M. Zuin 13th IEA/RFP WorkshopStockholm, October 9-11, 2008 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

M. Zuin 13th IEA/RFP WorkshopStockholm, October 9-11, 2008 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

M. Zuin 13th IEA/RFP WorkshopStockholm, October 9-11, 2008 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 [  n=8-15 (m=1, n) 2 ] 1/2 > 10  E   R

M. Zuin 13th IEA/RFP WorkshopStockholm, October 9-11, 2008 Quasi-SH at high current time in QSH flattop duration I p (MA) 90%

M. Zuin 13th IEA/RFP WorkshopStockholm, October 9-11, 2008 But what interrupts QSH? QSH is transiently perturbed by partial crashes, caused by a toroidally-localized magnetic field perturbation time (ms) toroidal angle (deg) b  (mT) (m=1, n=-7) more details in M. Zuin et al., submitted to Plasma Phys. Control. Fusion Discrete reconection events (generation of field-aligned current sheet in the edge region)

M. Zuin 13th IEA/RFP WorkshopStockholm, October 9-11, 2008 Lundquist number scaling S =  R /  A = Dominant mode (m = 1, n = -7) Secondary modes (1,-8 to -15) b dom b secd 5% 0.2% == 25 b/B (%) S S dw dt = C  [  ’(w) -  ’ w] Rutherford eq. predicts no dependence of the island width w on S (R.B White et al., Phys. Fluids 20, ) At saturation

M. Zuin 13th IEA/RFP WorkshopStockholm, October 9-11, 2008 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

M. Zuin 13th IEA/RFP WorkshopStockholm, October 9-11, 2008 SH dynamo - edge Dominant mode (1,-7) Magnetic field perturbation b/B (%) S Dominant mode (1,-7) Electric field perturbation S E loop + =  j ~ S -1 E 1,-7  B B 2 v 1,-7 

M. Zuin 13th IEA/RFP WorkshopStockholm, October 9-11, 2008 Helical transport barrier S, Lundquist number

M. Zuin 13th IEA/RFP WorkshopStockholm, October 9-11, 2008 Helical transport barrier S, Lundquist number

M. Zuin 13th IEA/RFP WorkshopStockholm, October 9-11, 2008 Helical transport barrier b  / B  4%

M. Zuin 13th IEA/RFP WorkshopStockholm, October 9-11, 2008 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 (QSH i ). b  / B  2% b  / B  3% b  / B  4% b  / B  5%

M. Zuin 13th IEA/RFP WorkshopStockholm, October 9-11, 2008 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. QSH i SHAx Dominant mode amplitude (%) Thermal structure width (m) MH SHAx QSH i T e (ev) r (m) QSH i = QSH with island

M. Zuin 13th IEA/RFP WorkshopStockholm, October 9-11, 2008 SHAx occur beyond a threshold on the n=7 mode SHAx states, as detected from T e profiles, appear only when the dominant mode exceeds a threshold (which corresponds to a threshold of the ratio secondary/dominant) B r at resonance (reconstr.) B  at wall (measured) Dom. Sec. Dom./Sec. Dom. Sec. Dom./Sec.

M. Zuin 13th IEA/RFP WorkshopStockholm, October 9-11, 2008 SHAx are more chaos-resilient QSH i SHAx Dominant mode only All modes More remnant helical flux surfaces + broad region of sticky magnetic field lines

M. Zuin 13th IEA/RFP WorkshopStockholm, October 9-11, 2008 Energy confinement time  larger thermal content  reduced Ohmic input power 95% percentiles without separatrix b/B > 4% with separatrix b/B <4%  E (ms) secondary mode amplitude (%) assuming T e = T i

M. Zuin 13th IEA/RFP WorkshopStockholm, October 9-11, 2008 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 – nF 0 + (m  mn -nf mn )exp[i(m -n  )] -  0 and F 0 poloidal and toroidal fluxes of the axisymmetric equilibrium -  mn and f mn 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.

M. Zuin 13th IEA/RFP WorkshopStockholm, October 9-11, 2008 Mapping of T e 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

M. Zuin 13th IEA/RFP WorkshopStockholm, October 9-11, 2008 Open issues and near-future plans  Experiments up to 2MA foreseen for 2009

M. Zuin 13th IEA/RFP WorkshopStockholm, October 9-11, 2008

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

M. Zuin 13th IEA/RFP WorkshopStockholm, October 9-11, 2008 Energy confinement time doubles After the separatrix disappearance the energy confinement time doubles assuming T e = T i

M. Zuin 13th IEA/RFP WorkshopStockholm, October 9-11, 2008

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

M. Zuin 13th IEA/RFP WorkshopStockholm, October 9-11, 2008

Magnetic topology changes b  / B  3% b  / B  5% Soft-x-ray tomography (at different toroidal angle)

M. Zuin 13th IEA/RFP WorkshopStockholm, October 9-11, 2008

The single helicity RFP 3D nonlinear MHD codes (SpeCyl, NIMROD) predict single helicity RFP equilibria q, safety factor r/a (m=1, n=-7)  HELICAL FLUX SURFACES  LAMINAR DYNAMO E loop + =  j S. Cappello, PPCF 46, B313 (2004)

M. Zuin 13th IEA/RFP WorkshopStockholm, October 9-11, 2008

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

M. Zuin 13th IEA/RFP WorkshopStockholm, October 9-11, 2008

RFX-mod: a facility for MHD feedback control Up to 2MA plasma current at low magnetic field B  (a) < 0.1T Full coverage, 192 saddle coils Multi-mode feedback control R 0 =2m a=0.46m

M. Zuin 13th IEA/RFP WorkshopStockholm, October 9-11, 2008