Resonant magnetic perturbation effect on the tearing mode dynamics in EXTRAP T2R: experimental...
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Transcript of Resonant magnetic perturbation effect on the tearing mode dynamics in EXTRAP T2R: experimental...
Resonant magnetic perturbation effect
on the tearing mode dynamicsin EXTRAP T2R:
experimental results and modelingL. Frassinetti, K.E.J. Olofsson, P.R. Brunsell, J.R. Drake
Alfvén Laboratory, Royal Institute of Technology KTH
Stockholm
OUTLINE
• Resonant magnetic perturbation (RMP)Resonant magnetic perturbation (RMP) Why are RMPs important? Why are RMPs studied in EXTRAP T2R?
MachineDiagnosticsFeedback system
TM dynamics with low RMP amplitudeTM dynamics with high RMP amplitudeTM locking to a RMP
Fitzpatrick theoryInterpretation of experimental results
• Modelling Modelling resultsresults
• Experimental resultsExperimental results
• EXTRAP T2REXTRAP T2R
WHY ARE RMPs IMPORTANT?
[Abdullaev, PoP 16, 030701 (2009)]
[Evans, NF 2008, 48 024002]
1. Neo-classical tearing mode stabilization RMP can interact with the NTM with stabilizing effects RMP can rotate a locked mode to move the O-point in the best position for ECCD stabilization
[La Haye, PoP 9, 2051 (2002)][Volpe, PoP 16, 102052 (2009)]
RMPs can produce stochasticity in the plasma outer region
the pressure gradient is reducedand the ELM effect mitigated. DIIID [Evans, NF 2008, 48 024002] JET [Liang, PRL 2007, 98 265004]
2. ELM suppression:
(2,1
) TM
am
plitu
de (
a.u.
) Hender NF 1992COMPASS-C
Ivers,PoP 1996 HBT-EP
time
WHY TO STUDY RMP?
2. There are many theoretical papers that investigate the interaction between an RMP and a TM
3. But recently, not so many experimental results directly investigate the RMP effect on TMs
2. RMPs can be easily produced with EXTRAP T2R feedback system
1. The mechanisms for ELM mitigation are not yet totally understood
1. EXTRAP T2R plasma is characterized by rotating TMs
WHY TO STUDY RMP in EXTRAP T2R?
EXTRAP T2R is a good device to test new feedback algorithms and study the MHD mode response to external perturbations
m=1
-30 -25 -20 -15 -10 -5
20
10
0
-10
0.3
0.2
0.1
0.0
b1,
n (m
T)
1,
n (k
rad
/s)
n
EXTRAP T2R
EXTRAP T2R is a RFP with:
• R=1.24m• a=0.18m
• Ip ≈ 80-150kA• ne ≈ 1019m-3
• Te ≈ 200-400eV
• tpulse≈ 20ms (no FeedBack)• tpulse≈ 90ms (with IS)
TM diagnosticb 4 poloidal x 64 toroidal local sensors (m=1 connected) located inside the shell. Sensitive to fast rotation.
TM
The device
(1,-12) is often larger than the other TMs
-12 -13-14
0.0 0.2 0.4 0.6 0.8 1.0r/a
0.100.080.060.040.020.00
-0.02-0.04
q(r
)
Poincare map of magnetic field lines(poloidal section)
(1,-12) island
-1.0 -0.5 0.0 0.5 1.0x/a
1.0
0.5
0.0
-0.5
-1.0
z/a
byOlofsson E.
• shell≈13.8ms (nominal) shell
EXTRAP T2R
bc
Sensor coils
Sensor coils
• SENSOR COILS 4 poloidal x 32 toroidal sensor saddle coils (m=1 connected) located inside the shell
Activecoils
Active coils
• ACTIVE COILS 4 poloidal x 32 toroidal active saddle coils (m=1 connected) located outside the shell
Digitalcontroller
• DIGITAL CONTROLLER
The feedback
plasma
external helical magnetic
perturbations shell
b1,n bc
Fourier harmonics in real time
inputto active coils
Vc(t) V1,n min[ |b1,n(t)-ref| ]
[Olofsson, Fusion Engineering and Design 84, 1455 (2009)]
m=1n=-12
0 20 40 60Time (ms)
0.6
0.4
0.2
0.0b r
1,n (
mT
)
0 20 40 60Time (ms)
80
60
40
20
0
v1,-1
2 (
km/s
)
80
60
40
20
0
vOV (
km/s
)
1.00.8
0.6
0.4
0.2
0.0
b r1,
n (
mT
)
120100
8060
40
200
Ip (
)kA
m=1n=-12
0 20 40 60Time (ms)
0.6
0.4
0.2
0.0
b r1,
n (
mT
)
At present In EXTRAP T2R RMPs are applied to study:
- effect on TM dynamics (present talk)
- effect on the plasma flow (wednsday talk)
Present RMP studies on EXTRAP T2R
TM DYNAMICS
average of all other TMs(1,-12)
Natural TM dynamics TM dynamics with low RMP amplitude
RMP ≈ 0.3mT
1- amplitude: “modulated”
RMP effect on the rotating TM:
2- velocity: “modulated”
NO RMP
0 20 40 60
0.6
0.4
0.20.0
b r1,
n (
mT
)
10080604020
0
Ip (
kA)
0.6
0.4
0.20.0
b r1,
n (
mT
)
10080604020
0
Ip (
kA)
0 20 40 60Time (ms)Time (ms)
19.60 19.65 19.70
ph
ase
Time (ms)
40
30
20
10
0
(
kra
d/s
) b
m,n (
mT
)
0.60.50.40.30.20.1
ph
ase
40
30
20
10
0
(
kra
d/s
) b
m,n (
mT
)
0.4
0.3
0.2
0.1
14.68 14.70 14.72 14.74 14.76 14.78
Time (ms)
b 1
,-1
2 (
mT
)
(kr
ad/s
)
40
30
20
10
0
0.20
0.15
0.10
0.05
0.00
AMPLIFICATIONSUPPRESSION
=0=
TM amplitudeamplitude and velocityvelocity are correlatedcorrelatedwith the phase shiftphase shift between TM and RMP
ampl.ampl. suppression
TM DYNAMICS with low RMP amplitude
decel.accelerationdecel.
Phenomenological explanation (wrong!)
Toroidal angle
bTM
Toroidal angle
Toroidal angle
bTM
bRMP
b 1
,-1
2 (
mT
)
0.5
0.4
0.3
0.2
0.1
0.0
(
krad
/s)
20
15
10
5
0
RMP ≈ 0.5mT
TM DYNAMICS with high RMP amplitude
suppression
jump
am
plifi
cati
on
deceleration
acce
lera
tion
jump
0.6
0.4
0.2
0.0
b r1
,n (
mT
)
0 20 40 60Time (ms)
1- High oscillation with “complete” suppression
2- phase jumps
b m
,n (
mT
)
0.60.50.40.30.20.1
(
krad
/s)
25201510
5029.10 29.15 29.20
Time (ms)
MODELLING
Based on Fitzpatrick [Phys. Plasmas 8 4489 (2001)]
RMPc rW c b
TMrW c b
3 coupled partial differential equations:
1. TM evolution
2. Torque balance
with
3. Helical velocity
Viscous torque EM torque
braking torque due to eddy currentsIn the wall generated by the rotating TM
braking torque due to interactionof the rotating TM with the static RMP
2TMrb TM RMP
r rb b
Poloidal section
Amplification and
deceleration
suppressionand
deceleration
suppressionand
acceleration
amplificationand
acceleration
b 1
,-1
2 (
mT
)
(kr
ad/s
)
0.30
0.20
0.10
0.00
30
20
10
0
Time (ms)0.00 0.02 0.04 0.06 0.08 0.10
ne(0)=0.9x1019m-3
FREE PARAMETERSR=0.1ms=0.65 10-7 kg/(m∙s)
INITIAL CONDITIONS0=30krad/sb
TM(0)=0.12mT
Reasonable agreement between model and experiment
MODELLING the LOW RMP case
TM amplitude is modulated
TM velocity is modulated
amplitude reduction in time(not evident on this time scale)
velocity reduction in time(not evident on this time scale)
brRMP=0.3mT
b 1
,-1
2 (
mT
)
0.20
0.15
0.10
0.05
0.00
(
krad
/s)
40
30
20
10
0
b 1
,-1
2 (
mT
)
0.50
0.40
0.30
0.20
0.10
0.00
(kr
ad/s
) 15
10
5
0
Time (ms)0.20 0.22 0.24 0.26 0.28 0.30
Reasonable agreement between model and experiment
MODELLING the HIGH RMP case
brRMP=0.5mT
TM amplitude is modulated
TM velocity is modulated
amplitude increases in time
Phase jumps
ne(0)=0.9x1019m-3
FREE PARAMETERSR=0.1ms=0.65 10-7 kg/(m∙s)
INITIAL CONDITIONS0=50krad/sb
TM(0)=0.01mT
b 1
,-1
2 (
mT
)
0.50
0.40
0.30
0.20
0.10
0.00
(
krad
/s)
20
15
10
5
0
b 1
,-1
2 (
mT
)
0.50
0.40
0.30
0.20
0.10
Time (ms)
30.40 30.45 30.50 30.55
EXPERIMENT brRMP=0.4mT
TM LOCKING TO A RMP
-Low RMPLow RMP amplitude “weak” oscillationoscillation in the TM amplitude and velocity
-High RMPHigh RMP amplitude “strong” modulation in the TM amplitude and phase jumpsphase jumps
IS IT ALWAYS SO SIMPLE?IS IT ALWAYS SO SIMPLE?
lockinglockingoscillationsoscillations jumpsjumps lockinglockingoscillationsoscillations jumpsjumps
MODEL brRMP=0.4mT
R=0.1ms=0.65 10-7 kg/(m∙s) ne(0)=0.9x1019m-3
0=25krad/sb
TM(0)=0.2mT
b
1,-
12 (
mT
)
0.50
0.40
0.30
0.20
0.10
Time (ms)
0.00 0.05 0.10 0.15 0.20 0.20
SCALING OF THE TM DYNAMIC PROPERTIES WITH THE RMP AMPLITUDE
TM amplitude:
1- Suppression1- Suppression for “low” RMP amplitudes
2- Amplification2- Amplification for “high” RMP amplitudes
TM dynamics:
1- Full rotation1- Full rotation for “low” RMP amplitudes
2- Jumps2- Jumps for “high” RMP amplitudes
3- Locking3- Locking for “very high” RMP amplitudes
time averaged amplitude
Angle covered by the TM during one rotation
b 1
,-1
2 (
mT
)
0.50
0.40
0.30
0.20
0.10
0.00
0.0 0.2 0.4 0.6 0.8 1.0br
1,-12 (mT)
br1,-12 (mT)
0.0 0.2 0.4 0.6 0.8 1.0
SCALING OF THE TM DYNAMIC PROPERTIES WITH THE RMP AMPLITUDE
TM amplitude:
1- Suppression1- Suppression for “low” RMP amplitudes
2- Amplification2- Amplification for “high” RMP amplitudes
TM dynamics:
1- Full rotation1- Full rotation for “low” RMP amplitudes
2- Jumps2- Jumps for “high” RMP amplitudes
3- Locking3- Locking for “very high” RMP amplitudes
time averaged amplitude
Angle covered by the TM during one rotation
b 1
,-1
2 (
mT
)
0.50
0.40
0.30
0.20
0.10
0.00
0.0 0.2 0.4 0.6 0.8 1.0br
1,-12 (mT)
br1,-12 (mT)
0.0 0.2 0.4 0.6 0.8 1.0
CONCLUSIONS
• An external RMP can affect the rotating TM and the corresponding magnetic island
• The RMP producesRMP produces: TM amplitude amplification or suppression TM velocity acceleration or deceleration
• “Low” RMP amplitude “weak” oscillationoscillation in the TM amplitude and velocity• “High” RMP amplitude “strong” modulation in the TM amplitude and phase jumpsphase jumps• The locking to a RMP can be a complicated mechanism
• The Fitzpatrick modelFitzpatrick model gives a reasonable explanationreasonable explanation of these phenomena It is a useful tool for testing advanced feedback algorithmuseful tool for testing advanced feedback algorithm for TM control
• Work in progress and future work:
1- RMP with another helicity 2- RMP effect on plasma flow 3- …
depending on the phase shift