He

1
He Impurity transportIntroduction Remarks on
modeling aspects

• C. Angioni

with special thanks to C. Bourdelle, E. Fable, T.
Hein
J. Candy and R.E. Waltz are warmly acknowledged
for providing GYRO, M. Kotschenreuther and W.
Dorland for providing GS2
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Motivation

• Impurity transport produced by combination of
  neoclassical and turbulent effects

• Practical operational interest, to learn how to
  avoid too large dilution and radiation losses in
  the core

• Physical interest, impurity transport is the
  natural complement to electron transport in the
  validation of the entire theoretical paradigm of
  particle transport

• Theory of turbulent transport asked to reliably
  predict both D and V separately (and not only V/D
  like in electron particle transport)

• Size of D from turbulent transport is critical in
  determining the relative impact of the
  neoclassical pinch, and of the central source of
  He ash

• Impurity charge (and mass) provides additional
  handle to characterize experimental observations
  in terms of theoretically predicted transport
  processes

3
Turbulent transport, complex theoretical pattern
of inward and outward contributions

• Framework for theory validation Do experiment
  exhibit (qualititatively, quantitatively) the
  same pattern

4
Impurity charge provides additional handle to
identify different transport processes
Bourdelle PoP 07

• Although electrostatic turbulent transport is
  produced by fluctuating ExB drift, dependences on
  Z and A arise from the resonances, provided by
  the perpendicular and parallel gyro-centre motions

• Perpendicular motion, curvature and grad B drift
  prop. to 1/Z
• Parallel motion, electric force term proportional
  to Z/A, pressure term proportional to 1/A

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Relevant parameters for comparison between theory
and experiment

• Transient transport experiments by impurity laser
  ablation or gas puffs can determine both
  diffusion and convection separately

• One goal is to identify and agree on a set of
  parameters suited to compare experimental results
  with theoretical predictions

• Dimensionless forms have to be preferred, because
  not directly limited by the requirement of
  matching heat fluxes in simulations which have to
  predict absolute values (in m2/s) of the
  diffusivity

• Most natural choice (already adopted in several
  exp. papers)

where
and
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Application to He transport at typical H-mode
parameters (ITER standard scenario)

• Input parameter of linear and nonlinear
  simulations provided by a GLF23 simulation of the
  ITER standard scenario

• D is an actual (incremental )diffusivity, c is a
  power balance conductivity

• The predicted value of D/c does not change
  significantly with increasing values of R/LT
  (blue curve 20 smaller)

• Predicted values of D/c rather constant along
  minor radius and around 2, most of experimental
  estimates indicate lower values ( around 1 or
  less )

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b predicted to decrease ratio D/c

• Theoretically predicted dependence to be
  validated against experimental results
• Qualitatively in agreement with observations in
  DIII-D Petty PoP 04

Hein Angioni PoP 10

• Requires quantitative comparisons

• Could be of some concern for very high beta
  scenarios in case the drop of diffusivity becomes
  too large

• Too strong effect of central source of He ash on
  He peaking
• Too weak reduction of impact of neo inward pinch
  of high Z impurities by turbulent D

8
Turbulent convection of He at typical H-mode
parameters (ITER standard scenario)

• He found to be convected inward for typical
  H-mode parameters (outward thermodiffusion (ITG)
  does not compensate inward convection )
• The same takes place for heavier impurities (B,
  C), and this appears to not account for
  observations of flat/ hollow density profiles of
  B and C in H-modes AUG McDermott yesterday, JET
  Weisen (NF 05) and Giroud today

Angioni NF 09

• On the other hand, this He transport provides a
  He profile which has the same shape as the
  predicted electron density profile, in agreement
  with some observations DIII-D, Wade PoP 95

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b has some (limited) effect also on V / D
Hein Angioni PoP 10

• Note opposite direction of thermodiffusion
  between He and T due to the different charge
• Magnetic flutter practically negligible on
  diffusion thermodiffusion, gives up to 10
  correction for the pure convection piece

10
b has some (limited) effect also on V / D

• Summing all effects, beta is predicted to lead to
  weak accumulation of intermediately heavy
  impurities (typical H-mode parameters)
• b.t.w, this goes in the wrong direction to get
  flat/hollow C profiles in H-modes
• Effect on V/D of light impurities is weak

Hein Angioni PoP 10
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Outward turbulent convection

• The only mechanism identified so far which can
  produce a total outward turbulent convection of
  intermediate / heavy impurities is parallel
  compression of parallel velocity fluctuations
• This requires usually R/LTe gtgt R/LTi, as in the
  case of the simulations at r/a 0.2 in the
  presence of ECH ( AUG case, agrees with
  experimental measurements on Si )
• Note, at r/a 0.5 all Z go inward (in agreement
  with Si exp measurements, but also C is predicted
  inward )
• Still, one could speculate ( hope ) that by
  appropriate choice of parameters, for impurities
  like B and C, conditions where thermodiffusion
  (outward in ITG) is large enough to prevail over
  inward convection can be idenitified ( not yet
  though)

Angioni PPCF 07
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Outward turbulent convection in NL simulations

• The mechanism of outward impurity convection in
  the presence of electron drift propagating
  turbulence has been confirmed in nonlinear
  gyrokinetic simulations with GYRO (case Qe 2Qi
  )
• For ion and electron heat fluxes which are of
  comparable size, the pure convection is directed
  inward

Angioni NF 09
GYRO

• Observations of outward convection of impurities
  provide real challenges for theory / modelling
  and are effective for validation
• In turbulence, outward convection obtained only
  when specific transport processes prevail over
  the inward ExB compression pinch
• In addition, plasma conditions leading to
  outward (or weak inward) convection of impurities
  are also operationally attractive

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Conclusions

• The combination of intense current and past
  experimental studies on impurity transport (whose
  review with specific focus on He is the topic of
  the present session) should allow us to
  characterize experimental phenomenology in a more
  comprehensive way

• This gives also the conditions for an
  unprecedented effort in validation of turbulent
  theory of impurity transport

• Proposed key objectives

• Investigate of size and main parametric
  dependences of the ratio of the turbulent
  diffusivity to the effective heat conductivity

• Identify conditions leading to outward impurity
  convection, for more effective validation of
  theoretical predictions

• The combination of these studies with those on
  other transport channels and/or with additional
  informations from fluctuation measurements makes
  the validation effort more complete and
  conclusive