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ITPA / Stellarator-Tokamak Working Group

Profile dynamics, flows and confinement in Tokamaks and stellarators

Carlos Hidalgo

The presenting author (C. Hidalgo) would like to acknowledge the collaboration with my colleagues of the Stellarator/Heliotron Coordinating Working Group for fruitful and stimulating discussions.

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Profile dynamics, flows and confinement:

Tokamaks vs stellarators

Transport barrier physics:

What is the L-H transition trigger?: Role of steady state and dynamical flows

Confinement and Isotope effect:

What is the relevant scale?

Profile stiffness:

Role of magnetic topology?

Role of magnetic topology (RMPs, rationals)

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Profile dynamics, flows and confinement:

Tokamaks vs stellarators

Transport barrier physics:

What is the L-H transition trigger?: Role of steady state and dynamical flows

Confinement and Isotope effect:

What is the relevant scale?

Profile stiffness:

Role of magnetic topology?

Role of magnetic topology (RMPs, rationals)

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Turbulence and flows near the L-H threshold: evidence of fluctuating radial electric fields

ι/2π = 1.63 ι/2π = 1.53

T. Estrada, et al., EPL 92, 35001 (2010)

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Spectrogram of Doppler reflectometer signals: ñ (colour code) and Er (frequency)

The evolution of Er and ñ shows a predator-prey relation: periodic behaviour of Er and ñ with the predator (flow) following the prey (turbulence) with a phase delay of 90º, consistent with the L-H transition models based on turbulence driven flows.

Dynamics of turbulence and flows near the L-H threshold: evidence of predator prey relation

T. Estrada, et al., EPL 92, 35001 (2010)

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Dynamics of turbulence and flows and L-H trigger: Impact of 3-D magnetic configuration

0

10

20

30

40

ΔH IS

S04/H

ISS0

4 (

%) 3/2 8/5 5/3

4

6

8

10

12

14

1.5 1.55 1.6 1.65 1.7

HL

|Er| m

ax (

kV/m

)

ι/2π(a)

He-J

TJ-II

W7-AS

Low magnetic shear devices:

H-mode with stronger gain in confinement only occurs in certain ι-windows.

Iota windows (but not all) are characterized by minimum of poloidal viscosity right inside LCFS (W7-AS, H-J)

M. Hirsch et al., PPCF 50, 053001 (2008) F. Sano et al., NF 45, 1557 (2005)

T. Estrada et al., CPP 50, 501 (2010)

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Profile dynamics, flows and confinement:

Tokamaks vs stellarators

Transport barrier physics:

What is the L-H transition trigger?: Role of steady state and dynamical flows

Confinement and Isotope effect:

What is the relevant scale?

Profile stiffness:

Role of magnetic topology?

Role of magnetic topology (RMPs, rationals)

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Damping of long-range correlations (GAMs / zonal flows) by magnetic perturbations

Y. Xu et al., IAEA-2010 / Nuclear Fusion 2011

Comparative studies in the level of long-range toroidal correlations in different toroidal magnetic configurations (Tokamak, stellarators, Reversed Field Pinches) and RMP studies in TEXTOR have shown the importance of magnetic perturbation in the level of long-range correlations.

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  Dynamic magnetic configuration scan performed during the discharge in narrow iota range (5 - 10%).

  Presence of different rational surfaces (8/5, 3/2, 5/3,…).

  The LRC shows a significant variation during configuration scan.

M.A. Pedrosa, EU TTG workshop, Córdoba 2010 / EPS-2011

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Long-range toroidal correlations Radial dynamics of GAMs and fluctuations

Y. Xu et al., PPCF-2011

First evidence of turbulence spreading during the H-L transition in the TJ-II stellarator (T. Estrada et al., NF-2011 / TTF-2011 3-D session)

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Profile dynamics, flows and confinement:

Tokamaks vs stellarators

Transport barrier physics:

What is the L-H transition trigger?: Role of steady state and dynamical flows

Confinement and Isotope effect:

What is the relevant scale?

Profile stiffness:

Role of magnetic topology?

Role of magnetic topology (RMPs, rationals)

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Physics of Isotope effect: a fundamental open question

There is experimental evidence that at comparable discharge parameters deuterium discharges have improved confinement properties as compared with hydrogen ones.

The isotope effect is weaker in stellarators (W7-AS, CHS) than in tokamaks. WHY?

While Bohm or gyro-Bohm behaviour are widely used to describe empirical confinement time, they have the wrong isotopic mass dependence: M 0.0 (Bohm) or M-0.5 (Gyro-Bohm).

ITER scaling law (ITER - 98) τ E,th= 0.0562 M 0.19 κa 0.78 R 1.39 a 0.58 Ip 0.9 BT 0.15 ne 0.41 P -0.69

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What scales are involved in the isotope effect physics ?

Local transport parameters? If the ion Larmor radius has a critical size in relation to the turbulence, a change in the Larmor radius might have a strong effect on transport (e.g. Garbet X 1997 Plasma Phys. Control. Fusion 39 B91).

Radial correlation and mass scaling in the TJ-K stellarator M. Ramish et al., PPCF 2008

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What scales are involved in the isotope effect physics ?

Multi-scale mechanisms?: Zonal flows and isotope effects (IAEA-2010)

Isotope Effects on Zonal Flows and Turbulence in Helical Configurations with Equilibrium-Scale Radial Electric Fields

Watanabe, T.H., Sugama, H , Nunami, M.

Fine Scale Zonal Flow Dynamics and Its Effect on Isotopic Dependence of Confinement

Hahm, T.S. , Wang, L ,Yoon, E.S.

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Diagnostic development as trigger of new physics (zonal flow physics): China, EU,

Japan, US,…. Two HIBP systems in the CHS stellarator: Evidence of core zonal flows instellarators

A. Fujisawa et al., Phys. Rev. Lett – 2004 (CHS)

Two Langmuir probe arrays systems separated toroidally / poloidally

María A. Pedrosa (TJ-II) et al. Phys. Rev. Lett -2008; P. Manz (TJ-K) et al., Phys of Plasmas 2009; Y. Xu (TEXTOR) et al., Phys of Plasmas 2009, K. J. Zhao (HL-2A) et al. PRL-2009; R. Wilcox (HSX) et al., TTF-2011

BES: 2-D visualization of core plasma turbulence and flows

George McKee et al., PPCF-2003 / D. K Gupta et al. PRL-2006 (DIIID)

Electric fields and fluctuations by Doppler Reflectometry: role of fluctuating electric fields as L-H trigger

Teresa Estrada (TJ-II) et al., EPL-2010; G. Conway (AUG) et al., Phys. Rev. Lett -2011

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Isotope effect: Multi-scale mechanism?

Characterization of H vs D plasmas in terms of:

•  local correlation lengths •  large scale (zonal) flows

in tokamaks and stellarators

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Profile dynamics, flows and confinement:

Tokamaks vs stellarators

Transport barrier physics:

What is the L-H transition trigger?: Role of steady state and dynamical flows

Confinement and Isotope effect:

What is the relevant scale?

Profile stiffness:

Role of magnetic topology?

Role of magnetic topology (RMPs, rationals)

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Profile stiffness, low magnetic shear and flows (JET)

Ion stiffness is reduced by the combined effect of low magnetic shear and high rotational shear, allowing higher Ti peaking and thereby improving fusion performance/easing pedestal requirements.

[P. Mantica et al., PRL-2009 / EFPW, December 2010]

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Magnetic configuration: tokamaks and stellarators

Magnetic shear

-4

-3

-2

-1

0

1

0 0.25 0.5 0.75 1

ρ/ι dι /dρ

ρ

TJ-II

LHD

W7-AS

CHS

tokamak

H-J

Rotational transform

0

1

2

0 0.25 0.5 0.75 1

ι/2π

ρ

TJ-II

LHD

W7-AS

tokamak

CHS

H-J

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Lack of profile stiffness in stellarators ? (on versus off axis ECRH in W7-A)

F. Wagner et al., Phys of Plasmas 12 (2005) 072509

Consistent with ratio of heat pulse to power balance thermal diffusivities close to one.

But both tokamaks and stellarators show similar confinement degradation scaling with heating power.

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Investigate threshold from power balance (On-and off-axis ECH in W7-AS)

•  R/LTc ≈ 13

•  step in diffusivity

•  flat profile for zero central power

F. Ryter et al., PPCF-2007

Existence of a threshold seems plausible.

Role of large aspect ratio, trapping configuration effects, flat magnetic shear ?

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Magnetic shear and stiffness in stellarators: an open question

D. López – Bruna et al., Nuclear Fusion 44 (2004) 645

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ACTIONS TO BE TAKEN / Tokamaks vs stellarators Profile dynamics, flows and confinement

TRANSPORT BARRIER PHYSICS: The ExB shear paradigm should include both mean and (low) frequency fluctuating radial electric fields. fluctuating electric fields as a trigger of the L-H transition?

Prey-predator mechanisms and L-H trigger : Role of viscosity?. Configuration scan experiments in stellarators

3-D EFFECTS and ZONAL FLOWS: 3-D magnetic topology effects (stochasticity, rationals) in the interplay between equilibrium radial electric fields and zonal flows. Impact on L-H power threshold and background transport?

Radial dynamic of zonal flows / GAMs and turbulence spreading (TTF)

CONFINEMENT AND ISOTOPE EFFECT: Characterization of H vs D in term of local correlation lengths and large scale (zonal) flows. Isotope effect as multi-scale mechanism?

PROFILE DYNAMICS / STIFFNESS: Role of magnetic shear on profile dynamics and zonal flows