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3. Attraction Region of Planar Linear Systems with One Unstable Pole and Saturated Feedback

Author

Favez, J.-Y, Mullhaupt, Ph, Srinivasan, B., Bonvin, D., Favez, J.-Y, Mullhaupt, Ph, Srinivasan, B., and Bonvin, D.

Abstract

The bifurcation of the attraction region for planar systems with one stable and one unstable pole under a saturated linear state feedback is considered. The attraction region can have either an unbounded hyperbolic shape or be bounded by a limit cycle. An analytical condition, under which either of these boundary shapes occurs, is given with a formal proof. This condition is based on the relationship between the stable and unstable manifolds associated with secondary saddle equilibrium points, whose presence is caused by the saturation on the input

Published
2018

5. Feedback and rotational stabilization of resistive wall modes in ITER

Author

Liu, Yueqiang, primary, Bondeson, A, additional, Chu, M.S, additional, Favez, J.-Y, additional, Gribov, Y, additional, Gryaznevich, M, additional, Hender, T.C, additional, Howell, D.F, additional, Haye, R.J. La, additional, Lister, J.B, additional, Vries, P. de, additional, and Contributors, EFDA JET, additional

Published
2005
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7. An overview of results from the TCV tokamak

Author

Goodman, T.P, primary, Ahmed, S.M, additional, Alberti, S, additional, Andrèbe, Y, additional, Angioni, C, additional, Appert, K, additional, Arnoux, G, additional, Behn, R, additional, Blanchard, P, additional, Bosshard, P, additional, Camenen, Y, additional, Chavan, R, additional, Coda, S, additional, Condrea, I, additional, Degeling, A, additional, Duval, B.P, additional, Etienne, P, additional, Fasel, D, additional, Fasoli, A, additional, Favez, J.-Y, additional, Furno, I, additional, Henderson, M, additional, Hofmann, F, additional, Hogge, J.-P, additional, Horacek, J, additional, Isoz, P, additional, Joye, B, additional, Karpushov, A, additional, Klimanov, I, additional, Lavanchy, P, additional, Lister, J.B, additional, Llobet, X, additional, Magnin, J.-C, additional, Manini, A, additional, Marlétaz, B, additional, Marmillod, P, additional, Martin, Y, additional, Martynov, An, additional, Mayor, J.-M, additional, Mlynar, J, additional, Moret, J.-M, additional, Nelson-Melby, E, additional, Nikkola, P, additional, Paris, P.J, additional, Perez, A, additional, Peysson, Y, additional, Pitts, R.A, additional, Pochelon, A, additional, Porte, L, additional, Raju, D, additional, Reimerdes, H, additional, Sauter, O, additional, Scarabosio, A, additional, Scavino, E, additional, Seo, S.H, additional, Siravo, U, additional, Sushkov, A, additional, Tonetti, G, additional, Tran, M.Q, additional, Weisen, H, additional, Wischmeier, M, additional, Zabolotsky, A, additional, and Zhuang, G, additional

Published
2003
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8. Accessibility and properties of ELMy H-mode and ITB plasmas in TCV

Author

Martin, Y R, primary, Henderson, M A, additional, Alberti, S, additional, Amorim, P, additional, Andrebe, Y, additional, Appert, K, additional, Arnoux, G, additional, Behn, R, additional, Blanchard, P, additional, Bosshard, P, additional, Bottino, A, additional, Camenen, Y, additional, Chavan, R, additional, Coda, S, additional, Condrea, I, additional, Degeling, A W, additional, Dokouka, V N, additional, Duval, B P, additional, Fasel, D, additional, Fasoli, A, additional, Favez, J-Y, additional, Ferrando, S, additional, Goodman, T P, additional, Hogge, J-P, additional, Horacek, J, additional, Isoz, P, additional, Joye, B, additional, Karpushov, A, additional, Khayrutdinov, R R, additional, Klimanov, I, additional, Lister, J B, additional, Llobet, X, additional, Lukash, V E, additional, Madeira, T, additional, Marletaz, B, additional, Marmillod, P, additional, Martynov, A A, additional, Medvedev, S Yu, additional, Moret, J-M, additional, Nelson-Melby, E, additional, Nikkola, P, additional, Paris, P J, additional, Perez, A, additional, Pitts, R A, additional, Pochelon, A, additional, Porte, L, additional, Sauter, O, additional, Scarabosio, A, additional, Scavino, E, additional, Seo, S-H, additional, Siravo, U, additional, Tonetti, G, additional, Tran, M Q, additional, Villard, L, additional, Weisen, H, additional, Wischmeier, M, additional, Zabolotsky, A, additional, and Zhuang, G, additional

Published
2003
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9. Recent results from the electron cyclotron heated plasmas in Tokamak à Configuration Variable (TCV)

Author

Henderson, M. A., primary, Alberti, S., additional, Angioni, C., additional, Arnoux, G., additional, Behn, R., additional, Blanchard, P., additional, Bosshard, P., additional, Camenen, Y., additional, Coda, S., additional, Condrea, I., additional, Goodman, T. P., additional, Hofmann, F., additional, Hogge, J.-Ph., additional, Karpushov, A., additional, Manini, A., additional, Martynov, An., additional, Moret, J.-M., additional, Nikkola, P., additional, Nelson-Melby, E., additional, Pochelon, A., additional, Porte, L., additional, Sauter, O., additional, Ahmed, S. M., additional, Andrèbe, Y., additional, Appert, K., additional, Chavan, R., additional, Degeling, A., additional, Duval, B. P., additional, Etienne, P., additional, Fasel, D., additional, Fasoli, A., additional, Favez, J.-Y., additional, Furno, I., additional, Horacek, J., additional, Isoz, P., additional, Joye, B., additional, Klimanov, I., additional, Lavanchy, P., additional, Lister, J. B., additional, Llobet, X., additional, Magnin, J.-C., additional, Marlétaz, B., additional, Marmillod, P., additional, Martin, Y., additional, Mayor, J.-M., additional, Mylnar, J., additional, Paris, P. J., additional, Perez, A., additional, Peysson, Y., additional, Pitts, R. A., additional, Raju, D., additional, Reimerdes, H., additional, Scarabosio, A., additional, Scavino, E., additional, Seo, S. H., additional, Siravo, U., additional, Sushkov, A., additional, Tonetti, G., additional, Tran, M. Q., additional, Weisen, H., additional, Wischmeier, M., additional, Zabolotsky, A., additional, and Yhuang, G., additional

Published
2003
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10. ECH physics and new operational regimes on TCV

Author

Moret, J-M, primary, Ahmed, S M, additional, Alberti, S, additional, Andrebe, Y, additional, Appert, K, additional, Arnoux, G, additional, Behn, R, additional, Blanchard, P, additional, Bosshard, P, additional, Camenen, Y, additional, Chavan, R, additional, Coda, S, additional, Condrea, I, additional, Degeling, A, additional, Duval, B P, additional, Fasel, D, additional, Fasoli, A, additional, Favez, J-Y, additional, Goodman, T, additional, Henderson, M, additional, Hofmann, F, additional, Hogge, J-P, additional, Horacek, J, additional, Isoz, P, additional, Joye, B, additional, Karpushov, A, additional, Klimanov, I, additional, Lister, J B, additional, Llobet, X, additional, Madeira, T, additional, Magnin, J-C, additional, Manini, A, additional, Marl taz, B, additional, Marmillod, P, additional, Martin, Y, additional, Martynov, A, additional, Mayor, J-M, additional, Mlynar, J, additional, Nelson-Melby, E, additional, Nikkola, P, additional, Paris, P J, additional, Perez, A, additional, Peysson, Y, additional, Pitts, R A, additional, Pochelon, A, additional, Porte, L, additional, Sauter, O, additional, Scarabosio, A, additional, Scavino, E, additional, Seo, S-H, additional, Siravo, U, additional, Sushkov, A, additional, Tonetti, G, additional, Tran, M Q, additional, Weisen, H, additional, Wischmeier, M, additional, Zabolotsky, A, additional, and Zhuang, G, additional

Published
2002
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12. Stability and energy confinement of highly elongated plasmas in TCV

Author

Hofmann, F, primary, Behn, R, additional, Coda, S, additional, Goodman, T P, additional, Henderson, M, additional, Lavanchy, P, additional, Marmillod, Ph, additional, Martin, Y, additional, Martynov, A, additional, Mlynar, J, additional, Moret, J-M, additional, Pochelon, A, additional, Reimerdes, H, additional, Sauter, O, additional, Alberti, S, additional, Angioni, C, additional, Appert, K, additional, Bakos, J, additional, Blanchard, P, additional, Bosshard, P, additional, Chavan, R, additional, Condrea, I, additional, Degeling, A, additional, Duval, B P, additional, Fasel, D, additional, Favez, J-Y, additional, Favre, A, additional, Furno, I, additional, Gomez, P, additional, Gorgerat, P, additional, Hogge, J-P, additional, Isoz, P-F, additional, Joye, B, additional, Klimanov, I, additional, Lister, J B, additional, Llobet, X, additional, Magnin, J-C, additional, Manini, A, additional, Marlétaz, B, additional, Mayor, J-M, additional, Nikkola, P, additional, Paris, P J, additional, Perez, A, additional, Pietrzyk, Z A, additional, Piffl, V, additional, Pitts, R A, additional, Scarabosio, A, additional, Scavino, E, additional, Sushkov, A, additional, Tonetti, G, additional, Tran, M Q, additional, Weisen, H, additional, and Zabolotsky, A, additional

Published
2001
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13. Overview of TCV results

Author

Weisen, H., primary, Alberti, S., additional, Angioni, C., additional, Appert, K., additional, Bakos, J., additional, Behn, R., additional, Blanchard, P., additional, Bosshard, P., additional, Chavan, R., additional, Coda, S., additional, Condrea, I., additional, Degeling, A., additional, Duval, B.P., additional, Fasel, D., additional, Favez, J.-Y., additional, Favre, A., additional, Furno, I., additional, Gomez, P., additional, Goodman, T.P., additional, Henderson, M.A., additional, Hofmann, F., additional, Kayruthdinov, R.R., additional, Lavanchy, P., additional, Lister, J.B., additional, Llobet, X., additional, Loarte, A., additional, Lukash, V.E., additional, Gorgerat, P., additional, Hogge, J.-P., additional, Isoz, P.-F., additional, Joye, B., additional, Magnin, J.-C., additional, Manini, A., additional, Marlétaz, B., additional, Marmillod, P., additional, Martin, Y., additional, Martynov, A., additional, Mayor, J.-M., additional, Minardi, E., additional, Mlynar, J., additional, Moret, J.-M., additional, Nikkola, P., additional, Paris, P.J., additional, Perez, A., additional, Peysson, Y., additional, Pietrzyk, Z.A., additional, Piffl, V., additional, Pitts, R.A., additional, Pochelon, A., additional, Reimerdes, H., additional, Rommers, J.H., additional, Sauter, O., additional, Scavino, E., additional, Sushkov, A., additional, Tonetti, G., additional, Tran, M.Q., additional, and Zabolotsky, A., additional

Published
2001
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15. Steady-state fully noninductive operation with electron cyclotron current drive and current profile control in the tokamak à configuration variable (TCV)

Author

Sauter, O., primary, Angioni, C., additional, Coda, S., additional, Gomez, P., additional, Goodman, T. P., additional, Henderson, M. A., additional, Hofmann, F., additional, Hogge, J.-P., additional, Moret, J.-M., additional, Nikkola, P., additional, Pietrzyk, Z. A., additional, Weisen, H., additional, Alberti, S., additional, Appert, K., additional, Bakos, J., additional, Behn, R., additional, Blanchard, P., additional, Bosshard, P., additional, Chavan, R., additional, Condrea, I., additional, Degeling, A., additional, Duval, B. P., additional, Fasel, D., additional, Favez, J.-Y., additional, Favre, A., additional, Furno, I., additional, Kayruthdinov, R. R., additional, Lavanchy, P., additional, Lister, J. B., additional, Llobet, X., additional, Lukash, V. E., additional, Gorgerat, P., additional, Isoz, P.-F., additional, Joye, B., additional, Magnin, J.-C., additional, Manini, A., additional, Marlétaz, B., additional, Marmillod, P., additional, Martin, Y. R., additional, Martynov, An., additional, Mayor, J.-M., additional, Minardi, E., additional, Mlynar, J., additional, Paris, P. J., additional, Perez, A., additional, Peysson, Y., additional, Piffl, V., additional, Pitts, R. A., additional, Pochelon, A., additional, Reimerdes, H., additional, Rommers, J. H., additional, Scavino, E., additional, Sushkov, A., additional, Tonetti, G., additional, Tran, M. Q., additional, and Zabolotsky, A., additional

Published
2001
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16. Improving tokamak vertical position control in the presence of power supply voltage saturation

Author

Favez, J. Y., Lister, J. B., Müllhaupt, Philippe, and Srinivasan, B.

Subjects
JET, ITER
Abstract

The control of the current, position and shape of an elongated cross-section tokamak plasma is complicated by the so-called instability of the current vertical position. Linearized models all share the feature of a single unstable eigenmode, attributable to this vertical instability of the plasma equilibrium movement, and a large number of stable or marginally stable eigenmodes, attributable to zero or positive resistance in all other model circuit equations. Due to the size and therefore cost of the ITER tokamak, there will naturally be smaller margins in the poloidal field coil power supplies, implying that the feedback control will experience actuator saturation during large transients due to a variety of plasma disturbances. Current saturation is relatively benign, due to the integrating nature of the tokamak, resulting in a reasonable time horizon for strategically handling the approach to saturation which leads to the loss of one degree of freedom in the feedback control for each saturated coil. On the other hand, voltage saturation is produced. by the feedback controller itself, with no intrinsic delay. This paper presents a feedback controller design approach which explicitly takes saturation of the power supply voltage into account when producing the power supply demand signals. We consider the vertically stabilizing part of the ITER controller (fast controller) with one power supply and therefore a single saturated input. We. consider an existing ITER controller and enlarge its region of attraction to the full null controllable region by adding a continuous nonlinearity into the control. In a system with a single unstable eigenmode and a single stable eigenmode we have already provided a proof of the asymptotical stability of the closed loop system, and we have examined the performance of this new continuous nonlinear controller. We have subsequently extended this analysis to a system with a single eigenmode and multiple stable eigenmodes. The method requires state feedback control, and therefore a reconstruction of the states is indispensable. We discuss the feasibility of extracting these states from the available diagnostic information as well as other implementation details. As a complement to our ITER simulations we confirm the enlargement of the region of attraction by the new controller by a JET simulation.

18. Stability and energy confinement of highly elongated plasmas in TCV

Author

Hofmann, F., Behn, R., Coda, S., Goodman, T. P., Henderson, M., Lavanchy, P., Marmillod, P., Martin, Y., Martynov, A., Jan Mlynář, Moret, J. M., Pochelon, A., Reimerdes, H., Sauter, O., Alberti, S., Angioni, C., Appert, K., Bakos, J., Blanchard, P., Bosshard, P., Chavan, R., Condrea, I., Degeling, A., Duval, B. P., Fasel, D., Favez, J. Y., Favre, A., Furno, I., Gomez, P., Gorgerat, P., Hogge, J. P., Isoz, P. F., Joye, B., Klimanov, I., Lister, J. B., Llobet, X., Magnin, J. C., Manini, A., Marletaz, B., Mayor, J. M., Nikkola, P., Paris, P. J., Perez, A., Pietrzyk, Z. A., Piffl, V., Pitts, R. A., Scarabosio, A., Scavino, E., Sushkov, A., Tonetti, G., Tran, M. Q., Weisen, H., and Zabolotsky, A.

Subjects
Physics::Plasma Physics
Abstract

The operating space of the TCV tokamak has been extended to higher elongation, kappa = 2.8, and higher normalized current, I-N = I-p/aB = 3.6MA/mT, than were previously attainable. This has been achieved by optimizing the parameters of the vertical position control system and by optimizing the plasma shape. Experimental current and beta limits were found to be consistent with ideal MHD stability calculations, using measured plasma shapes and profiles. The sawtooth period was measured as a function of elongation and sawtooth oscillations are found to disappear, at high elongation, when the internal inductance drops below l(i) similar to 0.69. MHD events at high elongation have been analysed, using magnetic fluctuation measurements. The electron energy confinement time at high elongation, 2.2 < kappa < 2.7, shows a strong dependence on density and power flux through the plasma surface, but no statistically significant dependence on K. Finally, we have applied off-axis, second harmonic, X-mode electron cyclotron resonance heating (ECRH) in order to flatten the current profile and improve vertical stability. This gave access to previously inaccessible domains in kappa-IN space.

19. Feedback and rotational stabilization of resistive wall modes in ITER

Author

Liu, Y. Q., Bondeson, A., Chu, M. S., Favez, J. Y., Gribov, Y., Gryaznevich, M., Hender, T. C., Howell, D. R., La Haye, R. J., Lister, J. B., and de Vries, P.

Subjects
JET, ITER
Abstract

Different models have been introduced in the stability code MARS-F in order to study the damping effect on resistive wall modes (RWM) in rotating plasmas. Benchmarks of MARS-F calculations with RWM experiments on JET and DIII-D indicate that the semi-kinetic damping model is a good candidate for explaining the damping mechanisms. Based on these results, the critical rotation speeds required for RWM stabilization in advanced ITER scenarios are predicted. Active feedback control of the n = 1 RWM in ITER is also studied using the MARS-F code.

20. Accessibility and properties of ELMy H-mode and ITB plasmas in TCV

Author

Martin, Y. R., Henderson, M. A., Alberti, S., Amorim, P., Andrebe, Y., Appert, K., Arnoux, G., Behn, R., Blanchard, P., Bosshard, P., Bottino, A., Camenen, Y., Chavan, R., Coda, S., Condrea, I., Degeling, A. W., Dokouka, V. N., Duval, B. P., Fasel, D., Fasoli, A., Favez, J. -Y, Ferrando, S., Goodman, T. P., Hogge, J. -P, Horacek, J., Isoz, P., Joye, B., Karpushov, A., Khayrutdinov, R. R., Klimanov, I., Lister, J. B., Llobet, X., Lukash, V. E., Madeira, T., Marletaz, B., Marmillod, P., Martynov, A. A., Sergey Medvedev, Moret, J. -M, Nelson-Melby, E., Nikkola, P., Paris, P. J., Perez, A., Pitts, R. A., Pochelon, A., Porte, L., Sauter, O., Scarabosio, A., Scavino, E., Seo, S. -H, Siravo, U., Tonetti, G., Tran, M. Q., Villard, L., Weisen, H., Wischmeier, M., Zabolotsky, A., and Zhuang, G.

Abstract

This paper presents experimental results on the accessibility and the properties of plasmas with improved confinement in TCV. First, the H-mode threshold power is measured in Ohmic plasmas. Above an Ohmic threshold density, the threshold power increases with the density. A lower threshold density is found when additional electron cyclotron heating (ECH) is applied. At these low densities, the threshold power increases dramatically with decreasing density. Only a small fraction of the wide operational domain leading to the Ohmic H-mode is found to lead to a stationary regime with edge localized modes (ELMs). The ELMs have an irregular frequency, but in TCV they can be triggered by an external magnetic perturbation that induces a rapid vertical movement of the plasma. With this perturbation, the ELM frequency can be increased. The ELM triggering mechanism is provided by the vertical movement of the plasma away from the X-point of a single null configuration. This movement induces a positive current at the plasma edge, and we deduce that the ELMs are being controlled by this modification of the plasma edge current. Electron internal transport barriers (eITBs) are produced deep in the plasma during the stationary phase of TCV discharges. Different scenarios of ECH or selectron cyclotron current drive (ECCD) at different radial locations have been used to obtain eITBs with and without inductively driven current. The eITBs are characterized by steep electron temperature gradients, high confinement improvement and a large fraction of bootstrap current. In plasmas with fully non-inductively driven current the size and the strength of the eITB are controlled by the location of the power deposition and by the co- or counter-direction of the central ECCD. Finally, a small inductive perturbation of an otherwise non-inductively driven plasma current profile progressively shrinks the eITB, confirming the link between current profiles and eITBs.

22. Attraction Region of Planar Linear Systems with One Unstable Pole and Saturated Feedback

Author

Favez, J.-Y, Mullhaupt, Ph, Srinivasan, B., Bonvin, D., Favez, J.-Y, Mullhaupt, Ph, Srinivasan, B., and Bonvin, D.

Abstract

The bifurcation of the attraction region for planar systems with one stable and one unstable pole under a saturated linear state feedback is considered. The attraction region can have either an unbounded hyperbolic shape or be bounded by a limit cycle. An analytical condition, under which either of these boundary shapes occurs, is given with a formal proof. This condition is based on the relationship between the stable and unstable manifolds associated with secondary saddle equilibrium points, whose presence is caused by the saturation on the input

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