1. Correlation reflectometry for pitch angle measurements on NSTX 2005/7/20 A. Ejiri Univ. Tokyo Outline Correlation reflectometry and pitch angle measurement Operation and analysis Results Conclusion

2. Various configurations of correlation reflectometry Radial Correlation O/O-modeL R O/X-mode|B| (Tried in 2001 firstly, and M.Gilmore wrote a paper in 2003) Perpendicular Correlation Multi Antenna L  Longitudinal Correlation Multi AntennaB/|B| (Preliminary analysis was tried in 2003) Those two have been tried during this visit. (L R was also measured simultaneously.)

3. Principle and expected behaviors (I) B Toroidal Poloidal Ref. #1 Ref. #2 d Correlation d Ref. #1 (26-40GHz Swept & 31GHz fixsd)) Refl. #2 (30GHz fixed) Field line LL L  LRLR Contour of correlation Correlation d/r Pitch angle scan Pitch angle/radial scan Refl. #3, #4,.. Flux surface Generally, L   L , L R -> pitch angle measurements radial scan pitch angle scan pitch angle scan

4. Principle and expected behaviors (II) Squared Correlation d/r Pitch angle/radial scan Frequency Sweep radial scan 26GHz 40GHz 26GHz 40GHz Correlation at the same location Correlation at a different location 1 <1 Note that, noise reduces the peak and increase the floor. Bandpass filtering is very efficient to reduce the noise effect.

5. Calculation of correlation y 0 :I-component of Ref.#2(30GHz fixed) y 1 :Q-component of Ref.#2 y 2 :Swept (homodyne) signal of Ref.#1 Normalized squared cross correlation  T is chosen to be 20  s. Parallel Correlation, Radial Correlation,

6. Discharges

7. Power spectral density of the reflectometer with 30GHz Time window [ms] Frequency [kHz] H-mode Typical frequency range is ~100kHz. Higher frequency components is small, and contaminated by noise Effective frequency range is >50kHz due to time window for calculation of correlation

8. Tracing a field line (I) Using EFIT02/EFIT01 results  (R i,Z j, t k ), F(  l,t k )=RB t for a fixed grid points,  and F are calculated for an arbitrary (R,Z) at t k.(B r,B t,B z ) is calculated from  and F. Using electron density profile n e (R m,t n ), R of the critical density for 30GHz is calculated, and  (R= R m,Z=0, t k ) for the critical density (cutoff) is calculated. t n and t k should be as close as possible. Intersections between the directions of two horns and  of the cutoff layer are calculated. These points are defined as the reflection points.  and directions of horns projected a poloidal cross section. Density profile and the position of the cutoff layer

9. Tracing a field line (II) Field lines from the two reflection points are traced toward each other using (B r,B t,B z ). Step size is 0.2 mm. Find the closest points on the field line to the other reflection point, and calculate the distance between them. These lines and points are on the same flux surface. The distance between the reflection points are. XYZ views of the horns, their directions, reflection points(*) and field lines. 30GHz 26-40GHz/30.2GHz 0.3m

10. Results (I) peaks Black curve represents standard O-mode radial correlation measurements. That is the correlation between 26-40GHz swept signal and 30.2GHz fixed homodyne signal, and it shows peaks (with height 1.0) at the timing of frequency matching. Red curve represents correlation between 26-40GHz swept signal and 30GHz IQ signal, which is about 30cm depart toroidally. Blue curve represents correlation between 30.2GHz fixed and 30GHz IQ. The bottom figure shows minimum (i.e. perpendicular) distance of the two field lines.

11. Results (I) peaks poor corr. Nose No Cutoff Clear peaks in (parallel) correlation were found. However, in some cases no clear peak was found where we expected. Direct effect of noise, and probably indirect effect resulting poor radial correlation seem to exist.

12. Results (II) Ohmic H-mode H-mode During H-phase, high correlation (red) was found. This suggest long parallel and/or perpendicular correlation length. Note that, high correlation between 30 and 30.2GHz. Before and after H- phase, no clear peak was found in parallel and/or perpendicular correlation (red), even though radial correlation is good and field line distance is short. ?

13. Conclusions The NSTX reflectometer was operated for pitch angle measurements successfully. Correlation at different toroidal location (0.3m apart) was found when the distance between the fields is within a few cm. However, usually, the correlation was low, partly due to the noise. Fluctuations during H-mode seems to have long perpendicular and parallel correlation length. More (controlled) experiments, sophisticated analysis, and noise reduction are required to determine the feasibility of pitch angle measurements by correlation reflectometry. A Lot of Thanks to PPPL and UCLA

14. Results (I) Low Ip case