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Resonant magnetic perturbation effect
on the tearing mode dynamics
in EXTRAP T2R:
experimental results and modeling
L. Frassinetti, K.E.J. Olofsson, P.R. Brunsell, J.R. Drake
Alfvén Laboratory,
Royal Institute of Technology KTH
Stockholm
OUTLINE
• Resonant magnetic
perturbation (RMP)
Why are RMPs important?
Why are RMPs studied in EXTRAP T2R?
•
EXTRAP T2R
Machine
Diagnostics
Feedback system
•
Experimental results
TM dynamics with low RMP amplitude
TM dynamics with high RMP amplitude
TM locking to a RMP
•
Modelling results
Fitzpatrick theory
Interpretation of experimental results
WHY ARE RMPs IMPORTANT?
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
[La Haye, PoP 9, 2051 (2002)]
position for ECCD stabilization
[Volpe, PoP 16, 102052 (2009)]
2. ELM suppression:
RMPs can produce stochasticity
in the plasma outer region
the pressure gradient is reduced
and the ELM effect mitigated.
DIIID [Evans, NF 2008, 48 024002]
JET [Liang, PRL 2007, 98 265004]
[Abdullaev, PoP 16, 030701 (2009)]
[Evans, NF 2008, 48 024002]
WHY TO STUDY RMP?
1. The mechanisms for ELM mitigation are not yet totally understood
(2,1) TM amplitude (a.u.)
2. There are many theoretical papers that investigate the
interaction between an RMP and a TM
Hender NF 1992
COMPASS-C
Ivers,PoP 1996 HBT-EP
time
3. But recently, not so many experimental results directly investigate
the RMP effect on TMs
WHY TO STUDY RMP in EXTRAP T2R?
1. EXTRAP T2R plasma is characterized by rotating TMs
2. RMPs can be easily produced with EXTRAP T2R feedback system
 EXTRAP T2R is a good device to test new feedback algorithms
and study the MHD mode response to external perturbations
EXTRAP T2R
The device
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)
(1,-12) is often larger
than the other TMs
TM diagnostic
0.3
-12 -13
-14
0.2 0.4 0.6
r/a
0.2
Poincare map of magnetic field lines
(poloidal section)
1.0
0.5
0.1
0.0
0.8
1.0
m=1
z/a
0.10
0.08
0.06
0.04
0.02
0.00
-0.02
-0.04
0.0
w1,n (krad/s)
q(r)
local sensors (m=1 connected)
located inside the shell.
Sensitive to fast rotation.
bq1,n (mT)
bq  4 poloidal x 64 toroidal
TM
20
0.0
-0.5
(1,-12) island
10
-1.0
0
-10
-30 -25
-1.0 -0.5
-20
n
-15
-10
-5
0.0
x/a
0.5
1.0
EXTRAP T2R
The feedback
• tshell≈13.8ms
•
by
Olofsson E.
shell
(nominal)
SENSOR COILS
4 poloidal x 32 toroidal
sensor saddle coils (m=1 connected)
located inside the shell
• ACTIVE COILS
4 poloidal x 32 toroidal
active saddle coils (m=1 connected)
located outside the shell
Active
coils
• DIGITAL CONTROLLER
Sensor
coils
shell
external helical
magnetic
perturbations
plasma
Active coils
Sensor coils
bc
input
to active coils
Vc(t)  V1,n  min[ |b1,n(t)-ref| ]
Fourier harmonics
in real time
b1,n  bc
0.6
br1,n (mT)
Digital
controller
m=1
n=-12
0.4
0.2
0.0
[Olofsson, Fusion Engineering and Design 84, 1455 (2009)]
0
20
40
Time (ms)
60
Present RMP studies on EXTRAP T2R
120
100
80
60
40
20
0
1.0
0.8
0.0
0
20
40
Time (ms)
60
At present
In EXTRAP T2R RMPs are applied to study:
- effect on TM dynamics
br1,n (mT)
0.2
0.6
vOV (km/s)
0.4
Ip ()kA
m=1
n=-12
60
(present talk)
- effect on the plasma flow (wednsday talk)
0.4
0.2
0.0
80
40
20
0
80
v1,-12 (km/s)
br1,n (mT)
0.6
60
40
20
0
0
20
40
Time (ms)
60
TM dynamics with low RMP amplitude
Ip (kA)
Natural TM dynamics
(1,-12)
average of all other TMs
0.6
0.4
0.2
0.0
0
NO RMP
20
40
Time (ms)
0.6
0.4
0.2
0.0
20
40
Time (ms)
60
0.4
0.3
phase
p
p/2
0.1
2- velocity:
“modulated”
3p/2
p
p/2
0
40
30
20
10
0
40
30
20
10
0
w (krad/s)
0
19.65
Time (ms)
19.70
RMP effect on the
rotating TM:
1- amplitude:
“modulated”
0.2
2p
3p/2
19.60
RMP ≈ 0.3mT
0
bqm,n (mT)
bqm,n (mT)
100
80
60
40
20
0
60
0.6
0.5
0.4
0.3
0.2
0.1
2p
w (krad/s)
phase
100
80
60
40
20
0
br1,n (mT)
br1,n (mT)
Ip (kA)
TM DYNAMICS
14.68
14.70
14.72
14.74
Time (ms)
14.76
14.78
TM DYNAMICS with low RMP amplitude
TM amplitude and velocity are correlated
with the phase shift between TM and RMP
ampl.
suppression
Phenomenological explanation (wrong!)
bTM
ampl.
bq1,-12 (mT)
0.20
Toroidal angle
bRMP
0.15
=0
Df=
p
0.10
Toroidal angle
0.05
bTM
0.00
0
decel.
p/2
p 3p/2
Df
acceleration
2p
decel.
w (krad/s)
40
30
20
10
0
0
p/2
p 3p/2
Df
AMPLIFICATION
SUPPRESSION
2p
Toroidal angle
TM DYNAMICS with high RMP amplitude
0.6
0.5
br1,n (mT)
RMP ≈ 0.5mT
bq1,-12 (mT)
0.4
0.2
0.0
20
40
Time (ms)
60
0.6
0.5
0.4
0.3
0.2
0.1
2p
3p/2
0.3
0.2
0.1
1- High oscillation
with “complete” suppression
0.0
jump
0
p/2
p
3p/2
2p
p
3p/2
2p
Df
20
2- phase jumps
w (krad/s)
Df
bqm,n (mT)
0
0.4
p
p/2
0
15
10
w (krad/s)
5
25
20
15
10
5
0
29.10
0
0
p/2
Df
29.15
Time (ms)
29.20
MODELLING
Based on Fitzpatrick [Phys. Plasmas 8 4489 (2001)]
3 coupled partial differential equations:
1. TM evolution
Wc  c brRMP
W  c brTM
2. Torque balance
Viscous torque
with
b 
TM
r
braking torque due to eddy currents
In the wall generated by the rotating TM
3. Helical velocity
Poloidal section
EM torque
2
brTM brRMP
braking torque due to interaction
of the rotating TM with the static RMP
suppression
and
deceleration
suppression
and
acceleration
Amplification
and
deceleration
amplification
and
acceleration
MODELLING the LOW RMP case
ne(0)=0.9x1019m-3
TM amplitude is modulated
bq1,-12 (mT)
bq1,-12 (mT)
0.20
0.10
amplitude reduction in time
(not evident on this time scale)
0.00
3p/2
Df
0.15
0.10
0.05
0.00
0
p
p/2
0
TM velocity is modulated
30
20
10
velocity reduction in time
(not evident on this time scale)
0
0.00
p/2
p
3p/2
2p
p
3p/2
2p
Df
40
w (krad/s)
INITIAL CONDITIONS
w0=30krad/s
bqTM(0)=0.12mT
0.20
0.30
w (krad/s)
FREE PARAMETERS
tR=0.1ms
n=0.65 10-7 kg/(m∙s)
brRMP=0.3mT
0.02
0.04
0.06
Time (ms)
0.08
0.10
30
20
10
0
0
p/2
Df
Reasonable agreement between model and experiment
MODELLING the HIGH RMP case
ne(0)=0.9x1019m-3
0.50
0.40
0.50
TM amplitude is modulated
bq1,-12 (mT)
bq1,-12 (mT)
Df
0.30
0.20
0.10
0.00
0.30
0.20
0.10
3p/2
p
0.00
Phase jumps
p/2
0
0
p/2
0
p/2
Df
p
3p/2 2p
p
3p/2 2p
20
TM velocity is modulated
15
10
5
0
0.20
0.40
amplitude increases in time
w (krad/s)
INITIAL CONDITIONS
w0=50krad/s
bqTM(0)=0.01mT
w (krad/s)
FREE PARAMETERS
tR=0.1ms
n=0.65 10-7 kg/(m∙s)
brRMP=0.5mT
0.22
0.24
0.26 0.28
Time (ms)
0.30
15
10
5
0
Df
Reasonable agreement between model and experiment
TM LOCKING TO A RMP
-Low RMP amplitude  “weak” oscillation in the TM amplitude and velocity
-High RMP amplitude  “strong” modulation in the TM amplitude and phase jumps
IS IT ALWAYS SO SIMPLE?
EXPERIMENT
jumps
locking
oscillations
0.50
0.40
0.40
bq1,-12 (mT)
0.50
0.30
0.20
2p
2p
3p/2
3p/2
p
p
p/2
p/2
0
0
30.45
30.50
Time (ms)
30.55
jumps
locking
0.20
0.10
30.40
brRMP=0.4mT
0.30
0.10
Df
Df
bq1,-12 (mT)
oscillations
MODEL
brRMP=0.4mT
tR=0.1ms
n=0.65 10-7 kg/(m∙s)
ne(0)=0.9x1019m-3
w0=25krad/s
bqTM(0)=0.2mT
0.00
0.05
0.10
0.15
Time (ms)
0.20
0.20
SCALING OF THE TM DYNAMIC PROPERTIES
WITH THE RMP AMPLITUDE
0.50
time averaged amplitude
TM amplitude:
bq1,-12 (mT)
0.40
0.30
1- Suppression for “low” RMP amplitudes
0.20
2- Amplification for “high” RMP amplitudes
0.10
0.00
0.0
2p
0.2
0.4
0.6
1,-12
br
(mT)
0.8
1.0
Angle covered by the TM during one rotation
TM dynamics:
z
3p/2
1- Full rotation for “low” RMP amplitudes
p
2- Jumps for “high” RMP amplitudes
3- Locking for “very high” RMP amplitudes
p/2
0
0.0
0.2
0.4
0.6
1,-12
br
(mT)
0.8
1.0
SCALING OF THE TM DYNAMIC PROPERTIES
WITH THE RMP AMPLITUDE
0.50
time averaged amplitude
TM amplitude:
bq1,-12 (mT)
0.40
0.30
1- Suppression for “low” RMP amplitudes
0.20
2- Amplification for “high” RMP amplitudes
0.10
0.00
0.0
2p
0.2
0.4
0.6
1,-12
br
(mT)
0.8
1.0
Angle covered by the TM during one rotation
TM dynamics:
z
3p/2
1- Full rotation for “low” RMP amplitudes
p
2- Jumps for “high” RMP amplitudes
3- Locking for “very high” RMP amplitudes
p/2
0
0.0
0.2
0.4
0.6
1,-12
br
(mT)
0.8
1.0
CONCLUSIONS
• An external RMP can affect the rotating TM and the corresponding magnetic island
• The RMP produces:
TM amplitude amplification or suppression
depending on the phase shift
TM velocity acceleration or deceleration
• “Low” RMP amplitude  “weak” oscillation in the TM amplitude and velocity
• “High” RMP amplitude  “strong” modulation in the TM amplitude and phase jumps
• The locking to a RMP can be a complicated mechanism
• The Fitzpatrick model gives a reasonable explanation of these phenomena
It is a useful 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- …