internal electron transport barriers in rfx-mod helical equilibria

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


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


The RFX-mod experiment

RFX-mod (Padua, Italy) is the largest RFP presently in operation (R0 = 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 independentlycontrolled and respective sensors


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 Ip

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)


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)]


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=m0 - nF0 + (mmn – nfmn) 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

Te is a function of mn

Axisymmetric field Dominant mode


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 Te flat in the core ?

2) if yes, are the MHD instabilities the only drive of transport through the e-ITB ?


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

This led us to infer that the flux surfaces are only weakly perturbed by the flux surfaces are only weakly perturbed by the magnetic chaos and become broken KAM surfaces (cantori), the magnetic chaos and become broken KAM surfaces (cantori), which can sustain strong temperature gradients which can sustain strong temperature gradients

[S.R. Hudson et al., PRL [S.R. Hudson et al., PRL 100100, 095001 (2008)], 095001 (2008)]

Question 1


... and to lowest <PB>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 LTe in the barrier:

Shortest LTes are achieved at lowest amplitudes of secondary MHD modes...

e

eTe T

TL

[R. Lorenzini et al, to be submitted]

><

... lowest values of <PB> are achieved at lowest values of b,sec


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’ ?


... LTe has a lower limit LTe,c~ 0.2 m

2) Evidence of a ‘critical’ gradient length

LTe shows a saturation of the minimum achieved value…

These results suggest the presence of a gradient length driven transport mechanisma gradient length driven transport mechanism

LTe,c~ 0.2 m


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


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/LTe,loc > 2, namely when LTe,loc < 0.2 m ~

LTe,c

~

a/Lte,loc


A reduction of stochastic transport is expected

Question 3

why is Te 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


A mixing mechanism flattens the profile

The numerical model solves the Braginskii EquationsThe numerical model solves the Braginskii Equations

An ‘elliptical’ domain mimics the ‘bean’ shape of a SHAx An ‘elliptical’ domain mimics the ‘bean’ shape of a SHAx

An effective diffusivity, which takes into account the An effective diffusivity, which takes into account the stochastic transport, is added to the BE, low in the core and stochastic transport, is added to the BE, low in the core and

high at the border of the domainhigh at the border of the domain

SHAx region (low

chaos)

profile

Li

Li

[F. Sattin et al., to be submitted]

The simulations show the onset of a compressible flowwhich,

as a mixing mechanism, flattens the Te profile in the

low region

time

xL,i )


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 ~ 1m2s-1

Heat flux is parametrized as a conductive + a convective term

Q=-nT+nTVpinch

Astra integrates the heat continuity equation up to the

convergence

The Te profile is flat in the core


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 Te in the core can be due to the presence of a flow generated by electrostatic turbulence


The role of the magnetic shear


The role of flow

Passive spectroscopy revealscorrelation between poloidalflow and dominant mode.


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

SqvpTn23

t

The numerical model solves the Braginskii equations:

electrons and ions do not move alike

+


What do we need for electrostatic transport?

The numerical model solves the Braginskii EquationsThe numerical model solves the Braginskii Equations

conservation of density

An ‘elliptical’ domain mimics the ‘bean’ shape of a SHAx An ‘elliptical’ domain mimics the ‘bean’ shape of a SHAx

A ‘magnetic’ diffusivity is added to the BE, low in the core A ‘magnetic’ diffusivity is added to the BE, low in the core and high at the border of the domainand 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

Li


Evidence of a ‘critical’ gradient length

The ‘strength’ of the barrier is quantified by means of the gradient length LTe in the barrier:

e

topTe T

TL

Ttop is Te averaged in the core region surrounded by the barrier

<> means the average in the region of the barrier


Evidence of a ‘critical’ gradient length

... experimentally the gradient length LTe has a lower limit LTe,c~ 0.2 m

Te shows a linear dependence from Ttop.

This dependence, if read in terms of gradient length LTe, means that ...

This result indicates that we are in presence of a gradient length driven transport mechanisma gradient length driven transport mechanism


A compressible flow flattens Te

The simulations show the onset of a compressible flow

[F. Sattin et al.,to be submitted]

which, as a mixing mechanism, flattens the Te profile in the

low region


The plasma likes to be helical

1

2

mm

nn

SW

WN

The synergistic scaling of the dominant and of secondary modes makes the QSH be purer

The spectral index NS=1 in Single Helicity condition

The plasma moves towards the SH condition

= SH

Pers

iste

ncy

%

Time spent in QSH

Flat top duration

Wn= energy of the m=1,n mode

... QSH phases become more frequent and longer increasing the plasma current

internal electron transport barriers in rfx-mod helical equilibria

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