Fast Acquisition System for the D3D MSE Diagnostic

Transcription

1 Fast Acquisition System for the D3D MSE Diagnostic M.A. Makowski, J. Jayakumar, R. Ellis, R. Geer, J. Moller, R. Wagner 5-9 November 2004 Savannah, Georgia aps04 mam 5-9 Nov 04

2 A Fast MSE System and Analysis Tools have been Developed for DIII-D A prototype PC based digital data acquisition system has been development for the DIII-D MSE diagnostic The signals are captured at the output of the PMTs and digitized at rates up MHz Digital signal processing techniques are then used to determine the pitch angle, which currently is done using analog lock-in amplifiers The analysis tools that have been developed can be applied to a wider range of problems MHD phenomena have been observed on the fast system and a method has been developed to interpret the signals has been developed aps04 mam 5-9 Nov 04 2

3 Prototype Fast MSE System has Flexible Configuration Currently, up to 8 channels of fast data can be acquired Fast channels can be selected from any of 36 channels Data is stored in a local MDSPlus server aps04 mam 5-9 Nov 04 3

4 Software Tools Developed for Analysis of the Data Software implementations of lock-in amplifiers have been developed Standard approach using reference signals from the PEMs Also have developed a Phase-Locked Loop (PLL) demodulation technique that does not rely on PEM reference signals Both methods work well and reproduce the signal obtained from the analog lock-ins Software techniques allow greater flexibility in the processing of the data Can adjust filter constants Can test performance of different types of filters Can analyze data with different algorithms aps04 mam 5-9 Nov 04 4

5 Phase-Locked Loop Generates Its Own Reference Signal Basic Lock-In Amplifier Lock-in with PLL aps04 mam 5-9 Nov 04 5

6 Pitch Angle Derived from Fast System Agrees with that from Analog System aps04 mam 5-9 Nov 04 6

7 Signatures of MHD Activity Observed on Fast MSE System Signatures of MHD activity that are well correlated with other diagnostics are observed on fast MSE data However, the fast MSE system measures the total intensity (proportional to n e n b ) which is sensitive to changes in both the density and pitch angle. Perturbations are taken as γ + ƒcos( γ ω t + ϕ ) n [ + nƒcos( ω t+ ϕ )] 0 The primary challenge in the analysis of these data is to simultaneously determine the phase and amplitude of the density and pitch angle contributions A method of doing so has been developed. mhd mhd g n aps04 mam 5-9 Nov 04 7

8 Measured Quantities can be Related to the Phases and Amplitudes of the Perturbations In the absence of MHD activity, peaks at the PEM frequencies 2f and 2f 2 are normally present in the spectrum Fluctuations in the measured intensity induced by MHD activity mix with the PEM modulation frequencies giving rise to spectral bands at f mhd, 2f mhd, 2f ±f mhd, and 2f 2 ±f mhd aps04 mam 5-9 Nov 04 8

9 Signature of MHD Oscillations is Observed on Fast MSE Signals aps04 mam 5-9 Nov 04 9

10 Analysis Technique (Continued) The measured phases and amplitudes of various spectral peaks of the auto-correlation function can be related to the phase and amplitude of the density and pitch angle perturbations aps04 mam 5-9 Nov 04 0

11 Amplitudes & Phases of Spectral Components ω ω mhd 2ω 2ω + ω mhd 2ω ω mhd 2ω 2 2ω 2 2ω 2 + ω mhd ω mhd 4 { Amplitude ( I ) ƒ 0( 2)cos2 4ƒ π + Iσ n [ PJ A γ]+ γ P J0 ( A2)sin 2γ [ ] + 4Pƒƒ γnj0( A2)sin 2γ PJ0( A2)cos2γ cos( ϕg ϕn) ( Iπ Iσ) J2( A)cos2γ 2 ( I I ) J2( A){ƒ n cos 2 4ƒ π σ γ + γ sin 2γ 2 4nƒƒcos γ 2γsin2γcos( ϕ )} / g ϕn ( I ) 2( ){ƒ cos 2 4ƒ π Iσ J A n γ + γ sin 2γ 2 4ƒƒcos γ 2γ sin2γ cos( ϕ ϕ )} / n g n ( Iπ Iσ) J2( A2)sin 2γ 2 ( I ) 2( 2){ƒ sin 2 4ƒ π Iσ J A n γ + γ cos 2γ + 4ƒƒcos γn 2γsin2γcos( ϕ )} / g ϕn ( I ) 2( 2){ƒ sin 2 4ƒ π Iσ J A n γ + γ cos 2γ + 4ƒƒcos γ 2γ sin2γ cos( ϕ ϕ )} / n g n } / tan Phase [ PJ ( A )cos2γ] sin ϕ + ( )sin sin n rpj A 2γ ϕg [ PJ0( A2)cos2γ] cos ϕn+ rpj0( A2)sin 2γ cosϕg ϕ sin( + ) tan sin( + ) ϕn 2ϕ r 2γ ϕg 2ϕ tan cos( ϕn+ 2ϕ) r tan 2γcos( ϕg+ 2ϕ) tan sin( ϕ n 2ϕ ) r tan 2γ sin( ϕg 2ϕ ) cos( ϕn 2ϕ) r tan 2γcos( ϕg 2ϕ) 2ϕ 2 sin( + )tan + sin( + ) ϕn 2ϕγ r ϕg 2ϕ2 tan cos( ϕn+ 2ϕ2)tan 2γ+ r cos( ϕg+ 2ϕ2) tan sin( ϕ + n 2ϕ )tan 2γ r sin( ϕg 2ϕ ) cos( ϕn 2ϕ2)tan 2γ+ r cos( ϕg 2ϕ2) 2 2 aps04 mam 5-9 Nov 04

12 I P J π, I σ π σ = I -I Symbols, J = Bessel functions of first kind of order 0 and A, A 2 A = Common PEM modulation amplitude ( assumes A = A ) ƒ, γ nƒ = pitch angle and density perturbation amplitudes ϕ, ϕ ϕ, ϕ n = Intensity of the πand σlines I +I π σ = Polarization ratio = Amplitudes of the PEM modulation 2 2 r= 2ƒ/ γ nƒ = ratio of fluctuation amplitudes g 2 = phases of the pitch angle and density pertubations = phases of the PEM modulations γ = γ π/ 8 = magnetic pitch angle at the measurement location aps04 mam 5-9 Nov 04 2

13 Consistent Solution to Equations Can be Found This leads to a set of coupled transcendental equations for the unknown phases (ϕ g, ϕ n ) and perturbation amplitudes ( = the density and ƒγ = the pitch angle) ƒn Non-linear equations have multiple roots and the system of equation is over-determined yielding a multiplicity of solutions However, consistent solutions can be found aps04 mam 5-9 Nov 04 3

14 Theory Distinguishes Different Types of Perturbations Above case yields ƒγ = 0.04º (δb z = 2 G) and ƒn = 0.3%. This is comparable to the magnitude of the T e fluctuation level ~ 0.6% These are sensible values, but the results need further validation Method clearly differentiates pure density, pure pitch angle, and mixed density/pitch angle perturbations Density Pitch Angle ρ= ρ2 = nƒ θ pm, = 2ϕ± ϕn, θ2pm, = 2ϕ2± ϕn θ = ϕ 0 n ρ= ƒtan γ 2γ, ρ2 = ƒcot γ 2γ θ pm, = 2ϕ± ϕg, θ2pm, = 2ϕ2± ϕg θ = ϕ, θ = 2ϕ 0 g 02 g aps04 mam 5-9 Nov 04 4

15 Measured Phase Difference Inferred by PLL and Mode Analysis Code Agree To validate the PLL technique, a comparison of the phase difference of magnetic probe signals with that predicted by the MHD mode analysis code, MODE was made Very good agreement has been obtained aps04 mam 5-9 Nov 04 5

16 The Analysis Tools Developed Can be Applied to a Wider Range of Problems Using PLL techniques, the relative phase of any two signals can be tracked versus time aps04 mam 5-9 Nov 04 6

17 Summary and Conclusions Prototype fast data acquisition system has been assembled and tested Pitch angles calculated using software algorithms agree with those derived from the analog system MHD oscillations have been observed on the fast signals Method has been developed for analysis of these signals Method has been applied to the analysis of a tearing mode, but results not yet fully validated Software algorithms have a more general applicability and can be used determine the phase between arbitrary signals aps04 mam 5-9 Nov 04 7