Challenges in RFP physicsD.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 crashesExistence of ohmic SH equilibria?Why is shallow reversal a good option?

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

Reversal does not mean high Vloop

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 equilibriumIn a stellarator q is decreasing without any edge current or dynamo

M. Gobbin 2010

Edge current cannot provide reversal in an ohmic RFP

d < Bz > /d= A() < Bz > +S ; A ~ E0 / < B2 >

= pinch term proportional to Vloop

+ stellarator term S independent of Vloop

and vanishing in the axis-symmetric casePinch-stellarator equation First written and discussed by Pustovitov (1982)Derived in a different way by Finn et al. 19921st order linear equation: if S=0 reversal impossible

“Cowling” theoremq ~ < Bz >Only S negative can produce edge axial field reversal

Helical Grad-Shafranov equation + Ohm’s law

Edge reversal without edge current: makes S more efficientVery different from the traditional 1D non ohmic view (BFM) : “An edge current must be present to produce reversalImplies high Vloop since edge highly resistive”

Benefits of shallow reversalSmall Bz0(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 Vloop, and therefore a high energetic cost

To diminish viscous dissipation and beta: choose shallow FPerturbed ultimate paramagnetic pinch (PUPP)Analytical model with small Bz0(a) and |F| with a highly resistive edge: makes S more efficientProvides a necessary criterion for reversalVerified in SpeCyl simulations (D. Bonfiglio)And in RFX for non zero Br(a) (P. Zanca)F<0 more easy than qhelicoidal <0

A path to describe ETB’s?*ETB’s develop in regimes where the secondary modes are relatively low: decreases chaosIndeed ETB’s develop where ordered magnetic surfaces start to show up out of the chaotic region at inner radiiMakes strong grad T possible at r/a=0.8 and not only at reversal as in MH or standard QSHTherefore reversal occurs in a low temperature domain D, like in PUPPThere no current and constant Bz 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 PUPPRemark: the conducting duct narrows, but Vloop not stronger for same I; reminds JET from limiter to divertor

Drawback of a high helical modulation

A priori implies a high dynamo velocity fieldThus high viscous dissipation and beta

Notice: there is a dissipation related to vambipolar too!

QSH Crashes & Ohmic equilibrium

An example of relaxation process: the “Tantale” vase

Not due to the linear instability of an equilibriumMaximum level not unstableAbove this level no equilibrium at all

Is a stationary SHAx state possible?

The system might try to reach oneThen might discover there is noneand would crash without any linear instabilityExponential trend for crashes never found with SpeCyl or experimentallyWith Br(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

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 axisSuggestive of an ohmic trend in the center

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 statesNot obvious to get temperature and q profiles in agreement with SHAx states

= 1.32Bz(1)/Bz(0) = 6.2%T(1)/T(0) = 0.13

Synergy of chaos decrease and shallow reversal

If chaos decreases, resistivity is constant along magnetic surfacesApproximation by (r) questionable

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

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

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

ConclusionBrainstorming about some challenging issues in RFP physics:

How to decrease the Vloop?Shallow reversal a good optionLow dominant mode amplitude (also good for plasma-wall interaction)

Nature of QSH crashes: possibly not due to linear instabilitiesExistence of ohmic SH equilibria: edge ohmic, but center?

Needs of the theory-modeling activity as far as data analysis is concernedPIXIE3D 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-organizationM. 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