АLFVEN CASCADE (AC) EIGENMODES IN AT DISCHARGES WITH REVERSED MAGNETIC SHEAR

Experimental Observations

Experiments designed for generating ITBs in reversed-shear JET plasmas reveal discrete spectrum of Alfven perturbations with predominantly upward frequency sweeping. These experiments are characterised by a hollow plasma current profile often facilitated by LHCD before the main heating power phase. The AEs observed are driven by ICRH-accelerated ions. Let us consider a typical example of observing the AEs in an ITB discharge [9.3]. Figure 9.4 shows a comparison of two very similar AT discharges on JET, in which the main heating power was applied at ~3.5 s during inductive current ramp-up (the current temporal evolution is shown by broken line). The only difference between these two discharges is LHCD of low power, -2.5 MW, applied in one of the discharges, pulse #49382).

Figure 9.5a and b show magnetic fluctuation data measured by the magnetic pick-up coils in the Alfven frequency range during the pre-heating phase of the two discharges in Figure 9.4. A comparison of Figure 9.4a and b reveals that the discrete spectra of AEs are very different in the two discharges. In the discharge without LHCD (pulse #49384), the ICRH-accelerated H-minority ions

Power wave-forms of NBI

FIGURE 9.4 Power wave-forms of NBI (grey color), ICRH (black), and LHCD (black thick broken line) in two comparison JET discharges (pulses #49384 in the top and #49382 in the bottom) with Br = 2.6 T and Ipa% = 2.2 MA. The heating power and LHCD are applied during current ramp-up phase when the current increases from lP = 1.1 MA at I = 2s to lP = 2.2 MA at / = 5s, see broken thin trace showing the current evolution. A non-monotonic q-profile is measured in the pulse #49382 with LHCD, while the pulse #49384 has monotonic q-profile.

excited usual TAEs, as shown in Figure 9.5a, whose frequency followed the increase of plasma current in time (shown by the black line in the left top corner of the figure). The comparison discharge with LHCD exhibits some AEs with the frequency sweeping below the TAE frequency, as shown in Figure 9.5b. These are AC eigenmodes, or RSAEs.

We note here that ACs were observed in discharge #49382 even when LHCD was switched off. This shows that ACs are associated with plasma equilibrium created by LHCD, rather than with LHCD itself. At the same time, because no ACs were observed without ICRH in JET discharges, we conclude that ICRH-accelerated ions are essential for ACs.

Analysis of the Experimental Observations

The toroidal mode numbers of ACs shown in Figure 9.4b do not change for each branch of the perturbation as the relevant mode frequency sweeps upward. The frequency of the ACs starts from 40 to 90kHz, that is, well below the TAE frequency observed in the comparison discharge (pulse #49384). During the cascade evolution, the frequency increases up to the frequency of the TAE-gap, so that the TAE-gap forms an “envelope” of ACs at their highest frequencies. The rate of increase in the AC frequency is proportional to the mode number n and modes of different n occur at different times, sometimes in isolation, and sometimes clustering with other modes of different n's. Interestingly, the temporal evolution of ACs shown in Figure 9.5(b) exhibits a characteristic pattern typical of plots of several branches of Alfven continuum with different n's plotted on top of each other as, for example, in the CSCAS modelling part of Figure 7.9. This indicates that one needs to investigate in depth the Alfven continuum as a function of time and different n's for explaining the ACs.

For each branch of the AC, the frequency changes on a time scale r=0.1 -h0.5 s, which is significantly longer than the time scale observed for non-linear “chirping” modes described in Chapter 7. On the other hand, the time scale of the frequency change is of the order of the current increase in time scale shown in Figure 9.4b. We conclude that the temporal evolution of plasma equilibrium, and especially the temporal evolution of plasma current and associated qr(r)-profile, are important ingredients for explaining the frequency evolution of ACs. A direct measurement of the qr(r)-profiles

(a) Spectrogram of the magnetic perturbations, бB (T), measured by the Mirnov coils in JET

FIGURE 9.5 (a) Spectrogram of the magnetic perturbations, бBp (T), measured by the Mirnov coils in JET

discharge #49384. TAEs are observed at frequencies/TAEs80-200kElz. Evolution of TAE frequency in time is caused by the plasma current increase shown with black trace in the left top corner, (b) Magnetic spectrogram in JET discharge #49382. Multiple branches of Alfven cascades ranging from n =1 to n = 6 are observed at frequencies well below TAE frequency range,/AC=30-100 kHz«/TAE, with the frequency sweeping rate proportional to n. The black trace in the left top corner shows the plasma current increase.

in the two comparison discharges was performed with motional stark effect (MSE) technique [9.12]. Figure 9.6 shows a dramatic difference in the c/(r)-protiles: the discharge #49384 (no LHCD) had a monotonic Safety factor profiles

FIGURE 9.6 Safety factor profiles Cross-correlation spectrogram for the amplitude ^ and the phase ф of an Alfven cascade

FIGURE 9.7 Cross-correlation spectrogram for the amplitude ^ and the phase ф of an Alfven cascade. The radial location of the perturbation at Я = 3.4 m (which corresponds to //«~ 0.4) is inferred from the crosscorrelation between the external magnetics and the 48-channel ECE diagnostic.

In some JET discharges with high ICRH power, internal plasma measurements with the electron cyclotron emission (ECE) and soft X-ray (SXR) diagnostics were also available for identifying the radial position of ACs. An example of such measurements is shown in Figure 9.7 for JET plasmas with non-monotonic q(r) and ICRH power in excess of 7 MW (pulse #53494). This level of ICRH power in this discharge was much higher than the ~2 MW power threshold needed to excite the ACs.

In the pulse with internal measurements, for a certain time interval of ~200 ms when two branches of ACs were observed at 85 kHz and 110 kHz, the cross-correlation analysis between the perturbed electron temperature, 8/, and the magnetic perturbations, 6fipol, was performed, as shown in Figure 9.7. The perturbed electron temperature is measured with 48-channel ECE diagnostics with radially separated lines-of-sight, so that the radial mode structure in the plasma core could be determined. The two pictures on top of Figure 9.7 show' the amplitude and phase of the cross-correlation integral I(r) of the type

where the minor radius r is different for the different ECE channels and the time interval for the integration is 200 ms. From Figure 9.7 one can estimate the mode location on the low-field side of the torus as seen from the top. The two ACs, n=3 at/=85 kHz and n=6 at/= 110kHz, are found to be localised at major radius, ~3.4m (magnetic axis is at 2.97m), corresponding to r/a~0.4. This is close to the zero magnetic shear region where the «/-profile has its lowest value of min. It is interesting to note that the modes of significantly different frequencies and toroidal mode numbers are localised at nearly the same position in radius.

A similar technique of cross-correlation between SXR measurements (which also depends on electron temperature perturbation, 8T^) and magnetic perturbation, 8J? „ gives an estimate of the localisation of the AC in vertical direction because the X-ray camera has horizontal lines-of-sight. It is found that the mode at/=85 kHz has localisation peaks at a vertical minor radius of ~60cm, which is again close to the zero magnetic shear region (taking into account the elliptical cross- section of JET plasma). No clear correlation was found on SXR for the mode at/=110kHz. The measurements were repeated in this discharge 1 s later. For the branches of the Alfven cascades seen at that time, n=2 at/=70 kHz, /г=3 at/=95 kHz, and n=4 at/= 120 kHz, we found from the ECE measurements that the mode localisation is at -3.3 m, that is, still at position close to the AC region in Figure 9.7. The X-ray measurements indicate that the vertical localisation of the modes is also close to the one measured at an earlier time.

Therefore, we conclude that AC localisation region is (1) close to the position of mi„; (2) it is the same for different mode numbers; and (3) the mode localisation does not change significantly on a time scale of ~ s.

 
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