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
Various configurations of correlation reflectometryRadial Correlation
O/O-mode LR
O/X-mode |B|
(Tried in 2001 firstly, and M.Gilmore wrote a paper in 2003)
Perpendicular Correlation
Multi Antenna L
Longitudinal Correlation
Multi Antenna B/|B|
(Preliminary analysis was tried in 2003)
Those two have been tried during this visit.(LR was also measured simultaneously.)
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
LR
Contour of correlation
Correlation
d/r
Pitch angle scan
Pitch angle/radial scanRefl. #3, #4,..
Flux surface
Generally, LL, LR
-> pitch angle measurements
radial scan
pitch angle scan
pitch anglescan
Principle and expected behaviors (II)
Squared Correlation
d/r
Pitch angle/radial scan
Frequency Sweep
radial scan
26GHz
40GHz
26GHz
40GHz
Correlationat the samelocation
Correlationat a differentlocation
1
<1
Note that, noise reduces the peak and increase the floor. Bandpass filtering is very efficient to reduce the noise effect.
Calculation of correlation • y0:I-component of Ref.#2(30GHz fixed)• y1:Q-component of Ref.#2• y2:Swept (homodyne) signal of Ref.#1Normalized squared cross correlation
T is chosen to be 20s.
TT
T
TT
T
yyyy
yy
yyyy
yy
2211
2
21
2200
2
20
~~~~
~~
~~~~
~~
ParallelCorrelation <y0y2>, <y1y2>
RadialCorrelation <y3y2>, <y3y2>
Discharges
Power spectral density of the reflectometer with 30GHzTime 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
Tracing a field line (I)
Using EFIT02/EFIT01 results (Ri,Zj , tk), F(l ,tk)=RBt for a fixed grid points, and F are calculated for an arbitrary (R,Z) at tk.(Br,Bt,Bz) is calculated from and F.
Using electron density profile ne
(Rm,tn), R of the critical density for 30GHz is calculated, and (R= Rm,Z=0 , tk) for the critical density (cutoff) is calculated. tn and tk 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
Tracing a field line (II)
Field lines from the two reflection points are traced toward each other using (Br,Bt,Bz) . 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
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.
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.
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.
?
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
Results (I) Low Ip case