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Resistive Wall Mode Stability and Control in the Reversed Field Pinch
KTH, School of Electrical Engineering (EES), Centres, Alfvén Laboratory Centre for Space and Fusion Plasma Physics.
2006 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

Control of MHD instabilities using a conducting wall together with external magnetic fields is an important route to improved performance and reliability in fusion devices. Active control of MHD modes is of interest for both the Advanced Tokamak and the Reversed Field Pinch (RFP) configurations. A wide range of unstable, current driven MHD modes is present in the RFP. An ideally conducting wall facing the plasma can in principle provide stabilization to these modes. However, a real, resistive wall characterized by a wall field diffusion time, cannot stabilize the ideal MHD modes unless they rotate with Alfvénic velocity, which is usually not the case. With a resistive wall, the ideal modes are converted into resistive wall modes (RWM) with growth rates comparable to the inverse wall time. Resistive wall modes have been studied in the EXTRAP T2R thin shell RFP device. Growth rates have been measured and found in agreement with linear MHD stability calculations. An advanced system for active control has been developed and installed on the EXTRAP T2R device. The system includes an array of 128 active saddle coils, fully covering the torus surface. Experiments on EXTRAP T2R have for the first time demonstrated simultaneous active suppression of multiple independent RWMs. In experiments with a partial array, coupling of different modes due to the limited number of feedback coils has been observed, in agreement with theory. Different feedback strategies, such as the intelligent shell, the rotating shell, and mode control have been studied. Further, feedback operation with different types of magnetic field sensors, measuring either the radial or the toroidal field components have been compared

Place, publisher, year, edition, pages
Stockholm: KTH , 2006. , viii, 46 p.
Series
Trita-EE, ISSN 1653-5146 ; 2006:005
Keyword [en]
Resistive wall modes, RWM, active control, feedback, MHD modes, Reversed-Field pinch, RFP, intelligent shell, mode control
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
URN: urn:nbn:se:kth:diva-3867ISBN: 91-7178-285-0 (print)OAI: oai:DiVA.org:kth-3867DiVA: diva2:9793
Public defence
2006-03-17, H1, Teknikringen 33, Stockholm, 10:30
Opponent
Supervisors
Note
QC 20100929Available from: 2006-03-08 Created: 2006-03-08 Last updated: 2010-09-29Bibliographically approved
List of papers
1. Comparision of experimental resistive wall mode growth rates in the EXTRAP T2R reversed field pinch with linear theory
Open this publication in new window or tab >>Comparision of experimental resistive wall mode growth rates in the EXTRAP T2R reversed field pinch with linear theory
2003 (English)In: 30th Eruopean Physical Society Conference on Controlled Fusion and Plasma Physics: St. Petersburg 2003, 2003Conference paper, Published paper (Refereed)
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:kth:diva-5422 (URN)
Note
QC 20100929Available from: 2006-03-08 Created: 2006-03-08 Last updated: 2010-09-29Bibliographically approved
2. Resistive wall modes in the EXTRAP T2R reversed-field pinch
Open this publication in new window or tab >>Resistive wall modes in the EXTRAP T2R reversed-field pinch
2003 (English)In: Physics of Plasmas, ISSN 1070-664X, E-ISSN 1089-7674, Vol. 10, 3823- p.Article in journal (Refereed) Published
Abstract [en]

Resistive wall modes (RWM) in the reversed field pinch are studied and a detailed comparison of experimental growth rates and linear magnetohydrodynamic (MHD) theory is made. RWM growth rates are experimentally measured in the thin shell device EXTRAP T2R [P. R. Brunsell , Plasma Phys. Controlled Fusion 43, 1 (2001)]. Linear MHD calculations of RWM growth rates are based on experimental equilibria. Experimental and linear MHD RWM growth rate dependency on the equilibrium profiles is investigated experimentally by varying the pinch parameter Theta=B-theta(a)/<B-phi> in the range Theta=1.5-1.8. Quantitative agreement between experimental and linear MHD growth rates is seen. The dominating RWMs are the internal on-axis modes (having the same helicity as the central equilibrium field). At high Theta, external nonresonant modes are also observed. For internal modes experimental growth rates decrease with Theta while for external modes, growth rates increase with Theta. The effect of RWMs on the reversed-field pinch plasma performance is discussed.

Keyword
magnetohydrodynamic stability, shell, instabilities, configurations, rotation, distant, hbtx1c
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:kth:diva-5423 (URN)10.1063/1.1604775 (DOI)000185422500003 ()
Note
QC 20100929Available from: 2006-03-08 Created: 2006-03-08 Last updated: 2017-11-21Bibliographically approved
3. Feedback controller for saddle coils for suppression of resistive wall modes in EXTRAP T2R
Open this publication in new window or tab >>Feedback controller for saddle coils for suppression of resistive wall modes in EXTRAP T2R
Show others...
2004 (English)In: 31st European Physical Society Conference on Controlled Fusion and Plasma Physics, 2004Conference paper, Published paper (Refereed)
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:kth:diva-5424 (URN)
Note
QC 20100929Available from: 2006-03-08 Created: 2006-03-08 Last updated: 2010-09-29Bibliographically approved
4. Feedback Stabilization of Multiple Resistive Wall Modes
Open this publication in new window or tab >>Feedback Stabilization of Multiple Resistive Wall Modes
Show others...
2004 (English)In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 93, no 22, 225001- p.Article in journal (Refereed) Published
Abstract [en]

Active feedback stabilization of multiple independent resistive wall modes is experimentally demonstrated in a reversed-field pinch plasma. A reproducible simultaneous suppression of several nonresonant resistive wall modes is achieved. Coupling of different modes due to the limited number of the feedback coils is observed in agreement with theory. The feedback stabilization of nonresonant RWMs also has an effect on tearing modes that are resonant in the central plasma, leading to a significant prolongation of the discharge pulse.

Keyword
Feedback coils, Feedback stabilization, Multiple resistive wall modes, Reversed-field pinch (RFP)
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:kth:diva-5425 (URN)10.1103/PhysRevLett.93.225001 (DOI)000225326300028 ()2-s2.0-42749106489 (Scopus ID)
Note
QC 20100915Available from: 2006-03-08 Created: 2006-03-08 Last updated: 2017-11-21Bibliographically approved
5. Experimental and theoretical studies of active control of resistive wall mode growth in the EXTRAP T2R reversed-field pinch
Open this publication in new window or tab >>Experimental and theoretical studies of active control of resistive wall mode growth in the EXTRAP T2R reversed-field pinch
Show others...
2005 (English)In: Nuclear Fusion, ISSN 0029-5515, E-ISSN 1741-4326, Vol. 45, no 7, 557-564 p.Article in journal (Refereed) Published
Abstract [en]

Active feedback control of resistive wall modes (RWMs) has been demonstrated in the EXTRAP T2R reversed-field pinch experiment. The control system includes a sensor consisting of an array of magnetic coils (measuring mode harmonics) and an actuator consisting of a saddle coil array (producing control harmonics). Closed-loop (feedback) experiments using a digital controller based on a real time Fourier transform of sensor data have been studied for cases where the feedback gain was constant and real for all harmonics (corresponding to an intelligent-shell) and cases where the feedback gain could be set for selected harmonics, with both real and complex values (targeted harmonics). The growth of the dominant RWMs can be reduced by feedback for both the intelligent-shell and targeted-harmonic control systems. Because the number of toroidal positions of the saddle coils in the array is half the number of the sensors, it is predicted and observed experimentally that the control harmonic spectrum has sidebands. Individual unstable harmonics can be controlled with real gains. However if there are two unstable mode harmonics coupled by the sideband effect, control is much less effective with real gains. According to the theory, complex gains give better results for (slowly) rotating RWMs, and experiments support this prediction. In addition, open loop experiments have been used to observe the effects of resonant field errors applied to unstable, marginally stable and robustly stable modes. The observed effects of field errors are consistent with the thin-wall model, where mode growth is proportional to the resonant field error amplitude and the wall penetration time for that mode harmonic.

Keyword
Computer simulation, Control systems, Feedback, Fourier transforms, Harmonic analysis, Magnetohydrodynamics, Mathematical models, Perturbation techniques, Pinch effect, Plasma theory, Vacuum
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:kth:diva-5426 (URN)10.1088/0029-5515/45/7/002 (DOI)000231000300003 ()2-s2.0-22644431572 (Scopus ID)
Note
QC 20100914Available from: 2006-03-08 Created: 2006-03-08 Last updated: 2017-11-21Bibliographically approved
6. Feedback stabilization of resistive wall modes in a reversed-field pinch
Open this publication in new window or tab >>Feedback stabilization of resistive wall modes in a reversed-field pinch
Show others...
2005 (English)In: Physics of Plasmas, ISSN 1070-664X, E-ISSN 1089-7674, Vol. 12, no 9, 092508- p.Article in journal (Refereed) Published
Abstract [en]

An array of saddle coils having Nc =16 equally spaced positions along the toroidal direction has been installed for feedback control of resistive wall modes (RWMs) on the EXTRAP T2R reversed-field pinch [P. R. Brunsell, H. Bergsaker, M. Cecconello, Plasma Phys. Controlled Fusion 43, 1457 (2001)]. Using feedback, multiple nonresonant RWMs are simultaneously suppressed for three to four wall times. Feedback stabilization of RWMs results in a significant prolongation of the discharge duration. This is linked to a better sustainment of the plasma and tearing mode toroidal rotation with feedback. Due to the limited number of coils in the toroidal direction, pairs of modes with toroidal mode numbers n, n′ that fulfill the condition ∫n- n′ ∫ = Nc are coupled by the feedback action from the discrete coil array. With only one unstable mode in a pair of coupled modes, the suppression of the unstable mode is successful. If two modes are unstable in a coupled pair, two possibilities exist: partial suppression of both modes or, alternatively, complete stabilization of one target mode while the other is left unstable.

Keyword
Feedback, Feedback control, Plasmas, Resonance, Stability
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:kth:diva-5427 (URN)10.1063/1.2048168 (DOI)000232109000038 ()2-s2.0-27444433256 (Scopus ID)
Note
QC 20100915Available from: 2006-03-08 Created: 2006-03-08 Last updated: 2017-11-21Bibliographically approved
7. Active control of multiple resistive wall modes
Open this publication in new window or tab >>Active control of multiple resistive wall modes
Show others...
2005 (English)In: Plasma Physics and Controlled Fusion, ISSN 0741-3335, E-ISSN 1361-6587, Vol. 47, no 12 B, B25-B36 p.Article in journal (Refereed) Published
Abstract [en]

 A two-dimensional array of saddle coils at M-c poloidal and N-c toroidal positions is used on the EXTRAP T2R reversed-field pinch (Brunsell P R et al 2001 Plasma Phys. Control. Fusion 43 1457) to study active control of resistive wall modes (RWMs). Spontaneous growth of several RWMs with poloidal mode number m = 1 and different toroidal mode number n is observed experimentally, in agreement with linear MHD modelling. The measured plasma response to a controlled coil field and the plasma response computed using the linear circular cylinder MHD model are in quantitive agreement. Feedback control introduces a linear coupling of modes with toroidal mode numbers n, n' that fulfil the condition vertical bar n - n'vertical bar = N-c. Pairs of coupled unstable RWMs are present in feedback experiments with an array of Mc x Nc = 4 x 16 coils. Using intelligent shell feedback, the coupled modes are generally not controlled even though the field is suppressed at the active coils. A better suppression of coupled modes may be achieved in the case of rotating modes by using the mode control feedback scheme with individually set complex gains. In feedback with a larger array of Mc x Nc = 4 x 32 coils, the coupling effect largely disappears, and with this array, the main internal RWMs n = -11, -10, +5, +6 are all simultaneously suppressed throughout the discharge (7-8 wall times). With feedback there is a two-fold extension of the pulse length, compared to discharges without feedback.

Keyword
Electric coils; Feedback control; Growth (materials); Magnetohydrodynamics; Mathematical models; Plasmas
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-5428 (URN)10.1088/0741-3335/47/12B/S03 (DOI)000234420700005 ()2-s2.0-27744525924 (Scopus ID)
Note
QC 20100826Available from: 2006-03-08 Created: 2006-03-08 Last updated: 2017-11-21Bibliographically approved
8. Intelligent shell feedback control in EXTRAP T2R reversed field pinch with partial coverage of the toroidal surface by a discrete active coil array
Open this publication in new window or tab >>Intelligent shell feedback control in EXTRAP T2R reversed field pinch with partial coverage of the toroidal surface by a discrete active coil array
2006 (English)In: Plasma Physics and Controlled Fusion, ISSN 0741-3335, E-ISSN 1361-6587, Vol. 48, no 1, 1-14 p.Article in journal (Refereed) Published
Abstract [en]

An active feedback system is required for long pulse operation of the reversed field pinch (RFP) device to suppress resistive wall modes (RWMs). A general feature of a feedback system using a discrete active coil array is a coupling effect which arises when a set of side band modes determined by the number of active coils is produced. Recent results obtained on the EXTRAP T2R RFP demonstrated the suppression of independent m ≤ 1 RWMs using an active feedback system with a two-dimensional array of discrete active coils in the poloidal and toroidal directions. One of the feedback algorithms used is the intelligent shell feedback scheme. Active feedback systems having different number of active coils in the poloidal (Mc) and toroidal (N c) directions (Mc × Nc ≤ 2 × 32 and Mc × Nc ≤ 4 × 16) are studied. Different side band effects are seen for these configurations. A significant prolongation of the plasma discharge is achieved for the intelligent shell feedback scheme using the 2 × 32 active coil configuration. This is attributed to the side band sets including only one of the dominant unstable RWMs and avoiding coupling to resonant modes. Analog proportional-integral- derivative controllers are used in the feedback system. Regimes with different values of the proportional gain are studied. The requirement of the proportional-integral control for low proportional gain and proportional- derivative control for high proportional gain is seen in the experiments.

Keyword
Algorithms, Parallel processing systems, Plasma applications, Three term control systems
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:kth:diva-5429 (URN)10.1088/0741-3335/48/1/001 (DOI)000235451100002 ()2-s2.0-29244450166 (Scopus ID)
Note
QC 20100920Available from: 2006-03-08 Created: 2006-03-08 Last updated: 2017-11-21Bibliographically approved
9. Advanced feedback control methods in EXTRAP T2R
Open this publication in new window or tab >>Advanced feedback control methods in EXTRAP T2R
2006 (English)In: Physics of Plasmas, ISSN 1070-664X, E-ISSN 1089-7674, Vol. 13, no 7, 072109- p.Article in journal (Refereed) Published
Abstract [en]

Previous experiments in the EXTRAP T2R reversed field pinch device have shown the possibility of suppression of multiple resistive wall modes (RWM). A feedback system has been installed in EXTRAP T2R having 100% coverage of the toroidal surface by the active coil array. Predictions based on theory and the previous experimental results show that the number of active coils should be sufficient for independent stabilization of all unstable RWMs in the EXTRAP T2R. Experiments using different feedback schemes are performed, comparing the intelligent shell, the fake rotating shell, and the mode control with complex feedback gains. Stabilization of all unstable RWMs throughout the discharge duration of t(d)approximate to 10 tau(w) is seen using the intelligent shell feedback scheme. Mode rotation and the control of selected Fourier harmonics is obtained simultaneously using the mode control scheme with complex gains. Different sensor signals are studied. A feedback system with toroidal magnetic field sensors could have an advantage of lower feedback gain needed for the RWM suppression compared to the system with radial magnetic field sensors. In this study, RWM suppression is demonstrated, using also the toroidal field component as a sensor signal in the feedback system.

Keyword
Electric discharges; Feedback control; Magnetic fields; Sensors; Stabilization; Surface properties
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-5430 (URN)10.1063/1.2241980 (DOI)000239424400010 ()2-s2.0-33746926012 (Scopus ID)
Note
QC 20100826. Ändrat från submitted till published (20100826)Available from: 2006-03-08 Created: 2006-03-08 Last updated: 2017-11-21Bibliographically approved

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