recent work on the control of mhd instabilities at asdex upgrade
DESCRIPTION
Recent work on the control of MHD instabilities at ASDEX Upgrade. S. Günter, J. Hobirk, P. Lang, P. Merkel, A. M ück, G. Pereverzev, ASDEX Upgrade Team Max-Planck-Institut f ür Plasmaphysik Garching, Germany. Sawtooth control by ECCD ELM control by plasma shaping and pellets - PowerPoint PPT PresentationTRANSCRIPT
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!)