Effect of rotational transform and magnetic shear on
confinement of stellarators
E. Ascasíbar(1), D. López-Bruna(1), F. Castejón(1), V.I. Vargas(1), V. Tribaldos(1), H. Maassberg(2), C.D.
Beidler(2) R. Brakel(2), A. Dinklage(2) J. Geiger(2), J.H. Harris(3,4), A. Kus(2) T. Mizuuchi(5), S. Murakami(5), S.
Okamura(6), R. Preuss(2), F. Sano(5), U. Stroth(7), Y. Suzuki(6), J. Talmadge(8), K.Y. Watanabe(6), H.
Yamada(6), M. Yokoyama(6)(1) CIEMAT, Madrid, Spain(2) Max-Planck-Institut für Plasmaphysik, EURATOM Association, Greifswald, Germany(3) Oak Ridge National Laboratory, USA(4) Australian National University, Canberra, Australia(5) Kyoto University, Kyoto, Japan(6) National Institute for Fusion Science,322-6 Oroshi-cho, Toki 509-5292, Japan(7) Institut für Plasmaforschung, Universität Stuttgart, Germany(8) University of Wisconsin, USAInternational Stellarator/Heliotron Confinement Database and Profile Database(ISHCDB & ISHPDB)
http://iscdb.nifs.ac.jp/ and http://www.ipp.mpg.de/ISS

Introduction/motivation
2
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LHD
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rotationaltransform
and0.5magnetic
shear 1remain as two important elements whose role on
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confinement must be consideredin
futuredesigns
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fora
stellarator
reactorr/ar/aIntroduction/motivation
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1rotational transform and magnetic shear remain as two important elements whose role onconfinement must be considered in future designs of candidates for a stellarator reactor

2

Open questions•Is there a threshold for the magnetic shear over which low orderresonances lose their detrimental character? Does this threshold dependon the value of the rotational transform itself?
•What is the effect of resonances when the shear is above this threshold?
•Is the sign of the shear important, or is only its magnitude what matters?
•Impact of large shear: Is there a saturation or even degradation ofconfinement over a certain upper threshold?

Outline
Scope of the work restricted so far to low shear devices: W7-AS, TJ-IIand Heliotron J• Dependence of global confinement on iota
• Effect of low order resonances on confinement– Degraded confinement at low β with no shear– Improved electron transport in the vicinity of low order rationals• TJ-II specific: Local lowering of Xe when “moving” low order rationals
through the plasma• Role of (moderate) magnetic shear• SummaryImpact of iota and shear in ISS95 and ISS04: 0-d scaling–deduced from W7-AS–suported by intermachine analyses–configuration-dependent parameter needed for a unified scaling (s-parameter, related to shear)

ISS95 1τE ∝ iota2/3 0.4
ISS04 2,3–additionally supported by TJ-II individual resultsτE ∝ iota2/3–old s-parameter not sufficient for unified scaling

0.41–configuration-dependent renormalization factor needed, related to properties of the helical fieldstructure. i.e., effective helical ripple, plateau factor, elongation
W7-AS !-scan [Brakel, NF42 (2002)] (f=0.60)
IotaScan
00:34:40
9/10/07
TJ-II (ISS04data)(f=0.30)
Heliotron J (ISS04 data) (f=0.60)
ISS04 without !-dependence

20.41"ISS04 ! !

a2.28" exp/f * " ISS04

1.50-d scaling is not enough

10.5
1 Stroth et al., NF 1995

02 Yamada et al., NF 2005

00.5

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2

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3 Dinklage et al., FST 2007, NF 2007

Local transport analysis needed•Understanding the physics behind the configuration-dependent renormalization factor (role played byiota, rationals and shear) requires local transport analysis of density and temperature profiles.
•Warning: Particle confinement (also sources) can depend on edge iota and shear. Example fromW7-AS: a degradation of global tE, can have negligible impact on local Xe. Important to analyze
completely both density and temperature profiles.

Degraded confinement due to low orderresonances at low β, small shear: W7-AS
in the absence of magnetic shear, global confinement depends strongly on edge iota.
The variations correlate with changes in local electron energy transport (Brakel NF 02)

Degraded confinement due to low orderresonances at low β, no shear: TJ-II
ECH discharge with induced OH current•time evolution of effective Xe (obtained from power balance calculations). Te profiles from
ECE diagnostic•estimated time evolution of iota (assuming total current due to OH transformer): it isforced to flatten so that 3/2 occupies part of the plasma with no shear.

3/2 does not deteriorate transport until 1160-80 ms

Transient flattening of the pressure profileImproved electron transport in the vicinity of loworder resonances: W7-AS•Empirical model assuming that transport is enhanced at rational surfaces (MHD or turbulence).
This enhancement is reduced by magnetic shear (Brakel NF 02)•The favourable confinement close to rationals is due to the rarefaction of higher order rationals
in their vicinity•The model reproduces the iota-dependence of global confinement measured in W7-AS

Improved electron transport in the vicinity oflow order resonances: TJ-II<n e > (1019m-3)

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0.6
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Ti (eV)

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Ip (kA)•

Significant experimental evidence in TJ-II of the role of low order resonances as triggers fordifferent improved transport events.
Recent example of CERC in TJ-II: rational surface 4/2 with moderate shear (OH induced current)
triggers a transition with increase also in the ion temperature-2-3-4
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T. Estrada
P1-28 TuesdayImproved electron transport in the vicinity oflow order resonances: Heliotron Jiota windows for the high quality H-mode (τexp/ f×τISS04 > 1.5)
close to low order rationals

Tracking the local lowering of Xe due to low orderrationals in TJ-II plasmas
Moving low order rationals shot by shot: fixed shear (Vargas NF 07)•local power balance analysis: Xe Interpolated: pattern of grooves and ridges•small value of net plasma currents: iota estimation more reliable for ρ > 0.5•low order rationals retain fluxes at their radial location

13 configurations: sweeping therationals inwards through the confinedplasma as Ih increases

D. Lopez-Bruna

Xe contour plot
pattern of “ridges” and “grooves” P1-16 Tuesday

The role of (moderate) magnetic shear: W7-AS•The strong dependence of the energy content on configuration at zero shear is smoothed as thecurrent is raised and disappears at the highest current value. Confinement reaches its maximum
with high currents (Brakel PPCF 97).
•Local power balance analysis shows restoration of degraded confinement through a strong
reduction of Xe in the gradient region. The 1/2 surface can stay inside the plasma with nosignificant degradation of confinement•Confinement increases independently of shear signdischarges with identicallimiter aperture and densities

The role of (moderate) magnetic shear: TJ-II

202

thermal diffusivity (!=0.75), m /s

•Xe at ρ = 0.75 for six ECRH discharges with similar density, in plasmas with induced OHcurrent.
•largest Xe found around zero shear•confinement improved for both shear signs. Less clear for the positive case due to thesmaller accesible range

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Summary• In the absence of magnetic shear, global confinement is deterioratedby the islands caused by low order rationals• Narrow optimum confinement windows are found in W7-AS andHeliotron-J close to low order rational values. In TJ-II, provided asmall amount of magnetic shear, low order resonances trigger avariety of improved transport events. Fine configuration scans in thismachine show that low order rationals retain heat fluxes at theirradial location.
• Certain amount of shear allows the presence of even the lowest
order rationals within the confinement region. It is still unknown
whether the amount of shear needed depends on the iota value.
• The beneficial effect of shear on confinement does not depend on
the sign.
• (this work is just a sterting point!)

Looking to the future•Documentation: Continuing effort in data quality improvement (validated profiles, errors,uncertainties, ...)
•comparisons between W7-AS and TJ-II: lower threshold for the shear?, does it depend on
the iota-value?
•Tracking low order rationals experiments in TJ-II:–issue: Xe contour plot needs further confirmation and careful estimation of internalcurrents–new experiments in the pipeline : slow increase in the flat top value of helical coilcurrent (≈ 5 kA/s) -> dynamic change of configuration with fixed shear–will the effect survive in higher density NBI discharges?
•Impact of large shear: Comparison with CHS, LHD needed. Is there a saturation or evendegradation of confinement over a certain upper threshold?
•W7-X is the first device able to face the challenge of keeping the configuration free of loworder rationals. ECRH provides an additional tool to compensate internal currents

Introduction/motivation
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1rotational transform and magnetic shear remain as two important elements whose role onconfinement must be considered in future designs of candidates for a stellarator reactor2

Back up• The logic behind this type of questions is clear: Provided that low
order resonances do not deteriorate confinement anymore in thepresence of enough (perhaps very low) magnetic shear then thedesign constraints of future stellarators might be relieved: a strict
control of the magnetic shear (i.e. internal currents) would nolonger be necessary and the available configuration space tooptimize other physics aspects would expand.

Degraded confinement due to low order resonances
at low β, no shear: Heliotron J• Transient degradation for iotaa ≈ 0.59-0.62• No degradation for iotaa ≈ 0.49-0.51

Degraded confinement due to low orderresonances at low β, no shear: TJ-IIrotational transform

1.6
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t=1150 ms
t=1160 ms
t=1170 ms
t=1180 ms
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normalized minor radiusestimated time evolution of iota (assuming total current due to OH transformer)