Validation of iota dependence in helical systems

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Validation of iota dependence in helical
systems and remark on its comparison with tokamak
H.Yamada National Institute for Fusion Science
1. Looking back to the process in ISS95 2. ISS04
? Andreas 3. Limiter experiment in LHD 4. Remark
on translation between iota and plasma currents
Acknowledgements LHD experimental group, in
particular, K.Yamazaki, K.Ida S.Murakami,
M.Yokoyama, K.Y.Watanabe, K.Nishimura and
colleagues of the international stellarator
database J.H.Harris, A.Dinklage, E.Ascasibar,
F.Sano, U.Stroth, S.Okamura
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Energy confinement time Ansatz
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Brakel
W7-ASModelling of iota-dependence
Transport model c enhancement at rational iotas
ce(r, i, i) cneo can cmn
cmn S amn exp (- i - n/m - g i)
rmni
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Effect of Rotational Transform - still
remains a continuing concern -
Colinearity between i and Ap in helitorons
? Iota dependence is statistically unstable due
to colinearity with aspect ratio. ? Limiter scan
in Heliotron E plays a major role. Nonetheless,
for complete dataset, ? Omitting rotational
transform dependence gives a dimensionally
incorrect result. ? Significance of iota
dependence exists wherever iota is evaluated.
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Expressions are so similar to each other
whichever these are due to logical consequence or
a coincidence without logic
Anyway, this similarity has motivated a unified
scaling law
However, Iota dependence is delicate compared
with dependences of density, heating power and
magnetic field. Helitron/Torsatron line
Limited number of limiter insertion experiment
plays an essential role. Rely on negative
evidence Exclusion of iota dependence yields a
strange scaling impression
Wendelstein line Derived from a major
envelope Iota dependence is still an open
question.
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Supporting Evidence ? Limiter insertion in LHD
Iota dependence is unclear, but not denied and
may be better
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Comparison with tokamaks Limiter insertion in LHD
Tokamak like iota dependence is too strong
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Comparison with tokamak database with Ip (qa,
)
Translation of Ip to i
Different definition of a
? Performance of LHD is equivalent to tokamak
H-mode with q 5 ( qa of LHD is 0.6 ! ) ?
Tokamak H-mode above ISS95 by 3 ? Confinement
stellarator is comparable to L-mode
Are these true ?
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Translation between Ip and q ( ) as
representing indices
li dependence in tokamaks
Equivalent current
JT-60U, TFTR
Poloidal flux is the volume integral of iota
Poloidal flux explain both Ip and li dependences
The value at r2/3 is a good approximation of the
volume averaged value. ? Iota at r2/3 can
represent poloidal flux
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Comparison with tokamaks by stellarator scaling
with q(2/3)
Take the value of the rotational transform at
r2/3 assuming the profile
ISS95 gives tolerable fit to both H-mode and
L-mode in tokamaks
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Summary
Iota dependence of energy confinement time is
delicate. We have some supporting evidences
which are not sufficient to conclude.
Heliotron line Limiter insertion experiment,
Inter-machine comparison Wendelstein line
Trend of envelope of optimized configurations
Comparison with tokamaks requires iota
dependence. ? Extended study in TJ-II
broadens a horizon Possible contribution from
LHD Limiter insertion A few
tens data exist although the operation is limited
to low heating power.
Plasma current scan Currents up to
150 kA are observed in LHD
changing iota value by only 15
effect in the core may be larger
? require identification of iota
profile MSE
measurement is becoming available
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There exist systematic gaps between each
experiment.
1. W7-AS and heliotrons(ATF,H-E,CHS) still
unresolved
? Quite similar scaling expression from
independent analysis
combined dataset does not give a reasonable
result.

• Accept difference for magnetic configuration
• Artificial parameter express difference between
  HT W7-AS
• Shear parameter s, (s1 for HAC, s0 for
  W7-AS)
• ISS95

Sensitivity 1) simple regression RMSE0.0981
2) s fit RMSE0.0905
3) 0.85tE for W7-AS s-0.210.02 RMSE0.0898
4) 1.2a for W7-AS s-0.080.02
RMSE0.0899
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Revision of Database Both Interest and
Requirement are Emerging.
? New experiments have been launched since 1995
LHD, TJ-II, Heliotron-J, HSX ? extending
envelope of parameters and property of magnetic
configuration
? A variety of improved modes (W7-AS, CHS,
LHD) ? Deuterium beam injection into deuterium
plasmas (W7-AS) ? Island divertor (W7-AS, LHD)
? Charge from international stellarator steering
committee required for reactor assessment ?
Comprehensive understanding of transport in
net-current-free plasmas ? More comprehensive
understanding of transport in toroidal plasmas
together with tokamak database.
Reactor
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W7-AS a) Iota dependence of confinement
footprint of low-shear stellarators
iota profiles
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Comparison with Tokamak Database Provisional
Translation of Ip to i
Take the value of the rotational transform at
r2/3 ?
Different definition of a
Reasonable reconsideration of profile effect is
allowed.
L-mode HISS950.930.28 RMSE0.130 H-mode
HISS951.400.34 RMSE0.102
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Parameter dependence in each subset
? Careful consideration is required when
sub-groups are to be linked. ? ne , P and B
dependences can be found as a general trend in
subsets
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International Stellarator Database Under auspices
of IEA Implementing Agreement for Cooperation in
Development of the Stellarator Concept
Originally, the activity was launched from the
collaboration between ORNL(ATF) and IPP(W7-AS) ,
and then NIFS(CHS) and Heliotron E (Kyoto Univ.)
joined. Derivation of international stellarator
scaling 95 (ISS95) Nucl.Fusion (1996)
Addition of data from LHD, W7-AS, TJ-II and
Heliotron J (HSX will join soon). The presently
available data gt 2500
Database(web) is jointly hosted by NIFS and IPP.
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Heliotrons LHD,Heliotron E, CHS ATF
Advanced stellarators W7-AS, HSX, Heliotron J
Heliacs TJ-II, H-1
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TJ-IICorrelation matrices
(0.11-0.19)
(0.13-0.19)
(120-240)
(90-360)
(0.24-1.2)
(0.4-1.1)
(1.25-2.37)
(1.25-2.17)
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Comparison of ??dependence in both data sets

• All-metal Higher slope but not clear evidence of
  preferent confinement deterioration in the low-i
  region

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Towards a unified scaling expression - from
entire available data including LHD, TJ-II and
Heliotron J -
A simple regression analysis gives
RMSE0.101
? Dimensionally incorrect and strange
expression. ? Contradict knowledge from each
experiment, ex. gyro-Bohm, iota dependence. ?
Major cause can be attributed to an
unknown configuration dependent parameter.
LHD
However, a key configuration dependent parameter
has not been identified. ? A configuration
dependent parameter is ad hoc assumed for
the enhancement factor on the scaling
expression which starts from ISS95. ?
Renomalization fren ltHISS95 of subsetgt /
ltHISS95 of W7-AS with low iotagt Then
regression analysis of tEexp / fren . ? This
iteration process tends to converge into a
certain expression.
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Unified scaling providing upper envelope of
helical systems
Similar to ISS95 gyro-Bohm, no definitive
dependence on b an n, dimensionally correct
RMSE0.026
? Underlying physics of renormalization factors
which contains uncertainties peculiar to each
configuration. ? Investigation of correlation
of fren with physical parameters, ex. eeff. ?
Employment of renormalization factor ? Can we
derive size scaling ?
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Optimization of stellarators
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Possible geometrical effects on heat transport
? results from DCOM, DKES,MOCA guaranteed by
benchmarking neoclassical effect
Something else, ex., degradation of heating due
to losses during slowing down process, linkage
with anomalous transport through viscous flow
dumping.
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Potential effects of eeff
1. neoclassical transport in 1/n regime. 2.
Orbit losses during a slowing- down process of
energetic particles, leading to degradation of
heating efficiency. 3. Flow dumping, linked
with anomalous transport?
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Conclusions

• International collaboration of Stellarator
  Confinement DataBase is progressing to resolve
  diversity of stellarators towards a unified
  scaling.
• Dependences on heating power, density and
  magnetic field are found as a generic trend in
  sub-groups.
• Rotational transform dependence is prone to be
  statistically unstable and concomitantly size
  dependences as well. Nonetheless, experimental
  evidences support significance of that. And an
  unequivocal evidence is being available in a
  landmark experiment in TJ-II.
• A provisional unified scaling expression has been
  proposed, which is a gyro-Bohm type and has no
  definitive dependences on b an n.
• Configuration dependent difference is required
  for a unified expression.
• Configuration dependent difference has a good
  correlation with an effective helical ripple.

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Provisional comparison with tokamaks by tokamak
scalings Provisional
J.G.Cordey 4th ITPA (2003)
After renormalization RMSE0.136
After renormalization RMSE0.129
? Tokamak H-mode (IPB98(y,2)) has similar
expression to ISS95 except for b and i. ? Recent
model for the core has closer to ISS95 and gives
good fit for each subset.
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