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Experimental RFP results

Experimental RFP results. Emilio Martines Consorzio RFX, Padova, Italy email: emilio.martines@igi.cnr.it. A bit of history Magnetic configuration Discharge formation Dynamo PPCD-OPCD Oscillating Field Current Drive (OFCD) Transport mechanisms Scaling laws. The shell problem

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Experimental RFP results

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  1. Experimental RFP results Emilio Martines Consorzio RFX, Padova, Italy email: emilio.martines@igi.cnr.it

  2. A bit of history Magnetic configuration Discharge formation Dynamo PPCD-OPCD Oscillating Field Current Drive (OFCD) Transport mechanisms Scaling laws The shell problem Mode locking Advanced RFP: the Single Helicity paradigm Density limit Outline

  3. A bit of history: ZETA “Pinch device”. Operational from 1954 to 1968. R = 1.5 m, a = 0.5 m, Ip = 800 kA. Quiescent phase 25th January 1958 In the last operation phase some shots revealed a "quiescent period" of long stability in a system that otherwise appeared to prove itself unstable. This quiescent phase was characterized by a reversed toroidal field at the wall  RFP ! E.P. Butt et al., 2nd IAEA Fusion Energy Conference, Culham, vol. 2, p. 751 (1965). D.C. Robinson et al., 3rd IAEA Fusion Energy Conference, Novosibirsk, vol. I, p. 263 (1968).

  4. A bit of history: 40 years of RFP research Padova (Italy) Culham (UK) Los Alamos (USA) Tsukuba (Japan) Nagoya (Japan) San Diego (USA) Tokyo (Japan) Stockholm (Sweden) Chengdu (China) Madison (USA) 1st gen. (‘70s) ETA BETA I HTBX-1 ZT-1 TPE-1R, R(M) STP-1(M) - - - - - 2nd gen. (‘80s) ETA BETA II HTBX-1B, 1C ZT-40, ZT-40M TPE-1RM20, TPE-2M STP-3(M) OHTE REPUITE-1 Extrap-T1 SWIP-RFP - 3rd gen. (‘90s) RFX, RFX-mod - ZTH (canceled) TPE-RX - - RELAX Extrap-T2 - MST In red the experiments presently in operation.

  5. A bit of history: 40 years of RFP research 1st generation (‘70s): Small machines with non-conducting first wall and very fast current rise. 2nd generation (‘80s): Small machines with conducting wall, and slower current rise, motivated by Taylor’s theory of relaxation. 3rd generation (‘90s to present): Larger machines with higher plasma current (RFX: 2 MA, TPE-RX: 1 MA, MST: 0.55 MA)

  6. Magnetic configuration: F- plot The RFP state is often described through the pinch parameter  and the reversal parameter F. Experimental points are found to lie on a well-defined curve on the F- plane. H.A.B. Bodin, A.A. Newton, NF 20, 1255 (1980) If the operator determines given values of plasma current and toroidal field at the edge, the plasma will adjust the toroidal flux so as to lie on the F - curve.

  7. Magnetic configuration: F- plot The curve in the F- plane is also followed during the discharge formation in every shot, regardless of the reached plasma current. Ip (MA) t (s) F 

  8. Magnetic configuration: RFP profiles The RFP magnetic field profiles have been measured in ETA BETA II using insertable pick-up coils at Ip ~ 100 kA and  ~ 1.9. The reconstructed q profile confirms that q(0) ~ 2a/3R. The  profile is flat only in the core, and decreases towards the edge. V. Antoni et al., PPCF 29, 279 (1987) V. Antoni et al., NF 29, 1759 (1989)

  9. Magnetic configuration: RFP profiles The magnetic field profiles have been measured by insertable pick-up coils also in HTBX. H.A.B. Bodin, IAEA Fusion Energy Conference, Lausanne, vol. 1, p. 417 (1984)

  10. Discharge formation: Self and aided reversal The first RFP plasma were obtained by “self-reversal”, that is exploiting the presence of a toroidal flux conserver (either the shell or the toroidal field coils). This is still possible in modern machines, by short-circuiting the toroidal field coils when the plasma current is started. However, the most usual approach is to aid the reversal by reversing the current in the toroidal field coils, and then sustain this current to chosen level. self-reversal aided reversal RFX-mod shots 23287, 20276

  11. Discharge formation: Different start-up scenarios • Three basic start-up types: • Ramped: reversal happens early, then Ip is raised in a RFP state, increasing the toroidal flux. • Aided: the toroidal flux is reduced by the discharge formation • Matched: the toroidal flux is kept constant 15978 Ramped 15962 Matched 15938 Aided

  12. Discharge formation: Different start-up scenarios According to Sprott’s 0D modeling, the ramped scenario is the most expensive and the aided one is the most economic in terms of volt-second consumption (stored magnetizing flux). In practice, flux consumption is much larger than expected because of resistive losses (ignored in Sprott’s model). The different start-up modes appear to be not so different in terms of volt-second consumption J. C. Sprott, Phys, Fluids 31, 2266 (1988).

  13. Dynamo: Basic concept The poloidal current in the RFP is sustained against resistive diffusion, which would tend to flatten the toroidal field profile, by the non-linear effect of m=1 tearing modes which are resonant inside the reversal surface. This process is called dynamo. These modes are therefore intrinsic to the configuration. m = 1 MHD modes

  14. Dynamo: Measurement of the dynamo field In MST the dynamo acts in bursts, called Discrete Relaxation Events (true also in RFX, but only at deep reversal). The MHD dynamo term in Ohm’s law has been measured, and turns out to be consistent with expectations in the edge. Deeper inside, an additional Hall term has to be invoked. P.W. Fontana et al., PRL 85, 566 (2000) W.X. Ding, PRL 93, 045002 (2004)

  15. Pulsed Poloidal Current Drive (PPCD) The PPCD technique, for transiently reducing magnetic fluctuations and improving confinement, was pioneered by the MST group. The rationale is to “help” the dynamo by inducing a poloidal current through a sudden decrease of the toroidal field at the wall. A poloidal beta of 15% and a tenfold increase of confinement time (up to 10 ms) in sawtooth-free plasmas have been achieved by this method. J.S. Sarff, PRL 72, 3670 (1994) B. Chapman, PRL 87, 205001 (2001)

  16. Pulsed Poloidal Current Drive (PPCD) The MST experiments demonstrate that PPCD suppresses the dynamo (the applied electric field matches the current density), and induces a transition from a Multiple Helicity state to a state with one or two dominant modes, as shown by tomographic reconstructions. S.C. Prager et al., NF 45, S276 (2005) Standard PPCD Equilibrium reconstruction with many constraints, including Faraday rotation, motional Stark effect, Thomson scattering and interferometry.

  17. Pulsed Poloidal Current Drive (PPCD) An enhanced hard X-ray spectrum, attributed to high energy electrons, is observed in MST during PPCD, together with a reduction of magnetic fluctuations. This suggests that core transport may not be due any more to magnetic field line ergodicity. R. O’Connell et al., PRL 91, 045002 (2003)

  18. PPCD Standard Standard PPCD Pulsed Poloidal Current Drive (PPCD) In RFX the PPCD experiments could be reproduced, although the performance increase was less pronounced. In particular, the core thermal diffusivity was reduced by a factor of 3. R. Bartiromo et al., PRL 83, 1462 (1999)

  19. Oscillating poloidal current drive (OPCD) OPCD is a periodic PPCD, obtained oscillating the current in the toroidal field coils. In RFX-mod it was shown that it periodically induces a QSH condition. D. Terranova et al., PRL 99, 095001 (2007) QSH Dominant mode (%) MH Secondary modes (%)

  20. Oscillating Field Current Drive A current drive concept, in principle very efficient, has been proposed for obtaining a steady state RFP. Called Oscillating Field Current Drive (OFCD), or F- pumping, it is based on oscillating the toroidal and poloidal loop voltages (the latter by oscillating the current in the toroidal field coils) with proper phasing. On ZT-40M, where the technique was originally proposed, the outcome was mixed: antidrive worked as expected, but no drive was observed, because of enhance plasma-wall interaction. M.K. Bevir, et al., PF 28, 1826 (1985) K. Schoenberg et al., PF 31, 2287 (1988) Helicity balance ( ): In stationary conditions K should be constant. An additional source can be obtained by oscillating toroidal voltage Vt and toroidal flux  with frequency . The resulting term is VtVpsin()/, which is maximum for  = /2

  21. Oscillating Field Current Drive In MST 10% of the total plasma current has been produced by OFCD. The optimal phase difference  between Vt and Vp has been found to be smaller than the theoretical /2 value. Efficiency was the same as for steady induction (0.1 A/W). K.J. McCollam et al., PRL 96, 035003 (2006)

  22. Transport mechanisms: magnetic topology In standard RFPs dynamo is usually driven by many m = 1 modes. The superposition of the mode islands causes a stochastization of the plasma core good confinement only in the outer region. This is called Multiple Helicity (MH) condition Reversal surface (m=0 resonance) Poincaré plot In r- plane Chaotic core region

  23. Transport mechanisms: core The particle and energy transport inside the reversal surface have been measured to be due to magnetic turbulence, related to the dynamo modes. The thermal conductivity in the plasma core is consistent with expectations from theory of transport in a stochastic magnetic field. G. Fiksel et al., PPCF 38, A213 (1996) T.M. Biewer et al., PRL 91, 045004 (2003)

  24. Transport mechanisms: edge Measurements of the edge particle flux induced by electrostatic turbulence in RFX have given values compatible with the total particle flux predicted by transport simulations. The energy flux driven by magnetic turbulence was found to be small, and the one driven by electrostatic turbulence accounts at most for 30% of the total. The nature of this flux is still unclear: better attention should be paid to magnetic topology and toroidal asymmetries. V. Antoni et al., PRL 80, 4185 (1998) G. Serianni et al., PPCF 43, 919 (2001) E. Martines et al., NF 39, 581 (1999).

  25. Transport mechanisms: momentum transport In RFX the perpendicular (toroidal) flow profile has been measured using the Gundestrup probe technique. The profile is consistent with the EB profile due to the radial electric field. The profile displays a double shear layer, one across the plasma boundary and the other more internal (confirmed by spectroscopic flow measurements). The electrostatic Reynolds stress in T2 and RFX displays a gradient on the shear layers, suggesting that the electrostatic turbulence is responsible for momentum transport. The magnetic Reynolds stress is found to be negligible. V. Antoni, PRL 79, 4814 (1997) N. Vianello, PRL 94, 135001 (2005)

  26. Scaling laws: The constant beta scaling A good fit to the RFP confinement database is given by the constant  scaling, also named Connor-Taylor scaling. This would predict ohmic ignition at 10-20 MA of plasma current. RFX was designed according to this scaling, which predicts E = 10 ms at 2 MA. Data from: K. A. Werley et al, NF 36, 629 (1996). MST & RFX points are OLD! N = na2 All in SI units, Ip in MA, Ip/N in 10-14 Am Notice that Ip/N = (n/ng)-1

  27. Scaling laws: Improved confinement in MST Recent results from MST (unpublished): It is worth mentioning that these are values obtained in transient experiments.

  28. Scaling laws: Comparison MST-tokamak • Approach: compare to an H-mode tokamak with: • same size and input power • Bt = 1 T J. Sarff et al., Nucl. Fusion 43, 1684 (2003).

  29. The shell problem: Need for a conducting shell • All RFP machines were built with a conducting shell around the vacuum vessel. • Motivations: • To control the horizontal plasma position (but can be done with vertical field coils) • To provide a flux conserver for toroidal field reversal (but not needed with aided reversal) • To provide a Br = 0 boundary condition for MHD instabilities (crucial !). • A conducting shell is however not feasible for a steady-state reactor.

  30. The shell problem: Thin shell and RWM The Culham team equipped the HBTX device with a thin shell (HBTX1C) having a time constant of 0.5 ms (shorter than the discharge duration). The growth of non-resonant m=1 wall-locked MHD modes (Resistive Wall Modes) on a time constant of the order of the shell constant was observed, leading to premature discharge termination. B. Alper et al., PPCF 31, 205 (1989)

  31. The shell problem: The RFX-mod virtual shell During the 1999-2004 shutdown the RFX experiment has been equipped with a 50 ms shell (previously 400 ms) and a sophisticated system of 192 feedback-controlled saddle coils covering the whole torus surface. upgraded MHD active control: june 2007 with MHD active control: 2006 no MHD active control The new system led to enhanced performance (500 ms discharges), RWM suppression and mitigation of tearing mode amplitude and locking phenomena. L. Marrelli et al., PPCF 49, B359 (2007)

  32. plasma current mode control m=1,n=-6 mode amplitude logarithmic mode amplitude t [s] mode control mode control The shell problem: RWM control in RFX-mod In particular, the system of feedback-controlled saddle coils has been shown to be able to completely suppress the Resistive Wall Modes, thus eliminating the need of a shell with long time constant. Future RFPs will only need a thin shell (possibly the vessel itself), for the fast time scales. See also T. Bolzonella’s lesson tomorrow.

  33. Mode locking: The RFX experience • In RFX, since the early operations, the dynamo m=1 tearing modes locked routinely yielding: • Phase locking: all modes superpose coherently at one toroidal angle, giving rise to a localized magnetic perturbation. • Wall locking: the localized perturbation is stationary, and causes a strong interaction in one limited area of the first wall. • These phenomena limited for many years the achievable plasma current to 1 MA. P. Zanca et al, PP 8, 516 (2001)

  34. Mode locking: The RFX experience The m=0 modes (low n) also lock in phase, superposing their nodes, giving rise to a funnel-like shape of the plasma column. Overall, a local shift of 2-3 cm was measured, giving rise to strong plasma-wall interaction. P. Zanca et al, PP 8, 516 (2001) m=0 m=1

  35. Mode locking: The MST experience In MST the m=1 dynamo modes are typically found to rotate at frequencies ~ 10 kHz. Occasionally, the modes slow down and lock to the wall, while the plasma continues to rotate at reduced speed. This happens especially in QSH states. Mode locking does not lead to disruptions, as is the case for tokamaks. B.E. Chapman et al., PP 11, 2156 (2004). Often, the modes afterwards unlock spontaneously.

  36. Mode locking: rotation by m=0 perturbation In RFX a rotation the localized magnetic perturbation could be unlocked by applying an m=0 rotating perturbation using the toroidal field coils. The non-linear coupling between m=0 and m=1 modes is exploited. R. Bartiromo et al., PRL 83, 1779 (1999)

  37. #22805 Clean Mode Control #18942 Intelligent Shell Mode locking: unlocking by active control In RFX-mod the wall locking is removed by the feedback-controlled saddle coil system, since the so-called “Clean Mode Control” (with sideband removal from the measurements) has been implemented. P. Zanca et al., NF 47, 1825 (2007) Plasma surface distortion

  38. Mode locking: unlocking by active control Mode rotation can be made more reproducible by slightly modifying the feedback algorithm, i.e. by setting a non-zero reference value for selected helicities (in this case the m=1/n=7 mode). L. Marrelli et al., PPCF 49, B359 (2007). Mode amplitudes n=7 phase (deg)

  39. Advanced RFP: Multiple Helicity In low current RFPs dynamo is usually driven by many m = 1 modes. The superposition of the mode islands causes a stochastization of the plasma core good confinement only in the outer region. This is called Multiple Helicity (MH) condition Poincaré plot In r- plane Chaotic core region

  40. Advanced RFP: From MH to SH (theory) In principle, it is possible to have the B reversal with one mode only (laminar dynamo). This is called Single Helicity (SH) state. 3D MHD simulations have shown the spontaneous transition from a MH state to a SH state when the Hartmann number is varied. In SH, good magnetic surfaces are recovered  good confinement over the whole plasma. S. Cappello et al., PRL 85, 3838 (2000)

  41. (m=1, n=-7) (1, -8) (1, -9) (1, -10) q, safety factor r/a Advanced RFP: From MH to (Q)SH (experiment) Quasi Single Helicity (QSH) states, where the most internally resonant mode (n = 7 for RFX-mod) dominates, and the secondary mode amplitudes are reduced, are routinely observed. A typical feature is the appearance of a hot magnetic island. Weak m=1 secondary modes

  42. Ip (MA) m=1,n=-7 <m=1,n=-8 to -15> bf/B(a) (%) > 10tE  tR time (s) Advanced RFP: Dynamic behaviour of QSH • Spontaneous intermittent transition from QSH to MH and back. • More likely at high current. Feedback control of edge Br is essential!

  43. S = tR / tA = bdom bsecd 5% 0.2% = = 25 Advanced RFP: Scaling with Lundquist number Lundquist number: Dominant mode (m = 1, n = -7) Secondary modes (1,-8 to -15) b/B (%) b/B (%) S S

  44. Advanced RFP: Scaling with plasma current Since S grows with Ip and Te, we have an encouraging scaling with Ip: the dominant mode saturates, the secondary modes keep decreasing. Dominant Secondary

  45. Advanced RFP: Relative duration of QSH The flat-top fraction spent in QSH state and the QSH duration increase with Lundquist number.

  46. bf / B  2% bf / B  3% bf / B  4% bf / B  5% Advanced RFP: Single Helical Axis (SHAx) states • When the dominant mode amplitude exceeds a threshold, the main magnetic axis collapses onto the island X-point and the separatrix is expelled. • The island O-point remains as the magnetic axis of a helically distorted plasma. • We call this condition Single Helical Axis (SHAx) state, as opposed do QSH with island (QSHi). • SHAx states are predicted to be more resilient to chaos. R. Lorenzini et al., Phys. Rev. Lett. 101, 025005 (2008)

  47. SHAx SHAx QSHi Te (ev) Thermal structure width (m) QSHi MH r (m) Dominant mode amplitude (%) Advanced RFP: Evidence of transition to SHAx The SHAx occurrence allows an enlargement of the hot region to the other side of the chamber geometrical axis, thus inducing an increase of the plasma thermal content. QSHi= QSH with island

  48. Dom. Dom. Sec. Sec. Dom./Sec. Dom./Sec. Advanced RFP: condition for SHAx occurrence SHAx states, as detected from Te profiles, appear only when the dominant mode exceeds a threshold (which corresponds to a threshold of the ratio secondary/dominant) Br at resonance (reconstr.) B at wall (measured)

  49. Advanced RFP: SHAx are more chaos-resilient Dominant mode only Dominant mode only SHAx QSHi All modes All modes

  50. Advanced RFP: Mapping of Te on helical flux

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