Acquisition and demodulation

In the following we describe the actual implementation of the data acquisition and demodulation. We have seen in chapter 2 that demodulation is done by splitting the acquired signal in two and

multiplying one part with a sine, the other with a cosine of ω_∆t followed by low pass filtering. Figure 7.4 shows the implemented layout of the

peripheral component interconnect (PCI) bus card [97]. The steps can schematically be written (for ONE channel):

1. 8 bit analogue to digital (A/D) conversion (160 MHz). This means 160 MB data per second.

2. Signal ik(t) split in two parts (called quadrature channels).

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Figure 7.4: (Colour) Acquisition electronics. The figure is taken from [133].

3. One part is multiplied by c(n) = Re[e^{i(ω∆t−nπ/2})] = cos(ω∆t−nπ/2), the other part by c(n+ 1) = sin(ω∆t−nπ/2) , where n = 0,1,2,3 because the multiplication is done four times per period. The step in n corresponds to a phase shift ofπ/2. The multiplication factors are written in table 7.1.

4. We have four samples per quadrature channel per period. If

quadrature channel 1 is to be our cosine channel, the c(n)’s become [1,0,-1,0] and the sine quadrature channel 2 c(n+ 1)’s are [0,-1,0,1].

These values are obtained by setting t = 0 in table 7.1 (phase locking). This means that every second sample is zero and can be thrown away without loss of information, leaving two samples per quadrature channel per period. So in total this means that 160 MB of data is transferred through the two quadrature channels per second.

5. Low pass filtering removes the 2ω∆ terms.

6. The data rate is reduced (decimated) by 4 resulting in 40 MB of data per second of acquisition.

7. The data is transferred to a computer by direct memory access (DMA) transfer.

8. The data is analysed off-line with software. The programming

language used both for data acquisition and analysis is the interactive

CHAPTER 7. EXPERIMENTAL SETUP 104 data language (IDL).

n e^−inπ/2 c(n), quadrature channel 1 c(n+ 1), quadrature channel 2

0 1 cos(ω∆t) sin(ω∆t)

1 -i cos(ω∆t−π/2) = sin(ω∆t) sin(ω∆t−π/2) = -cos(ω∆t) 2 -1 cos(ω∆t−π) = -cos(ω∆t) sin(ω∆t−π) = -sin(ω∆t) 3 i cos(ω∆t−3π/2) = -sin(ω∆t) sin(ω∆t−3π/2) = cos(ω∆t)

Table 7.1: Demodulation multiplication factors.

In conclusion, one quadrature channel contains samples of the

measurements multiplied by cosine, the other channel contains samples multiplied by sine, leading to real and imaginary parts of the signal after low pass filtering.

Fractional phase shifting

Due to the practical implementation of the acquisition card, the two quadrature channel signals are phase shifted by 1/160 µs. The technical reason for this is that the card was constructed using two instead of four A/D converters. That is to say, each of the two channels is sampled by a separate A/D converter. The phase shift can be understood as follows: The raw data out of the card (for TWO channels) has the sequence

1. Re[ik,1(n = 0)] =c(n= 0)ik,1(n= 0) 2. Im[ik,1(1)] =c(1)ik,1(1)

3. Re[ik,2(2)] =c(2)ik,2(2) 4. Im[ik,2(3)] =c(3)ik,2(3)

The second subscript on the photocurrent ik(n) refers to the channel number. If we now consider one channel, say number 1, the quadrature data is used to reconstruct the complex signal according to

i^shifted_k,1 =Re[ik,1(0)] + iIm[ik,1(1)] (7.22) We have now identified the problem; the real and imaginary parts of the complex signal are recorded by two successive A/D clock cycles. This means they are shifted by the sampling period 1/160 µs. The correction for this time delay is done off-line and is explained in detail in [133].

Investigated phenomena

This chapter contains analysis results of measurements obtained using the LOTUS diagnostic. Each section describes different discharges (except sections 8.1 and 8.2 treating the same series); the unifying theme of the chapter is confinement transitions.

Section 8.1 describes comparable discharges that can be viewed as quasi stationary when viewed over several ms.

Analysing the discharges introduced in section 8.1 on sub ms time scales, it is found that the plasmas dither spontaneously between two confinement states, the low (L) confinement and high (H) confinement mode. The relationship between the fast switching of confinement modes and the density fluctuations is the subject of section 8.2.

In section 8.3 we treat a single shot evolving through several confinement states: Initially it is in stationary L-mode, thereafter it exhibits pronounced dithering and finally enters the edge localised mode (ELM)-free H-mode (H^∗). ELMs are burst-like phenomena occurring in the outer parts of the confined plasma; they are associated with a flattening of the edge pressure gradients and lead to a loss of plasma energy. The goal of this section is to compare the analysis to that of section 8.2. The purpose of this comparison is to determine whether the hills and troughs of the dithering phase have the same properties as stationary L- and H-modes.

Having studied fast L-H confinement transitions, we turn to slow confinement transitions in section 8.4. The confinement quality of the discharges can be controlled by changing the rotational transform of the magnetic field, either using the external coils or by inducing a plasma current. The confinement transition can made as slow or fast as desired, meaning that a detailed study can be made of the mechanisms causing the transition. In this section we present spatially localised measurement of density fluctuations using two different methods, one being a novel concept.

105

CHAPTER 8. INVESTIGATED PHENOMENA 106 Our final section on measurements, section 8.5, contains an analysis of a new high density H-mode (HDH) regime found in W7-AS in 2001. This mode exists over a certain density threshold and has a fluctuation level significantly larger than that of the standard H-mode. LOTUS is very well suited to monitor this discharge type, since it is the only fluctuation diagnostic on W7-AS able to measure core fluctuations in high density plasmas.

8.1 Quasi steady-state

In this first section describing the analysis of measured density fluctuations, we treat a wavenumber scan. That is, a series of plasmas where the probed wavenumber of the density fluctuations was varied in steps from 14 to 62 cm⁻¹ in eight similar discharges. Table 8.1 summarises the corresponding shot/wavenumbers.

Shot 47133 47135 47136 47137 47138 47141 47142 47143

[cm⁻¹] 14 21 28 34 41 48 55 62

Table 8.1: Measured wavenumber for a given shot.

The section is organised as follows: Subsection 8.1.1 contains a review of the spectral analysis tools used for analysis. Subsection 8.1.2 describes the discharges analysed in this section and the next, and subsection 8.1.3 includes an overview of auxiliary diagnostics. Subsection 8.1.4 deals with the raw data from LOTUS and subsection 8.1.5 collects statistical analysis results of the density fluctuation data. Subsection 8.1.6 presents autopower spectra of the density fluctuations for the wavenumber scan and we discuss the results in subsection 8.1.7.