1. IEA RFP Workshop, April 26-28 2010 Padova Internal electron transport barriers in RFX-mod helical equilibria R. Lorenzini on behalf of the RFX-mod team Consorzio RFX, Euratom-ENEA Association, Padova, Italy

2. IEA RFP Workshop, April 26-28 2010 Padova Outline of the talk  New analyses on the electron Internal Transport Barriers e-ITBS observed in reversed field pinch experiment RFX-mod  These analyses are the result of a joint effort of theory, modelling and data analyses aimed at understanding the role of MHD and microturbulence in driving the transport on the barrier

3. IEA RFP Workshop, April 26-28 2010 Padova The RFX-mod experiment RFX-mod (Padua, Italy) is the largest RFP presently in operation (R 0 = 2 m, a = 0.46 m ) RFX-mod has two unique features: – the possibility of reaching Ip up to 2MA – the most advanced feedback coil system ever realized in a fusion device 4×48=192 feedback saddle coils independently controlled and respective sensors

4. IEA RFP Workshop, April 26-28 2010 Padova Evidence of a self organized helical plasma When the current increases the amplitude of the innermost resonant mode (m=1, n = -7) increases and eventually saturates while the secondary modes decrease. [P. Piovesan et al., NF 49, 085036 (2009)] Long lasting Quasi Single Helicity (QSH) states are routinely observed at I > 1MA. The plasma dithers between QSH and MH (Multiple Helicity) state (all the modes have a comparable amplitude), but QSH phases become more frequent, longer and purer increasing I p 10  E Theory and 3D MHD codes describe a helical ohmic equilibrium self-sustained by a single mode. This is the chaos-free Single Helicity ( SH ) state. [S. Cappello et al., PPCF 46 B313 (2004)

5. IEA RFP Workshop, April 26-28 2010 Padova A new magnetic topology: the SHAx When the amplitude of the dominant is large enough the magnetic topology has a Single Magnetic Axis (SHAx) SHAx states are known to be resilient to the magnetic chaos [D. F. Escande et al., PRL. 85, 3169 (2000)] In the SHAx we observe the onset of an electron internal transport barrier (e-ITBs) surrounding a large fraction of the plasma volume. [R. Lorenzini et al., PRL 101, 025005 (2008)]

6. IEA RFP Workshop, April 26-28 2010 Padova The e-ITBs are helically shaped The magnetic topology of a SHAx is well described in terms of the helical flux  mn (m=1,n=7)  mn =m  0 - nF 0 + (m  mn – nf mn ) exp i(m  -n  ) Analogous conclusion holds [R. Lorenzini et al., Nature Phys. 5, 570 (2009)] :  for soft X-ray measurements  electron density when significant gradients are induced in the core thanks to pellet injection T e is a function of  mn Axisymmetric fieldDominant mode

7. IEA RFP Workshop, April 26-28 2010 Padova Fascinating and challenging questions to be answered: 1) do MHD secondary modes play a role in the transport through the e-ITB ? 3) why is T e flat in the core ? 2) if yes, are the MHD instabilities the only drive of transport through the e-ITB ?

8. IEA RFP Workshop, April 26-28 2010 Padova do MHD secondary modes play a role in the transport through the e-ITB? When the plasma enters the SHAx state electron temperature and density become functions of the helical flux the flux surfaces are only weakly perturbed by the magnetic chaos and become broken KAM surfaces (cantori), which can sustain strong temperature gradients [S.R. Hudson et al., PRL 100, 095001 (2008)] This led us to infer that the flux surfaces are only weakly perturbed by the magnetic chaos and become broken KAM surfaces (cantori), which can sustain strong temperature gradients [S.R. Hudson et al., PRL 100, 095001 (2008)] Question 1

9. IEA RFP Workshop, April 26-28 2010 Padova... and to lowest s calculated with ASTRA in the static (i.e. power balance) analysis 1) MHD secondary modes play a role The ‘strength’ of the barrier is quantified by means of the gradient length L Te in the barrier: Shortest L Te s are achieved at lowest amplitudes of secondary MHD modes... [R. Lorenzini et al, to be submitted] ><... lowest values of are achieved at lowest values of b ,sec

10. IEA RFP Workshop, April 26-28 2010 Padova are the MHD instabilities the only drive of transport through the barrier? Question 2 According to the experience of the other configurations strong gradients are reservoirs of free energy which can trigger microinstabilities These microinstabilities enhance the local transport and damp the increase of temperature Are the e-ITB gradients ‘limited’ ?

11. IEA RFP Workshop, April 26-28 2010 Padova... L Te has a lower limit L Te,c ~ 0.2 m 2) Evidence of a ‘critical’ gradient length L Te shows a saturation of the minimum achieved value… a gradient length driven transport mechanism These results suggest the presence of a gradient length driven transport mechanism L Te,c ~ 0.2 m

12. IEA RFP Workshop, April 26-28 2010 Padova 2) ITG are stable but... In tokamaks electrostatic Ion Temperature Gradient (ITG) are a major instability and the main cause of transport However several studies agreed that present-days RFX profiles are sub-critical for triggering of ITG [S. C. Guo, PoP 15,122510 (2008), I. Predebon et al., PoP 17, 012304 (2010), F. Sattin et al., submitted ] Another class of instabilities are the high-wavenumber MicroTearing (MT) modes : these modes are driven linearly unstable by electron temperature gradients The linear stability of MT in SHAx states has been investigated by means of the gyrokinetic code GS2 adapted to RFP geometry

13. IEA RFP Workshop, April 26-28 2010 Padova 2)... MT are unstable! The simulations shows that MT are unstable for a significant range of wavenumbers on the barrier [ I. Predebon et al., to be submitted] A scan in a parameter range relevant for RFX-mod shows that a growth rate  > 0 is found when a/L Te,loc > 2, namely when L Te,loc < 0.2 m ~ L Te,c ~ a/L te,loc

14. IEA RFP Workshop, April 26-28 2010 Padova A reduction of stochastic transport is expected Question 3 why is T e flat in the core ? Despite the presence of secondary modes, field line tracing codes (FLiT, ORBIT…) reconstruct surfaces nearly conserved in the plasma core, where the Te profile is flat. However, since there is a significant deposited ohmic power,  is very high and diverges Is this the signature of a non diffusive transport mechanism ? A ‘toy’ model is used to study the electrostatic effects

15. IEA RFP Workshop, April 26-28 2010 Padova A mixing mechanism flattens the profile The numerical model solves the Braginskii Equations An ‘elliptical’ domain mimics the ‘bean’ shape of a SHAx An effective diffusivity, which takes into account the stochastic transport, is added to the BE, low in the core and high at the border of the domain SHAx region (low chaos)  profile  Li [ F. Sattin et al., to be submitted] The simulations show the onset of a compressible flow  which, as a mixing mechanism, flattens the Te profile in the low  region time x  L,i )

16. IEA RFP Workshop, April 26-28 2010 Padova How to include this model in a transport code The imposed  fits the  PB up to the middle of the barrier, then it is decreased to ~ 1m 2 s -1 Heat flux is parametrized as a conductive + a convective term Q =-n  T+nT V pinch Astra integrates the heat continuity equation up to the convergence The T e profile is flat in the core

17. IEA RFP Workshop, April 26-28 2010 Padova Conclusions  Many efforts are devoted to understand the transport through the e-ITBs  The picture we have is that the Te gradients develop thanks to the increased resilience of the SHAx topology to magnetic chaos induced to secondary MHD mode  A residual magnetic chaos due to MHD modes is still present, since steepest gradients and lowest transport are found when secondary modes are lowest  The simulations show that the MTs are unstable on the barrier and could be responsible of the limit on the gradient steepness  Modelling results suggest that the flattening of T e in the core can be due to the presence of a flow generated by electrostatic turbulence

18. IEA RFP Workshop, April 26-28 2010 Padova

19. The role of the magnetic shear

20. IEA RFP Workshop, April 26-28 2010 Padova The role of flow Passive spectroscopy reveals correlation between poloidal flow and dominant mode.

21. IEA RFP Workshop, April 26-28 2010 Padova What do we need for electrostatic transport? electron energy transport with ohmic source conservation and motion of matter charge unbalance arises electric fields drifts. Hence, we must compute self-consistent electric field The numerical model solves the Braginskii equations: electrons and ions do not move alike +

22. IEA RFP Workshop, April 26-28 2010 Padova What do we need for electrostatic transport? The numerical model solves the Braginskii Equations conservation of density An ‘elliptical’ domain mimics the ‘bean’ shape of a SHAx A ‘magnetic’ diffusivity is added to the BE, low in the core and high at the border of the domain conservation of motion for ions and electrons electrons and ions do not move alike charge unbalance arises electric fields drifts conservation of charge heat continuity equation with a ohmic source SHAx region (low chaos)  profile  Li

23. IEA RFP Workshop, April 26-28 2010 Padova Evidence of a ‘critical’ gradient length The ‘strength’ of the barrier is quantified by means of the gradient length L Te in the barrier: T top is T e averaged in the core region surrounded by the barrier <> means the average in the region of the barrier

24. IEA RFP Workshop, April 26-28 2010 Padova Evidence of a ‘critical’ gradient length... experimentally the gradient length L Te has a lower limit L Te,c ~ 0.2 m Te shows a linear dependence from T top. This dependence, if read in terms of gradient length L Te, means that... a gradient length driven transport mechanism This result indicates that we are in presence of a gradient length driven transport mechanism

25. IEA RFP Workshop, April 26-28 2010 Padova A compressible flow flattens T e The simulations show the onset of a compressible flow [ F. Sattin et al.,to be submitted] which, as a mixing mechanism, flattens the T e profile in the low  region

26. IEA RFP Workshop, April 26-28 2010 Padova The plasma likes to be helical The synergistic scaling of the dominant and of secondary modes makes the QSH be purer The spectral index N S =1 in Single Helicity condition The plasma moves towards the SH condition = SH Persistency % Time spent in QSH Flat top duration W n = energy of the m=1,n mode... QSH phases become more frequent and longer increasing the plasma current

27. IEA RFP Workshop, April 26-28 2010 Padova