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Self-organized helical equilibria emerging at high current in RFX-mod

Self-organized helical equilibria emerging at high current in RFX-mod. Matteo Zuin on behalf of the RFX-mod team Consorzio RFX, Euratom-ENEA Association, Padova, Italy. Overview. Transition to helical states at high current SHAx states: a new magnetic topology Properties of SHAx states

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Self-organized helical equilibria emerging at high current in RFX-mod

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  1. Self-organized helical equilibria emerging at high current in RFX-mod Matteo Zuin on behalf of the RFX-mod team Consorzio RFX, Euratom-ENEA Association, Padova, Italy

  2. Overview • Transition to helical states at high current • SHAx states: a new magnetic topology • Properties of SHAx states • Helical transport barriers • Open issues and near-future plans

  3. Quasi-SH at high current • MHD control has allowed high-current operation up to 1.6 MA ( target 2MA) • Spontaneous transitions to Quasi-SH m=1,n=-7 > 10tE  tR [ n=8-15(m=1, n)2 ]1/2

  4. 90% time in QSH flattop duration Quasi-SH at high current Ip (MA)

  5. Discrete reconection events (generation of field-aligned current sheet in the edge region) more details in M. Zuin et al., submitted to Plasma Phys. Control. Fusion But what interrupts QSH? • QSH is transiently perturbed by partial crashes, caused by a toroidally-localized magnetic field perturbation (m=1, n=-7) bf (mT) toroidal angle (deg) time (ms)

  6. S = tR / tA = bdom bsecd 5% 0.2% = = 25 Rutherford eq. predicts no dependence of the island width w on S (R.B White et al., Phys. Fluids 20, 800 1977) dw dt = C h [D’(w) - a’ w] Lundquist number scaling Dominant mode (m = 1, n = -7) Secondary modes (1,-8 to -15) At saturation b/B (%) b/B (%) S S

  7. Lundquist number scaling • The mode saturation amplitude should not depend on S, but the linear growth rate does (see D. Biskamp, Nonlinear magnetohydrodynamics, Cambridge Univ. Press, pag. 107) • Both predictions consistent with experiment

  8. E1,-7  B B2 v 1,-7 Eloop + < v 1,-7 b 1,-7> = h j ~ S-1 SH dynamo - edge Dominant mode (1,-7) Magnetic field perturbation Dominant mode (1,-7) Electric field perturbation b/B (%) S S

  9. Helical transport barrier S, Lundquist number

  10. Helical transport barrier S, Lundquist number

  11. bf / B  4% Helical transport barrier

  12. bf / B  3% bf / B  4% bf / B  5% The island separatrix disappears • As the (1,-7) mode amplitude increases with S, the island separatrix disappears, and the plasma spontaneously reaches a single helical axis state resilient to magnetic chaos • Predicted by D.F. Escande et al., PRL 2000 • Recently observed (R. Lorenzini et al., PRL 2008) in QSH plasmas triggered by OPCD • We call this condition Single Helical Axis (SHAx) state, as opposed do QSH with island (QSHi). bf / B  2%

  13. SHAx SHAx QSHi Te (ev) Thermal structure width (m) QSHi MH r (m) Dominant mode amplitude (%) • 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

  14. SHAx occur beyond a threshold on the n=7 mode • 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) Dom. Dom. Br at resonance (reconstr.) Sec. Sec. B at wall (measured) Dom./Sec. Dom./Sec.

  15. More remnant helical flux surfaces + broad region of sticky magnetic field lines SHAx are more chaos-resilient Dominant mode only SHAx QSHi All modes

  16. Energy confinement time  reduced Ohmic input power  larger thermal content without separatrix b/B > 4% 95% percentiles tE (ms) with separatrix b/B <4% assuming Te = Ti secondary mode amplitude (%)

  17. Helical flux surfaces • We have a developed a relatively simple, yet effective, procedure to reconstruct the helical flux surfaces. • This involves starting with an axisymmetric equilibrium, and reconstructing the dominant mode eigenmode as a perturbation, using Newcomb’s equation supplemented with edge B measurements. • (r) given by  = m0 – nF0 + (mmn-nfmn)exp[i(m-n)] - 0 and F0 poloidal and toroidal fluxes of the axisymmetric equilibrium - mn and fmn poloidal and toroidal fluxes of the dominant mode -  and  are the flux coordinates B· = 0 • The resulting helical flux function can be used as an effective radial coordinate. • Temperature and soft X-ray (and density) emissivity measurements can be mapped on the computed helical surfaces in order to validate the procedure.

  18. Mapping of Te on helical flux function • The profile is asymmetric with respect to the geometric axis, strong gradient regions (shaded) different on the two sides. • The two half profiles collapse when plotted as a function of  = (/0)1/2 (0=helical flux at the plasma boundary) • Same method applied to Soft-X ray emissions shows that magnetic surfaces are isothermal and isoemissive

  19. Open issues and near-future plans  Experiments up to 2MA foreseen for 2009

  20. Mapping of line-integrated soft X-ray emissivity • The X-ray emissivity measured by silicon photodiode along 78 lines of sight in 4 fans • Measurements (red) are reconstructed using a simple three-parameter model of the form () = 0(1 - ) (black). • Resulting emissivity plotted as a function of  • 2D emissivity map resulting from the reconstructions

  21. Energy confinement time doubles • After the separatrix disappearance the energy confinement time doubles assuming Te = Ti

  22. More remnant helical flux surfaces + broad region of sticky magnetic field lines bf / B  5% Magnetic topology changes Remnant helical flux surfaces Thomson scattering bf / B  3%

  23. Magnetic topology changes bf / B  3% bf / B  5% Soft-x-ray tomography (at different toroidal angle)

  24. The single helicity RFP • 3D nonlinear MHD codes (SpeCyl, NIMROD) predict single helicity RFP equilibria S. Cappello, PPCF 46, B313 (2004)  LAMINAR DYNAMO • HELICAL FLUX SURFACES Eloop + < v1,-7  b1,-7 > = h j (m=1, n=-7) q, safety factor r/a

  25. low amplitude m=1 secondary modes Good confinement inside the remnant helical flux surfaces (1, -8) (1, -9) (1, -10) The single helicity RFP • Spontaneous transitions to Quasi– Single Helicity observed in experiment P. Martin et al., PPCF 49, A177 (2007) (m=1, n=-7) q, safety factor r/a

  26. RFX-mod: a facility for MHD feedback control • Up to 2MA plasma current at low magnetic field Bf(a) < 0.1T • Full coverage, 192 saddle coils • Multi-mode feedback control R0=2m a=0.46m

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