, Q8

A. Stäbler

Future two-beam experiments: try to match symmetricdeposition (closeness to DN)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.0 0.2 0.4 0.6 0.8 1.0

Q1 /+60 /z=+9.5Q2 /+70 /z=+9.5

Q3 /–70 /z=+9.5Q4 /–60 /z=+9.5

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.0 0.2 0.4 0.6 0.8 1.0

Q1 /+69.5 /z=±0

Q2 /+79.5 /z=±0Q3 /–60.5 /z=±0

Q4 /–50.5 /z=±0

Z = 0 z = 9.5 cm

Q5, Q6, Q7, Q8 A. Stäbler

CASTOR with antenna: calculate torque

Re P

jant B cos ~tor

Torque on the plasma due to external error fields:

1/

~

Maximum torque

An example: Interaction of NTMs with perturbation fields

No simultaneous large NTMs of different helicities observed in experiments

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

An example: Interaction of NTMs with 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

( )1//11//102

0 2

1−−⊥⊥ ∇⋅+∇⋅−=∇−

∂

∂qbqbTT

t

rrχ

2//10//11//012

1 qbqbqbTTt

∇⋅−∇⋅−∇⋅−=∇−∂∂

−⊥⊥

rrrχ

3//11//12//022

2 qbqbqbTTt

∇⋅−∇⋅−∇⋅−=∇−∂∂

−⊥⊥

rrrχ

( )1111//0// 2

1−− ∇⋅+∇⋅−= TbTbq

rrχ

( )211001//1// TbTbTbq ∇⋅+∇⋅+∇⋅−= −

rrrχ

( )312011//2// TbTbTbq ∇⋅+∇⋅+∇⋅−= −

rrrχ

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:

BBb ii

rrr=

… …

//2 qbTT

t∇⋅−=∇−

∂∂

⊥⊥ ( )Tbq ∇⋅−= //// χ

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

2//10//11//012

1 qbqbqbTTt

∇⋅−∇⋅−∇⋅−=∇−∂∂

−⊥⊥

rrrχ

3//11//12//022

2 qbqbqbTTt

∇⋅−∇⋅−∇⋅−=∇−∂∂

−⊥⊥

rrrχ

( )1111//0// 2

1−− ∇⋅+∇⋅−= TbTbq

rrχ

( )211001//1// TbTbTbq ∇⋅+∇⋅+∇⋅−= −

rrrχ

( )312011//2// TbTbTbq ∇⋅+∇⋅+∇⋅−= −

rrrχ

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:

BBb ii

rrr=

//2 qbTT

t∇⋅−=∇−

∂∂

⊥⊥ ( )Tbq ∇⋅−= //// χ

To lowest order (for explanation): include only terms up to first order in q

T2 adjusts itself such that q||1 becomes small

( )1//11//102

0 2

1−−⊥⊥ ∇⋅+∇⋅−=∇−

∂

∂qbqbTT

t

rrχ

What about the radial derivatives?

rrebbrr

11≈ bkib ⋅=∇⋅r

perturbation field:

1102

0 qr

bTTt r ∂

∂−=∇−

∂∂

−⊥

10112

1 qbkiTTt

⋅−=∇−∂∂

⊥

rχ

( )r

qqb

ii

r Δ

−−≈

−+

−

)12/()12/(

111

iqbki1

01 ⋅−≈r

1122

2 qr

bTTt r ∂

∂−=∇−

∂∂

⊥ ( )r

qqb

ii

r Δ

−−≈

−+ )12/()12/(

111

( )2

)2/1()2/1(

0111

−+ +⋅−≈

ii qqbk

Introduces an additional error or order (r)2 , but equations for each grid point ensure vanishing temperature gradients along perturbed field lines

simplest discretisationat i’s grid point

new scheme

Convergence properties: single magnetic island

||= 108

Still convergence only (r)2

But: absolute error reduced by factor of 10Improvement increases for larger ||

Magnetic islands with two helicities

Magnetic islands with two helicities

||= 1010

Magnetic islands seen in temperature contours, but still strong gradient in ergodic region

Magnetic islands with two helicities

||= 1012

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!)