8.4 Slow confinement transitions
8.4.2 Comparison between the density fluctuation autopower
Changes in the autopower spectrum
A wavenumber scan was performed in the two discharge types shown at the top of figure 8.38, with wavenumbers ranging between 25 and 61 cm−1. To study whether the density fluctuations behave disparately at different wavenumbers, we show two sets of autopower spectra for discharges initially experiencing good confinement in figure 8.43. The top row shows
autopower spectra at k = 25 cm−1 (left) and at 46 cm−1 (right). The good confinement (Ip = 0 kA) phase spectra are shown using dotted lines, and the bad confinement (Ip = 2 kA) spectra are solid lines. For the k = 25 cm−1 shot, the decrease of low frequency ([-500,500] kHz) fluctuations during the good to bad confinement transition is partly counteracted by an
CHAPTER 8. INVESTIGATED PHENOMENA 168
dB /dt [T/s]q
[kHz]
-6 6
0 120
60
Time [s]
0.0 0.2 0.4 0.6 0.8 1.0
Figure 8.42: (Colour) Magnetic field derivative in T/s from the ’MIRTIM’
monitor coil (top) and a spectrogram (bottom) covering 1.0 s.
increase of turbulence at higher frequencies. This is clear to see in the bottom left-hand plot of figure 8.43, where the ratio bad/good confinement autopower spectra is plotted. A value above 1 means an increase in power, a value below 1 a decrease. In contrast, the high frequency increase at the transition no longer exists for k = 46 cm−1; only the drop of low frequency autopower remains. Note that in the initial good confinement phase of the high-k shot the autopower seems to contain two features: A broad high frequency low amplitude component and a larger amplitude low frequency element.
The spectra treated above can be compared to corresponding spectra from discharges initially in bad confinement, see figure 8.44. The development of the autopower spectra is quite modest, the main result being a slight decrease in power up to ± 1 MHz. Note that the spectra are similar to those in figure 8.43 for Ip = 2 kA.
In figure 8.45 we show autopower spectra and their ratio for k = 15 cm−1. Here, the density fluctuation power increases strongly below ± 1 MHz;
further, the high frequency feature present during good confinement
decreases in frequency on top of the current ramp. Note that the frequency scale in figure 8.45 extends to ± 4 MHz compared to ±2 MHz for figures 8.43 and 8.44.
25 cm-1 46 cm-1
Autopower [a.u.]
102
100 4
0 1 Ratio
Frequency [MHz]
-2 2 -2 Frequency [MHz] 2
Autopower [a.u.]
102
100 4
0 1 Ratio
Figure 8.43: Top: Autopower spectra at Ip = 0 kA (dotted line) and on top of the current ramp (Ip = 2 kA, solid line) in good confinement discharges, bottom: The relative change in power. Left column: k = 25 cm−1, right column: k = 46 cm−1.
To summarise our findings: Two phenomena are present, a low frequency (<± 1 MHz) and a high frequency feature:
• The high frequency feature is symmetric in frequency and does not change at the confinement transition for k = [25,61] cm−1. At k = 15 cm−1, however, the feature is highly asymmetric and decreases in frequency during the transition.
• The low frequency feature changes at all k, but only increases at the transition for 15 cm−1. For higher wavenumbers, it drops and finally disappears at k = 46 cm−1.
CHAPTER 8. INVESTIGATED PHENOMENA 170
25 cm-1 46 cm-1
Autopower [a.u.]
102
100 4
0 1 Ratio
Frequency [MHz]
-2 2 -2 Frequency [MHz] 2
Autopower [a.u.]
102
100 4
0 1 Ratio
Figure 8.44: Top: Autopower spectra at Ip = 0 kA (dotted line) and on top of the current ramp (Ip = 2 kA, solid line) in bad confinement discharges, bottom: The relative change in power. Left column: k = 25 cm−1, right column: k = 46 cm−1.
Changes in the wavenumber spectrum
The observations made above can be condensed into wavenumber spectra, where fluctuations integrated over all frequencies are shown versus
wavenumber. Four cases are plotted, two for discharges initially in good confinement and two for discharges in bad confinement. In each case, the wavenumber spectrum is calculated before and during the current ramp.
The resulting spectra are fitted to power-laws (P ∝k−m) as was done in sections 8.1 and 8.2. The wavenumber spectrum for the shots starting in good confinement becomes steeper with the confinement deterioration; the power drops especially for high wavenumbers. The spectrum for the shots initially in bad confinement only changes in amplitude (it decreases) at the transition.
15 cm-1
Autopower [a.u.]
102
100
4
0 1 Ratio
Frequency [MHz]
-4 4
Frequency [MHz]
-4 4
Figure 8.45: Left: Autopower spectra at Ip = 0 kA (dotted line) and on top of the current ramp (Ip = 2 kA, solid line) at k = 15 cm−1 in a good confinement discharge, right: The relative change in power.
The fitted power-law exponents m can also be studied versus time into the discharges, see figure 8.47. Here, the exponents for wavenumber spectra calculated in 10 ms time windows are shown versus time for both the good and bad confinement series. We observe that the exponent changes in a different manner for the two discharge types: For the bad confinement shots, the current ramp causes a gradual increase of the exponent. The behaviour in the good confinement case is more complex: The initial response to the current ramp is a decrease of the exponent, reflecting the initial further confinement enhancement. Later, as the confinement degrades, the exponent increases and transiently exceeds that of the bad confinement discharges slightly. Our conclusion would be that the size of the exponent corresponds to the confinement quality: A smaller exponent is associated with improved confinement.
The trend of the slope of the fits in figure 8.46 suggests that the fluctuation power for k < 25 cm−1 could increase in bad confinement. That this is indeed the case is shown in figure 8.48, where the total fluctuation power in good confinement discharges measured at different wavenumbers is plotted.
For k= 32 cm−1, the total power drops as the confinement worsens, whereas for k = 15 cm−1 the total power increases significantly.
We have demonstrated that the wavenumber spectrum during the current ramp induced confinement degradation is very similar to the static bad
CHAPTER 8. INVESTIGATED PHENOMENA 172
wavenumber [cm ]-1 102
10-1
20 70
Autopower [a.u.]
Figure 8.46: Wavenumber spectra in initially good and bad confinement discharges. Plusses fitted by a solid line (asterisks fitted by a dotted line):
Good confinement discharge, Ip = 0 kA (Ip = 2 kA). Diamonds fitted by a dashed line (triangles fitted by a dot dashed line): Bad confinement discharge, Ip = 0 kA (Ip = 2 kA).
Time [s]
Exponent
4.5
2.00.3 0.6
Figure 8.47: Power-law exponents versus time for bad (dotted) and good (solid) confinement discharges.
32 cm-1 15 cm-1
0 10
0 25
Autopower [a.u.] Autopower [a.u.]
Time [s] Time [s]
0.3 0.6 0.3 0.6
Figure 8.48: Total fluctuation power versus time in good confinement dis-charges. Left: k= 32 cm−1, right: k = 15 cm−1.
confinement case. The results for k = 15 cm−1 (see figure 8.49) show the same tendency: The current induced bad confinement is very similar to the discharge at the bad confinement