Member of the Helmholtz Association T. Zhang | Institute of Energy Research – Plasma Physics | Association EURATOM – FZJ Radial Correlation Analysis of Turbulence inside H-mode pedestal on JET T.Zhang 1*, A.Fonseca 2, Y.Liang 1, A. Krämer-Flecken 1, S. Soldatov 1,3, Y.Xu 4, Y.Sun 1, C. Wiegmann 1, H. R. Koslowski 1 1 Insititute for Energy Research-Plasma Physics, Forchungszentrum Jülich GmbH 2 Associação EURATOM / IST, Centro de Fusão Nuclear, Av. Rovisco Pais, Lisboa, Portugal 3 FOM-Institute for Plasma Physics Rijnhuizen 4 Laboratory for Plasma Physics, Ecole Royale Militaire/Koninklijke Militaire School, Euratom-Belgian State Association, Avenue de la Renaissance 30, B-1000 Brussels, Belgium *

T.Zhang | Institute of Energy Research – Plasma Physics | Association EURATOM – FZJSeptember 22end, /13 Motivation  The confinement of plasma in tokamak is determined by the turbulence dominated transport.  A heuristic formula for turbulence dominated radial transport from the random walk model is in which the L r is the turbulence radial correlation length and  c is the de- correlation time.  The study of turbulence radial correlation inside pedestal of H-mode will give new insights to the understanding of pedestal physics. But rare reports about it.  Radial correlation reflectometry systems on JET can be used to study the density fluctuation correlation length inside the pedestal.

T.Zhang | Institute of Energy Research – Plasma Physics | Association EURATOM – FZJSeptember 22end, /13 Outline  The principle of radial correlation measurement by reflectometry and JET reflectometry systems.  Results: The dependence of correlation length and fluctuation level on pedestal parameters.  Summary

T.Zhang | Institute of Energy Research – Plasma Physics | Association EURATOM – FZJSeptember 22end, /13 The principle of radial correlation measurement by using Reflectometry Launching microwave with different frequency f 1 and f 2, the radial separation of cutoff layer is  r. A group of probing frequency [f 1,f 2,f 3,….]. Several radial separations [  r 1,  r 2,…..] of cutoff layers and corresponding normalized cross-correlations [  1,  2,….] Radial correlation length L R of Reflectometry signal. Cutoff layer 1 Zero-time lag Cross- correlation Cutoff layer 2

T.Zhang | Institute of Energy Research – Plasma Physics | Association EURATOM – FZJSeptember 22end, /13 Radial correlation Reflectometry on JET  Fast frequency scan in variable channel for radial correlation.  In Ohmic and L-mode plasma, correlation length can be measured from the analysis between fixed and variable channel for each system.  In some H-mode cases, the correlation length inside the steep pedestal can be measured by the inter-system correlation analysis.  This presentation concentrates the correlation analysis inside pedestal. Fixed channel variable channel

T.Zhang | Institute of Energy Research – Plasma Physics | Association EURATOM – FZJSeptember 22end, /13 One example of measurement inside pedestal  Take the 92 GHz (or GHz) as the reference, the cross correlation can be calculated for different combinations.  The cutoff layer can be calculated from the density and B t profiles.  The  r plot may be fitted by a Gaussian curve.  But, in order to get the real turbulence correlation length, more works needed…….

T.Zhang | Institute of Energy Research – Plasma Physics | Association EURATOM – FZJSeptember 22end, /13 First order The reflected wave can be expressed as: Then we can define a quantity: E Z Gusakov and A Yu Popov, PPCF 44 (2002) 2327 And the CCR is the normalized cross-correlation function of density fluctuation: The cross-correlation of complex signals from two different probing frequency: From reflectometry correlation length to turbulence correlation length using 1D WKB approximation (1) What we want to know! What we know from Exp.!

T.Zhang | Institute of Energy Research – Plasma Physics | Association EURATOM – FZJSeptember 22end, /13 And the CCR is the normalized cross-correlation function of density fluctuation: From reflectometry correlation length to turbulence correlation length using 1D WKB approximation (2) What we want to know! What we know from Exp.!  In experimental density and magnetic field profiles, we scan the  n /n and L r and do the double integration. Then compare the results to the experimental values. A best fitted values of  n /n and L r can be found!

T.Zhang | Institute of Energy Research – Plasma Physics | Association EURATOM – FZJSeptember 22end, /13 Dependence of correlation length with pedestal density gradient (scale length)  The real density fluctuation correlation length L r is some different from reflectometry correlation length L R, but very close in our case.  The result shows that the L r decreases (increases) with the increase of density gradient (density gradient scale length).

T.Zhang | Institute of Energy Research – Plasma Physics | Association EURATOM – FZJSeptember 22end, /13 Dependence of L r on the density pedestal width W ne ped  The correlation length L r is always less than the density pedestal width W ne ped for the current analyzed data.

T.Zhang | Institute of Energy Research – Plasma Physics | Association EURATOM – FZJSeptember 22end, /13 Dependence of density fluctuation level with pedestal density gradient (scale length)  Density fluctuation level  n /n is from ~1% to ~2% inside pedestal.   n /n seems to increase with the increase of density gradient.   n /n shows some increase with the increase of L r /L n, while the value is far less than the mixing length estimate, i.e,  n /n<<L r /L n.

T.Zhang | Institute of Energy Research – Plasma Physics | Association EURATOM – FZJSeptember 22end, /13 Summary  The density fluctuation correlation length inside JET pedestal has been measured by the reflectometry. The correlation length from Refl. has been converted to the real turbulence correlation length through the first order WKB approximation.  Results show that the correlation length L r is from 0.7 to 1.4 cm and it is always less than the density pedestal width. And L r decreases with the increase of the density gradient.  The fluctuation level  n /n is in the range of 1%~2% and far less than the mixing length estimate.  An 1D full wave code is constructed and the comparisons between 1D full wave result and WKB approximation show that the conversion procedure is reasonable for JET pedestal case.

T.Zhang | Institute of Energy Research – Plasma Physics | Association EURATOM – FZJSeptember 22end, /13 Thanks for your attention!

T.Zhang | Institute of Energy Research – Plasma Physics | Association EURATOM – FZJSeptember 22end, /13  Comparison of 1D full wave and WKB approximation for typical density and B t profiles.

T.Zhang | Institute of Energy Research – Plasma Physics | Association EURATOM – FZJSeptember 22end, /13 Density and Magnetic filed profiles.  In order to compare the WKB approximation and 1D full wave result, a typical density profile and B t profile are selected for our case.

T.Zhang | Institute of Energy Research – Plasma Physics | Association EURATOM – FZJSeptember 22end, /13 1D full wave simulation and WKB approximation  Start the numerical solution of the X-mode 1D time-independent equation from the over-dense region. WKB1WKB2 First order  Assume a spatial-temporal distributed density fluctuation: The wave number k j is chose to be in the range [0 ~ 6 cm -1 ] and 300 values. The phase  j is random distributed in the range [- ,  ]. The time points are 512 for statistic analysis.  The 3 methods, i.e, WKB1, WKB2 and full wave will be compared at different fluctuation level and different correlation length.

T.Zhang | Institute of Energy Research – Plasma Physics | Association EURATOM – FZJSeptember 22end, /13 Comparison at different fluctuation level (I)

T.Zhang | Institute of Energy Research – Plasma Physics | Association EURATOM – FZJSeptember 22end, /13  WKB1 gives a very good approximation to the full wave solution in the scanned parameter range.  WKB2 also gives good approximation up to  n /n ~ 7%, while deviates at higher fluctuation level since WKB2 is only the first order approximation of WKB1.  Since our results show that the  n /n is from 1% to 2% which is in the range of applicable range of WKB2, we conclude that our previous conversion procedure is applicable. Comparison at different fluctuation level (II)

T.Zhang | Institute of Energy Research – Plasma Physics | Association EURATOM – FZJSeptember 22end, /13 Comparison at different correlation length.  Three methods are compared at different correlation length Lc=0.55 cm, 1 cm and 2.7 cm with the same density fluctuation level  n /n ~  Good consistence of the three methods.

T.Zhang | Institute of Energy Research – Plasma Physics | Association EURATOM – FZJSeptember 22end, /13 The influence of fluctuation level on the radial correlation measurement by Reflectometry.  At the small fluctuation level, the measured correlation length from Reflectometry is some larger than the real correlation length.  But the correlation length from Refl. would decrease and be much smaller than the real correlation length at larger density fluctuation level.