experiments and modeling on active rwm rotation in rfp plasmas
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S.C. Guo 13th IEA/RFP Workshop, October 9-11, 2008, Stockholm 1
Experiments and modeling on active RWM rotation in RFP plasmas
S.C. Guo, M. Baruzzo, T. Bolzonella, V. Igochine(*), G. Marchiori, A. Soppelsa, D. Yadikin(*), H. Zohm(*)
Consorzio RFX, Associazione Euratom-ENEA sulla fusione, Padova, Italy(*) Max-Planck Institut fur Plasmaphysik, EURATOM Association, Garching, Germany
S.C. Guo 13th IEA/RFP Workshop, October 9-11, 2008, Stockholm 2
Outline
Introduction
RWM active rotation: experimental issues
RWM active rotation: first results
RWM active rotation modelling
Conclusions and future work
S.C. Guo 13th IEA/RFP Workshop, October 9-11, 2008, Stockholm 3
Introduction
• Resistive Wall Modes (RWMs) are MHD instabilities common to many toroidal devices
growing on timescales that depend on the typical penetration time of the surrounding
passive boundary.
• In both tokamaks and RFPs they can be viewed as serious performance limiting
phenomena and for this reason studies on their very nature and, ultimately, on their
control are very important.
• In the tokamak case the stabilizing role played by plasma rotation is one of the most
important open issues for present and future devices.
• In the RFP case, numerical modelling suggested that only fluid rotation much faster
than the ones normally observed in present RFP experiments can provide a similar role,
but, also due to the lack of strong momentum input sources, experimental data are
missing.
• The new sets of experiments done on RFX-mod, and recently replicated on T2R, aim at
providing inputs on both fundamental RWM physics and new possible control strategies.
S.C. Guo 13th IEA/RFP Workshop, October 9-11, 2008, Stockholm 4
RWM in RFPs: stabilization by rotation
S.C. Guo, J. P. Freidberg and R. Nachtrieb,”Stability of resistive wall modes in reversed field pinches with longitudinal flow and dissipative effects”, PoP (1999)
• In the RFP configuration plasma velocities needed for RWM stabilization are very high. The required flow velocities have to reach kVo ≈ k//VA ≈ A.
• Active feedback control is then, when implemented, the only stabilising mechanism for the RFP.
S.C. Guo 13th IEA/RFP Workshop, October 9-11, 2008, Stockholm 5
The RFX-mod active control system
Actuators:192 active coils100% coverage of the mechanical structure external surfaceEach saddle coil is fed with its own power supplyInputs (real time):192 independent saddle sensors (Br) + 192 pickup coils (Bt, for variable radius control) + 192 coil currents (for sideband correction) independent control on m=0,1,2 (partial), -23<n<24
Software control:Full PID digital controller. For the present experiments, optimized Clean Mode Control scheme was used (control gains relative to single Fourier modes)
S.C. Guo 13th IEA/RFP Workshop, October 9-11, 2008, Stockholm 6
RWM characterisation and control
RWM experimental growth rates can be calculated with a high degree of reliability (e.g. (m=1, n=-5), F=-0.07 in left figure).
Comparison with models can be done during the free growth and the active control phases. In right figure eigenfunction calculations done solving Newcomb equation (P. Zanca)
0.1
1
10
0 0.05 0.1 0.15 0.2 0.25 0.3
18623 - n=-5
n-5n-5bis
y = 0.084842 * e^(15.786x) R= 0.9979
n-5
time
0
2
4
6
8
0 0.2 0.4 0.6
n=-6 control (shot 17304)
t=10 mst=30 mst=149 mst=155 mst=200 ms
Mod
e a
mp
(mT
)
r (m)
Shot 17304
n=-3 ÷ -6 control off control on
S.C. Guo 13th IEA/RFP Workshop, October 9-11, 2008, Stockholm 7
The idea (feedback rotation control)
Perfect control
Incomplete control
External field
Plasma field
Incomplete controlwith phase shift
Total field≠0
External field
Plasma fieldTotal field=0
External field
Plasma fieldTotal field≠0
S.C. Guo 13th IEA/RFP Workshop, October 9-11, 2008, Stockholm 8
Proportional gain scan on n=-6; phase 0; F=-0.08
Effect of a real proportional gain scan on (1,-6) RWM: (a) mode amplitudes,(b) mode phases.
Black full traces Gp=800 (full control), red squares Gp=200, cyan circles Gp=150 , blue diamonds Gp=100.
Note that an extremely good reproducibility of the RWM growth rate can be obtained under controlled experimental conditions.
Control from 130 ms
S.C. Guo 13th IEA/RFP Workshop, October 9-11, 2008, Stockholm 9
Phase scan at fixed (normal) Gp: 400 kA
Effect of a complex proportional gain scan on 400 kA discharges: (a) mode amplitudes;(b) mode phases.
Black full traces represent a reference shot where (1,-6) RWM is free to grow up to 0.13s and then is fully controlled.
Red squares and blue diamonds traces show the effect of the application of a complex proportional gains: the rotation of a selected RWM can be induced in both opposite directions (feedbackin action from 0.1s).
The induced rotation does not depend on the chosen direction.
S.C. Guo 13th IEA/RFP Workshop, October 9-11, 2008, Stockholm 10
Phase scan at fixed (normal) Gp: 600 kA
The induced rotation work in the same way at different plasma currents.
400 kA experiments
600 kA experiments
S.C. Guo 13th IEA/RFP Workshop, October 9-11, 2008, Stockholm 11
Induced rotation data analysis
•Special care: sensor measurements (and Fourier components) during the control are relative to plasma+external fields! The question is then: what is actually rotating?
•From total br measurements to plasma vs external fields
• External br field at the measurement radius obtained from coil currents (including mutual inductances and machine structure). Model developed by G. Marchiori and A. Soppelsa
• Plasma br field by subtraction
• Time evolution of external and plasma harmonics
(amplitude and phase)
S.C. Guo 13th IEA/RFP Workshop, October 9-11, 2008, Stockholm 12
Measurement components
Decomposition of the measured mode amplitude and phase into plasma and external field components:
-full black line: total Br (1,-6) as measured by the sensor arrays;
- blue diamonds: reconstructed plasma Br,
- red squares: reconstructed external Br applied by the active control system.
-2
0
2
0 0.1 0.2 0.3
(1,-
6) P
hs [
rad]
Time [s]
(b)
0
1
2
3
(1,-
6) A
mp
[mT
]
(a)
S.C. Guo 13th IEA/RFP Workshop, October 9-11, 2008, Stockholm 13
Modeling of induced rotation
•Since the mode rational surface is
outside the plasma, the usual torque
theory is not appropriate to be
applied
• the following simple model is
proposed:
Consider only one (m,n) mode in
cylidrical geometry,
, ,( , , , ) ( ) expm n m nr t r i m n t
m,n satisfies Newcomb’s equation with extended boundary condition at rb (resistive wall b), m,n (∞)=0
Inside plasma:
b,b
r
r
n,mb E
dr
dr
b
b
(without feedback coils)
C. G. Gimblett, Nuclear Fusion (1986)
n,mrn,m rb
S.C. Guo 13th IEA/RFP Workshop, October 9-11, 2008, Stockholm 14
Modeling of induced rotation
)r(ˆ)r(ˆ)t,r( ffbbn,m In the
vacuum:
,, ,
b
b
r
m nb b b b f f b b
r
dr E E idr
, 2 2 2, , 0 ,
f
f
r
m nf b b f f f f f
r
dr E E S m n I m ndr
,
ˆ i
i
r
ji j
r
d rE r
dr
, ,i j b f
1)( bob r
r i
S(m,n) -the coefficient related to the structure of the feedback coils
for the feedback circuit:
,,
,
ˆˆ 0
1b f
b b bf f f
E GE i
E i
( )ff b f f
dIL G R Idt
Dispersion relation for
, ,, ,
,
ˆ f b b fb b b b
f f
E EE E
E 2 2 20ˆ
ff
SGG m n
R
f f fL R
(including effects of resistive wall and complex gain)
' 'ˆ ( ) ( ) ( )j m j mr A kr I kr B kr K kr
(G=Gr+iGi)
S.C. Guo 13th IEA/RFP Workshop, October 9-11, 2008, Stockholm 15
Modeling of induced rotation
Re(G)=const. ; Im(G)= Re(G)Tang()Parameter in modelling:F=-0.05, =1.47, o=0.23
Without feedback,
0G
b
b,bE
With real gain , 0Gi
,,
,
ˆˆ 0
1b f
b b bf f f
E GE i
E i
1f
f,b
f,fb,brcr E
EEGG
if
≤ 0 for
With complex gain rcr GG and )tan(GG rci
)tan(E
b
b,br
S.C. Guo 13th IEA/RFP Workshop, October 9-11, 2008, Stockholm 16
Conclusions
•It was demonstrated for the first time in RFPs that the internal non-resonant resistive wall mode can be detached from the resistive wall in a controlled way.
• The observed constant rotation of the mode depends on the phase shift between external perturbations and the mode.
• It was experimentally confirmed that plasma rotation, plasma current and coupling to other modes have no impact on the rotation frequency of the RWM in the range explored.
• Similar experiments started on T2R will allow better understanding of the boundary condition influences (both passive conductors and software control)
• The proposed simple analytical model gives good description of the experimental results. This model can be further improved.
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