two classes of rwms internally non- resonant with -11 ≤ n < 0 externally non- resonant...

1Alfven Laboratory Mode Control Workshop, Austin 2003

Intelligent shell experiments on EXTRAP T2R

EXTRAP T2R groupJ. R. Drake, Jenny-Ann Malmberg, Per Brunsell, Dmitriy Yadikin

Chalmers theory groupD. Gregoratto, Y. Liu, A. Bondeson

RFX R. Paccagnella, S. Ortolani, P. Martin, G. Manduchi + many others


Intelligent shell experiments on EXTRAP T2R

Outline of talk

1. Intro to RFP RWMs and motivation.

2. New RWM measurements on T2R

3. Description of T2R sensor and active coil arrays

4. Theory for feedback with partial shell coverage

5. First results with intelligent shell feedback applied

6. Plans for the future


Unstable modes in Extrap T2R

‘Internally resonanttearing modes’

‘Internally non-resonant’RWMs

‘Externally non-resonant’ RWMS

‘Externally resonant’

-14

-12-11

-10

+5

+4

-13

q0

q=0

q<0

qa

axis edge

Toroidal mode numbern for m=1 modes

m=0

Two classes of RWMs

Internally non-resonant with

-11 ≤ n < 0

Externally non-Resonant with

0 < n < 7


EXTRAP T2R front endNote:• The blue ”shell” surface• The spacing of the 64 TF coils


Suitability of EXTRAP T2R for resistive wall mode active control studies

1. -relaxation < -shell < -pulse.

2. Internally resonant modes are rotating so their b-radial perturbation is suppressed.

3. Extensive magnetic diagnostics to measure mode spectra and growth rates.

4. RWM perturbations measured at b-r / B-equilib ≈ 10-

3.

5. Both internally and externally non-resonant modes are

observed.

6. Growth rates are dependent on current density and pressure profiles.


Suitability of EXTRAP T2R for resistive wall mode active control studies (continued).

1. The surface where the saddle coils are installed is relatively accessable and well-defined.

2. Plasma current levels are low (<100 kA) so the power

requirements for the amplifiers for the active saddle coils is modest. Cheap loudspeaker amplifiers can

be used.


Active mode control methods studied.Collaboration Alfven Lab, Consorzio RFX

and Chalmers theory group.

1. Intelligent shell - Alfven Lab taking the lead

2. Mode analysis - RFX taking the lead

One sensor coil

One PID controller to freeze flux at zero

One active saddle coil coinciding with sensor coil

Sensor coil array

Real time mode analysis

Voltage output to an array of active saddle coils

SIMO controller


Relevance of resistive wall mode active control studies done on the T2R reversed-field pinch

1. The collaboration includes Anders Bondeson’s theory group at Chalmers and the RFX theory and

experiment groups. Emphasis is on comparison of theory and experiment.

2. There are features of feedback systems common for both the tokamak and the RFP i.e. The systems are based on fields produced by arrays of active external

coils interacting with plasma modes.

3. Role of field errors can be studied.


2 4 6 8 10

time (ms)

red: n = -2 Theoretically stable.-exp /-theory = negative Small initial amplitude.

green: n = -8Theoretically unstable. -exp /-theory = 1.3 Large initial amplitude.

blue : n = -10 Theoretically unstable. -exp /-theory = 1.5 Small initial amplitude.

Observed Growth rates (w) for three RWMS.

-9

-10

-11

Ip

80

60

40

20

0

logebn


2 4 6 8 10

time (ms)

n = -10(internally non res)

green: ”High ” equilibriumLower growth ratew= 1.4

blue :”Low ” equilibriumHigher growth ratew= 4.1

Observed Growth rates for n = -10 for two equilibria.

-9

-10

-11

Ip

80

60

40

20

0

logebn


2 4 6 8 10

time (ms)

n = +5

(externally non res)

green: ”High ” equilibriumHigher growth ratew= 1.9

blue :”Low ”StableNo growth

Observed Growth rates for n = +5 for two equilibria.

-9

-10

-11

Ip

80

60

40

20

0

logebn


n = -8• Unstable (Th & Exp)• Large ”initial”

amplitude• Mode phase is repro-

ducible in the lab frame

Observed phase of RWMs in fixed lab frame

n = -10• Unstable (Th & Exp)• Small ”initial”

amplitude• Mode phase is

random in the lab frame

• Slow rotation +

Five shots overlaid in each panel

2π8


n = -2• Theor stable - Exper

unstable• Small ”initial”

amplitude• Mode phase is repro-

ducible in the lab frame

Observed phase of RWMs in fixed lab frame

n = +5• Unstable (Th & Exp)• Small ”initial”

amplitude• Mode phase varies in

the lab frame• Sometimes slow

rotation


2π10


Low

• Some shot-to-shot variation.

• Amplitudes higher than the high case below.

Raw data m = 1 B-radial perturbation (inboard - outboard) at 8 ms into discharge


0 100˚ 200˚ 300˚ Toroidal angle

High

• No shot-to-shot variation (n = 8 domi-nated).

• Amplitudes lower than the low case above.


Summary of new experimental observations concerning RWM instabilities

1. For many theoretically unstable modes, the experimentally observed growth rates are fairly well described by theory including a dependence on equilibrium profiles.

2. Some theoretically stable modes are observed to be unstable (i.e. n = -2).

3. Concerning the role of field errors:

• Modes that have a high initial amplitude during the transient discharge start-up (i.e. n = -8), have

a fixed phase in the lab frame.

• The theoretically stable n = -2 mode has a fixed phase in the lab frame.


Feedback experiments underway on T2R1. Sensor coil array is in place in interspace between

vacuum vessel and shell.• 4 (poloidal) x 64 (toroidal)• saddle coils ”outboard-top-inboard-bottom”.

2. Active coils in place outside shell at eight toroidal positions.• coils are ”1/32” wide (i.e. double the width of

a sensor coil).• saddle coils ”outboard-top-inboard-bottom”.

3. ”m = 1” connected • Both sensor coils and saddle coils are series

connected (i.e. ”top & bottom” and ”inboard & outboard”).

4. Present active coil array covers 25% of surface.


61 62 63 64 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16

110-degree toroidal sector of T2R

toroidal direction

Polo

idal d

irecti

on

The frame of reference consists of 64 toroidal sectors numbered 1 to 64

337.5˚ 0˚ 28˚ 90˚

top

inboard

outboard

bottom

B-r sensor coils 4(poloidal) x 64 (toroidal) positions

diagnostic port sector outer shell weld shell gaps


61 62 63 64 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16


toroidal direction

Polo

idal d

irecti

on

The saddle coils for active feedback are twice the width of the sensor coils

337.5˚ 0˚ 28˚ 90˚

top

inboard

outboard

bottom

B-r sensor coils 4 (poloidal) x 64 (toroidal) positions


61 62 63 64 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16


toroidal direction

Polo

idal d

irecti

on

337.5˚ 0˚ 28˚ 90˚

top

inboard

outboard

bottom

Cartoon of an n = 8 mode


Theory for both intelligent shell control and mode control has been done. Assumptions for partial coverage feedback in the T2R RFP

1. Used T2R geometry and penetration times.But assume smooth resistive shell!

2. Assume B perturbation Fourier component information

corresponding to 4 x 32 sensor coils.

3. Use 4 x 8 active coils corresponding to actual coil geometry and partial coverage (side band

harmonics).

4. Consider only m = 1 nonresonant RW modes (i.e. zero

for resonant modes and higher m modes.

5. Examine both intelligent shell case and mode analysis/control case.


Theory for partial coverage feedback in an RFP

References:

1. Feedback control of resistive wall modes in RFPsPaccagnella, Gregoratto and BondesonNuc Fusion 42 (2002) pg 1102

2. Output feedback with 4 x 32 sensors and 4 x 8 coilsGregoratto, Paccagnella, Liu and BondesonManuscript


Features of the feedback theory

1. Assume Fourier component bn are known for themodes.

2. Eight active coil toroidal positions allows 8 control voltages Vn (n = -3,-2,-1,0,+1,+2,+3,+4)

3. Feedback law determines the 8 control voltages.

4. All the modes of interest are potentially ”controlled” (i.e. stabilised, destabilised, reduced growth rate, increased growth rate)

5. For intelligent shell case the gains in the feedback law

are equal and positive (i.e. negative feedback).

6. For mode control case gains in the feedback law are different and are optimised (can be positive

feedback).


Block diagram for the control of a single RWM

RFX figure


Experiments with anaog controlled intelligent shell have started

ControllerInput is m = 1 connected sensor coil pair

AmplifierOutput to m = 1 connected saddle coil pair

B-radial frozen at zero with feedback

B-radial grows without feedback

plasma current

B-radial

Active coil current

Vacuum vessel

Shell


Intelligent shell experiments

Unfortunately not all the controllers were ready as of last week. The first experiments have been done with 12 analog controllers.

This means that 6 of the 8 toroidal positions can be controlled.

First test:

Intelligent shell with 6 toroidal positions active which is equivalent to about 18% coverage).


Comparison of experiment with 6 toroidal positions and theory for 8 toroidal positions.

Summary of feedback theory for targeted moden = -8

Without feedback, the n = -8 mode is unstable and has a large initial amplitude.

The n = -8 mode should be stable for the intelligent shell controller at 8 toroidal positions.

The n = -8 should also be stable for the mode controller with active coils (1/32 wide) at 8 toroidal positions.


Partial intelligent shell. 6 toroidal positions - inboard/outboard+top/bottom (18% coverage)Green is without feedbackBlue is with feedback

With FB

n = -8

The initial amplitude is lower.

The growth rate is not changed.

The phase is unchanged.

Without FB

phase


n = -2 (impossible case)

The harmonics ”controlled” are n = -10, -2, +6, +14.

The n = -2 mode is theoretically stable but experimentally unstable.

The n = -10 and +6 modes are unstable both in theory and experiment. The n = +14 is stable in theory and experiment.

Feedback with partial coverage of 8 toroidal positions cannot stabilise all these modes.

For the intelligent shell controller, the n = -10 growth rate can be decreased but the n = -2 and n = +6 have higher growth rates and the n = 14 is destabilised!

The mode controller is better. However not all three unstable modes can be stabilised.



With FB n = -10

The initial amplitude is not changed.

The growth rate is not changed.

The phase is changed.

Without FB

phase



With FB

n = -2

The initial amplitude is slightly lower.

The growth rate is slightly increased (in agreeement with theory).

The phase is not changed.

Without FB

phase



With FB

n = +6

The initial amplitude is not changed.

The growth rate is slightly decreased (not in agreeement with theory).

The phase is not changed.

Without FB

phase


Test with 8 toroidal positions, but only inboard/outboard saddle coils activated.

Unexpected result:

The n = +6 mode is stabilised.

The other modes are only slightly changed.


Partial intelligent shell. 8 toroidal positions - inboard/outboard ( 12% coverage)Green is without feedbackBlue is with feedback

With FB

The n = +6 mode is stabilised.

b n = +6b n = -10

The n=-10 mode is slightly lower

Without FB

phase


Partial intelligent shell. 8 toroidal positions - inboard/outboard ( 12% coverage)Green is without feedbackBlue is with feedback

With FB

The n = -8 mode is unchanged..

b n = -8 b n = -10

The n=+14 mode has a higher amplitude

Without FB

phase



With FB

b-radial pertur-bation late in pulse.

Intelligent shell controllers at 6 toroidal positions indicated by vertical dashed line.

Without FB


Future experiments

With the present 8 toroidal position set up we will continue the studies and compare experiment with theory.

Both the intelligent shell controller and the RFX mode controller will be used (and compared with the analog IS).

For these studies destabilisation is as interesting as stabilisation since the goal is to verify that the theory models the relevant physics.

Study the field error effects.• initial amplitude.• destabilisation of a stable RWM.• phase.

Add more active coils. Next step is 50% coverage.

Use the flexibility of the RFX controller for mode rotation.

two classes of rwms internally non- resonant with -11 ≤ n < 0 externally non- resonant...

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