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RFP equilibrium

3. RFP equilibrium. The reversed field pinch magnetic equilibrium. RFP configuration. RFX-RFP configuration. RFX coils. toroidal magnetic field. poloidal magnetic field. induction of plasma current. mean magnetic field radial profiles. Tokamak and RFP profiles.

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RFP equilibrium

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  1. 3 RFP equilibrium

  2. The reversed field pinch magnetic equilibrium ORNL Colloquium – September 10th, 2009

  3. RFP configuration RFX-RFP configuration RFX coils toroidal magnetic field poloidal magnetic field induction of plasma current mean magnetic field radial profiles

  4. Tokamak and RFP profiles European Ph.D. course . - Garching 29.09.08) p.martin

  5. safety factor profiles in tok and RFP European Ph.D. course . - Garching 29.09.08) p.martin

  6. RFP B profile European Ph.D. course . - Garching 29.09.08) p.martin

  7. The reversed field pinch • Pinch configuration, with low magnetic field The toroidal field is 10 times smaller than in a tokamak with similar current Reactor issues: normal magnets, low force at the coils, high mass power density, no additional heating European Ph.D. course . - Garching 29.09.08) p.martin

  8. European Ph.D. course . - Garching 29.09.08) p.martin

  9. The reversed field pinch • Pinch configuration, with low magnetic field • Bp and Bthave comparable amplitude and Btreverses direction at the edge • Resonances in RFP : • low m (0-2) • high n (2*R/a) Safety factor European Ph.D. course . - Garching 29.09.08) p.martin

  10. The reversed field pinch • Pinch configuration, with low magnetic field • Bp and Bthave comparable amplitude and Btreverses direction at the edge • Most of the RFP magnetic field is generated by current flowing in the plasma Magnetic self-organization (dynamo) European Ph.D. course . - Garching 29.09.08) p.martin

  11. RFP dynamo 1 What we mean with “RFP dynamo effect ” 1/2 Ohm’s law Bz Bq at reversal Induction equation !! Jz Jq stationariety !!inconsistency

  12. RFP dynamo 2 What we mean with “RFP dynamo effect ” : 2/2 to resolve the previous inconsistency we need an “additional” mean electric field with respect to the one provided by mean B and mean v fields, i.e. -within resistive MHD- the contribution by coherent modulation of B and v: Edynamo = < v /\ B > In other words: Edynamo • Edynamo allows us to balance Ohm’s law • justifying that in stationary conditions: • less mean Jz is driven in the core • more mean Jq is driven in the edge • then expected by externally applied E.

  13. 4 About stability and its implication for RFP

  14. The basic destabilizing forces arise from: • Current density • Pressure gradients, combined with adverse magnetic field curvature • The resulting instabilities are divided in two categories • Ideal modes, i.e. instabilities which would occurr even if the plasma were perfectly conducting • Resistive modes, which are dependent on the finite resistivity of the plasma European Ph.D. course . - Garching 29.09.08) p.martin

  15. European Ph.D. course . - Garching 29.09.08) p.martin

  16. European Ph.D. course . - Garching 29.09.08) p.martin

  17. European Ph.D. course . - Garching 29.09.08) p.martin

  18. European Ph.D. course . - Garching 29.09.08) p.martin

  19. External Kink mode European Ph.D. course . - Garching 29.09.08) p.martin

  20. External Kink mode European Ph.D. course . - Garching 29.09.08) p.martin

  21. Current driven kink European Ph.D. course . - Garching 29.09.08) p.martin

  22. m=1 kink in tokamak European Ph.D. course . - Garching 29.09.08) p.martin

  23. Kruskal Shafranov limit for tokamak European Ph.D. course . - Garching 29.09.08) p.martin

  24. m=1, n =-5 m=1, n =-6 m=1, n=-7 m=1, n=-8 m=1, n=-9 m=0, all n MHD modes in RFP q (r) Resistive Wall Modes Tearing Modes Resistive Wall Modes m=1, n > 0 r (m) European Ph.D. course . - Garching 29.09.08) p.martin

  25. RFP stability diagram for m=1 modes European Ph.D. course . - Garching 29.09.08) p.martin

  26. RFP linear stability European Ph.D. course . - Garching 29.09.08) p.martin

  27. European Ph.D. course . - Garching 29.09.08) p.martin

  28. European Ph.D. course . - Garching 29.09.08) p.martin

  29. European Ph.D. course . - Garching 29.09.08) p.martin

  30. European Ph.D. course . - Garching 29.09.08) p.martin

  31. European Ph.D. course . - Garching 29.09.08) p.martin

  32. 5 MHD stability: its implication on RFP self-organization and its active control

  33. Electric field in the RFP • The RFP is an ohmically driven system: an inductive toroidal electric field, produced by transformer effect, continuously feeds energy into the plasma • Ohm’s law mismatch: the electrical currents flowing in a RFP can not be directly driven by the inductive electric field Eo overdriven ..but stationary ohmic RFP are routinely produced for times longer than the resistive diffusion time underdriven

  34. The RFP dynamo electric field • An additional electric field, besides that externally applied, is necessary to sustain and amplify the toroidal magnetic flux. • A Lorentz contribution v x B is necessary, which implies the existence of a self-organized velocity field in the plasma. Edynamo Edynamo

  35. The old paradigm: Multiple Helicity (MH) RFP • the safety factor q << 1 and the central peaking of the current density combine to destabilize MHD resistive instabilities. • For a long time a broad spectrum of MHD resistive instabilities ( m=0 and m=1, variable n ( “multiple helicity” –MH – spectrum), was considered a high, but necessary, price to pay for the sustainment of the configuration through the “dynamo” mechanism. br spectrum

  36. Wide k-spectrum  bulging in the physical space A wide spectrum of m=0 and m=1 modes can produce severe plasma-wall interaction if the modes lock in phase and to the wall ! • …

  37. At the leading edge of active stability control 192 coils arranged in 48 toroidal positions cover the whole plasma surface Each is independently driven (60 turns, 650 V x 400 A) Digital controller elaborates real-time 576 inputs RFX-mod has the best feedback system for real time control of MHD stability ever realized for a fusion device Full stabilization of multiple RWMs and control of individual tearing modes achieved in RFX-mod and EXTRAP T2-R Demonstrates that a thick stabilizing shell is NOT needed Strong integration between physics and control engineering key for success ORNL Colloquium – September 10th, 2009

  38. Feedback Control System Architecture Sensors: br, b, Icoil bEXT plasma 50 ms thin shell 576 INPUTS: 192br, 192b, 192Icoil 192 power amplifiers Each coil independently controlled Digital Controller: 7 computing nodes 2 Gflop/s computing power Cycle frequency = 2.5 kHz cycle latency (≤ 400 s). OUTPUTS: 192 Iref ORNL Colloquium – September 10th, 2009

  39. MHD stability feedback control • Full stabilization of multiple resistive wall modes in presence of a thin shell (and RWM physics/code benchmarking) • Control and tailoring of core resonant tearing modes – mitigation of mode-locking • Test of new algorithms and models for feedback control • Design of mode controllers EXPERIMENTAL PROPOSALS FOR 2009 FROM IPP (AUG), DIII-D, JT60-SA RFX PERFORMANCE IMPROVEMENT CONTRIBUTION TO THE GENERAL ISSUE OF MHD STABILITY ACTIVE CONTROL ORNL Colloquium – September 10th, 2009

  40. Steady progress in performance in a reliable device • Fully reliable MHD stability control system spring 2009 - unoptimized upgraded MHD active control: 2008 with MHD active control: 2006 no MHD active contro 2004 ORNL Colloquium – September 10th, 2009

  41. The value of flexibility: high perfomance RFP,…but not only RFP • Exploration of high current RFP allows for the discovery of new physics, with structural changes • ..but RFX can be run as a 150 kA Tokamak A test bed for MHD feedback control TOKAMAK Princeton Plasma Physics Laboratory Colloquium - June 4th, 2009

  42. Full control of a (2,1) mode in a ramped tokamak Follows an idea realized in DIII-D on a proposal by In, Okabayashi, et al (with RFX participation) Okabayashi et al., paper EX/P9-5 2008 IAEA FEC, Geneva RED: feedback OFF BLACK: feedback ON (Cavazzana, Marrelli, et al. 2009) ORNL Colloquium – September 10th, 2009

  43. RWM active rotation experiment: setup • 2 control time windows: • FIRST: the mode is not controlled • SECOND: the mode is initially feedback controlled with a pure real proportional gain. Gain scan performed (to obtain constant RWM amplitude) • The external field is always opposing the plasma error field with the same helicity and no net force is present to induce a controlled rotation. Byproduct: simulation of feedback control systems with not enough power to cope with the growth of the selected instability. Princeton Plasma Physics Laboratory Colloquium - June 4th, 2009

  44. Feedback rotation control principle Plasma field Perfect control Total field=0 External field Plasma field Incomplete control Total field≠0 External field Princeton Plasma Physics Laboratory Colloquium - June 4th, 2009

  45. Complex gains (k+ i) can be used Plasma field Perfect control Total field=0 External field Plasma field Incomplete control Total field≠0 External field Plasma field Incomplete control with phase shift Total field≠0 External field Princeton Plasma Physics Laboratory Colloquium - June 4th, 2009

  46. Advanced RWM control and mode un-locking Active rotation of non-resonant wall-locked RWM is induced by applying complex gains (keeping the mode at the desired constant amplitude) RWM amplitude RWM phase Bolzonella, Igochine et al, PRL 08 Princeton Plasma Physics Laboratory Colloquium - June 4th, 2009 2008 IAEA Fusion Energy Conference, Geneva - P. Martin

  47. The old story For a long time it was considered that…. ….a q < 1 configuration like the RFP would have been intrinsically unstable, with a broad spectrum of MHD resistive instabilities, causing magnetic chaos and driving anomalous transport. This was viewed as an interesting scientific case but a show-stopper for the RFP reactor ambitions Princeton Plasma Physics Laboratory Colloquium - June 4th, 2009

  48. An emerging view for the RFP For a long time it was considered that…. ….a q < 1 configuration like the RFP would have been intrinsically unstable, with a broad spectrum of MHD resistive instabilities, causing magnetic chaos and driving anomalous transport. This was viewed as an interesting scientific case but a show-stopper for the RFP reactor ambitions THE STORY IS CHANGED Princeton Plasma Physics Laboratory Colloquium - June 4th, 2009

  49. Two strategies for chaos-free RFP: 1 Control of the current profile to stabilize tearing modes Proof of principle experiment in MST to test RFP confinement and beta limits at the limit of negligible magnetic fluctuation (record values tE and b) (most recent results in Chapman et al, IAE FEC paper EX/7-1Ra, to appear in NF 2009) amplitude The solution The problem The problem m=1 and m=0 modes Toroidal mode number (~2R/a) Toroidal mode number (~2R/a) Princeton Plasma Physics Laboratory Colloquium - June 4th, 2009

  50. Dynamo modes active reduction • Pulsed Poloidal Current Drive (PPCD): • the induction of a poloidal current at the plasma edge causes a dramatic reduction of the magnetic turbulence and STRONG PLASMA HEATING It is TRANSIENT, but in RFX a quasi-stationary version has been implemented

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