1. Challenges in RFP physics D.F. Escande UMR 6633 CNRS/Aix-Marseille Université, France & Consorzio RFX, Padova, Italy Thanks to D. Bonfiglio, F. Sattin, and P. Zanca Brainstorming about some challenging issues in RFP physics: How to decrease the Vloop? Nature of QSH crashes Existence of ohmic SH equilibria? Why is shallow reversal a good option? Needs of the theory-modeling activity as far as data analysis is concerned

2. Reversal does not mean high V loop

3. Reversal of the magnetic field does not mean “edge current in highly resistive plasma” “high Vloop” Classical 1D view (BFM), but... Ohm’s law and helical equilibrium In a stellarator q is decreasing without any edge current or dynamo M. Gobbin 2010

4. Edge current cannot provide reversal in an ohmic RFP d /d  = A(  ) +S ; A ~ E 0 / = pinch term proportional to V loop + stellarator term S independent of V loop and vanishing in the axis-symmetric case Pinch-stellarator equation First written and discussed by Pustovitov (1982) Derived in a different way by Finn et al. 1992 1st order linear equation: if S=0 reversal impossible “Cowling” theorem q ~ Only S negative can produce edge axial field reversal Helical Grad-Shafranov equation + Ohm’s law Edge reversal without edge current: makes S more efficient Very different from the traditional 1D non ohmic view (BFM) : “An edge current must be present to produce reversal Implies high Vloop since edge highly resistive”

5. Benefits of shallow reversal Small B z0 (a) implies: - small helical perturbation sufficient for reversal - small dynamo velocity field implying: -small viscous dissipation -small viscous beta NB: in Navier-Stokes, viscous term plays a similar role to a pressure gradient: viscous beta in competition with kinetic one Good news: a priori there is no requirement for the dynamo to come with a high V loop, and therefore a high energetic cost To diminish viscous dissipation and beta: choose shallow F Perturbed ultimate paramagnetic pinch (PUPP) Analytical model with small B z0 (a) and |F| with a highly resistive edge: makes S more efficient Provides a necessary criterion for reversal Verified in SpeCyl simulations (D. Bonfiglio) And in RFX for non zero B r (a) (P. Zanca) F<0 more easy than q helicoidal <0

6. A path to describe ETB’s? *ETB’s develop in regimes where the secondary modes are relatively low: decreases chaos Indeed ETB’s develop where ordered magnetic surfaces start to show up out of the chaotic region at inner radii Makes strong grad T possible at r/a=0.8 and not only at reversal as in MH or standard QSH Therefore reversal occurs in a low temperature domain D, like in PUPP There no current and constant B z of UPP *Favored by regimes of shallow reversal, provided by PUPP *The onset of the ETB typically increases confinement by about 20% with respect to standard plasmas with similar density: consistent with lower viscous dissipation and beta in PUPP Remark: the conducting duct narrows, but V loop not stronger for same I; reminds JET from limiter to divertor

7. Drawback of a high helical modulation A priori implies a high dynamo velocity field Thus high viscous dissipation and beta Notice: there is a dissipation related to v ambipolar too!

8. QSH Crashes & Ohmic equilibrium

9. An example of relaxation process: the “Tantale” vase Not due to the linear instability of an equilibrium Maximum level not unstable Above this level no equilibrium at all

10. Is a stationary SHAx state possible? The system might try to reach one Then might discover there is none and would crash without any linear instability Exponential trend for crashes never found with SpeCyl or experimentally With B r (a) ~ 0 duration of SHAx smaller than  resistive Enough to verify edge Ohmic constraint What about the central one? Example: viscosity self-consistent with chaos: Chaos  high viscosity  bifurcation to SH  chaos killed Edge effect dominant? (M. Agostini) Interesting news from VMEC

11. High central temperature in SHAx should imply high central current in ohmic state Recent exercise with VMEC (M Gobbin et al., APS 2010) Need low central q to have a reasonable helical axis Suggestive of an ohmic trend in the center

12. 1D paramagnetic pinch equilibria Aim: input for PIXIE3D (D. Bonfiglio ) and RFP “Braginskii” equilibria (F. Sattin) Grad-Shafranov + Ohm: 2 codes D. Bonfiglio & F. Sattin: cross-check (with P. Zanca) Fairly easy to get temperature and q profiles in agreement with RFX MH states Not obvious to get temperature and q profiles in agreement with SHAx states  = 1.32 Bz(1)/Bz(0) = 6.2% T(1)/T(0) = 0.13

13. Synergy of chaos decrease and shallow reversal If chaos decreases, resistivity is constant along magnetic surfaces Approximation by  (r) questionable

14. Calculations with  (r)=constant (Bonfiglio, ICPP 2006): - reversal more shallow & smaller mode amplitude - smaller dynamo velocity field; thus less viscous dissipation Mainly due to  =  (  ) What happens if  (  ) not uniform?

15. Needs of the theory-modeling activity as far as data analysis is concerned

16. PIXIE3D with the feedback loop on the resistivity profile due to heat transport (D. Bonfiglio). In the past ad hoc  (r) Now ad hoc  e (r)! Therefore try and study cases close to the SHAx in RFX-mod (Cf. 1D models) Better MHD simulation of RFP plasmas: need better measurements and data analysis (B,  e ) Example: Statistics at high current of figures like in our Nature Physics 2009 ? Key publications; integrated work Cf. 6 blind men and the elephant

17. Conclusion Brainstorming about some challenging issues in RFP physics: How to decrease the Vloop? Shallow reversal a good option Low dominant mode amplitude (also good for plasma-wall interaction) Nature of QSH crashes: possibly not due to linear instabilities Existence of ohmic SH equilibria: edge ohmic, but center? Needs of the theory-modeling activity as far as data analysis is concerned PIXIE3D will benefit of more precise experimental results to be run in an RFX-mod relevant way What do we call equilibrium? RFP and stellarator views very different: importance of electron dynamics in self-organization M. Valisa: QSH limited by electron channel? Assessing ideal stability of an RFP requires very precise knowledge of the magnetic field Assessing the ambipolar electric field with non local tools