PROBING STABLE ALFVEN EIGENMODES WITH EXTERNAL TAE ANTENNA

The primary aim of theoretical and experimental studies of AEs is to describe their dispersion properties and to quantify the main mechanisms that damp or drive AE instabilities. Results of these studies can be used then to predict with a higher confidence the next-step operating regimes of DT plasmas in machines such as ITER. To investigate the spectrum of stable weakly damped AEs and their damping rates separately from the mode drive, a dedicated active diagnostic system was developed on JET [7.3,7.7,7.8]. This active TAE probing technique uses an external antenna for launching an electromagnetic wave into the plasma, with the wave frequency swept across the frequency range of AEs. A synchronous detection technique measures the plasma response to the wave launched. On JET, saddle coils were used initially as the external TAE antenna [7.3]. Saddle coils were chosen for this role owing to their extended structure covering the entire plasma in toroidal direction, thus allowing the launch of waves with parallel wave-vectors, kn ~ l / qR. relevant to TAEs. Figure 7.3 shows an example of the launched probing wave swept up and down across the TAE frequency, and measuring the plasma response as perturbed magnetic fields with synchronous detection using Mirnov coils (description of Mirnov coils is given in Appendix D). The peak response in the synchronous detection is associated with high-quality TAE resonance (low damping rate). The frequency of the resonance corresponds to TAE with the specific toroidal mode number n = l launched by the antenna, while the damping rate of the mode is characterised by the width of the resonance. The temporal evolution of the frequency and damping rate of TAE seen in Figure 7.3 are caused by the variation in the plasma parameters.

Each individual TAE resonance seen in the magnetic probe signal is represented in a complex plane, as shown in Figure 7.4, and a best-fit routine is used to assess the width of the resonance that provides the information on the mode damping. In the case of Figure 7.4, two upper saddle coils were used in phase and 180° apart toroidally.

One of the first scientific results obtained with the active TAE diagnostics was the experimental validation of the continuum damping of a TAE depending upon the alignment of TAE-gaps. Because the centre of the TAE-gap is determined by frequency /TAe = VA/(4nqRu), the radially separated TAE-gaps corresponding to different m (and the same n) have frequencies of their centres aligned if the plasma profiles satisfy

For the aligned TAE-gaps discharged with the profiles satisfying (7.1), the frequency of TAE does not cross the Alfven continuum anywhere in the plasma, and hence, there is no continuum

A TAE resonance is detected by the sweeping frequency of launched wave across estimated TAE frequency and measuring the plasma response with synchronous detection

FIGURE 7.3 A TAE resonance is detected by the sweeping frequency of launched wave across estimated TAE frequency and measuring the plasma response with synchronous detection. The measured signal provides information regarding individual TAE frequency and damping.

Example of a TAE resonance in the ohmic phase of JET shot #31638

FIGURE 7.4 Example of a TAE resonance in the ohmic phase of JET shot #31638. Real and imaginary parts (a) and complex plane representation (b) are shown of a magnetic probe signal, normalised to the driving current. The fit with (b)and (a) is also shown. giving/obs= 144.2±0.1 kHz. yj2k= 1400± 100s~'. fitor=2.8T, Ip~2.2 MA.()=3xlOl9m-

damping of TAE. However, if the condition (7.1) is not fulfilled, the eigenfrequency of TAE crosses the Alfven continuum line at some radius, and the TAE experiences a continuum damping at the crossing point, which may be quite significant, see Section 6.2.3 of Chapter 6 and the References therein.

Figure 7.5 shows the relevant experimental data for two comparison discharges on JET, one of which did not have the TAE-gap alignment condition (7.1) fulfilled, while the other had it fulfilled. The difference in the TAE damping rate for these two cases is about an order of magnitude. In the case of not aligned TAE-gaps, the damping of TAE is very high at approximately 5%, while TAE damping in the case of aligned gaps is only 0.6%. TAE with very high damping corresponds to quite significant continuum damping, as was expected from the plasma profiles not satisfying (7.1), as well as from the modelling [7.7].

The relationship between the profile o

FIGURE 7.5 The relationship between the profile of l(q(r)f> (r)'n) and the TAE damping. The profile (top) and the raw and fitted frequency responses (bottom) of a normalised magnetic probe signal are shown for two discharges. Excitation peaked at n=2 was used for both discharges; measurements were taken in the ohmic phase with similar plasma configuration; ne~4x 10l9nr3; (a) Bm~ 1.8 T. Ip~2 MA. (b) Вш~2.8 T, Ip~2.3 MA.

Another important study performed with the JET saddle coils as a TAE antenna was the demonstration of TAE-to-KTAE transition at increasing plasma temperatures [7.9]. Several heating options were explored to observe the structural changes in the TAE spectrum at increasing plasma temperature. Figure 7.6 shows one of these cases, in which higher electron temperature was achieved via ohmic heating of plasma in a discharge with a very significant increase in plasma current from 2 to4.IMA.

The TAE antenna was scanning, without tracking any resonances, the frequency from 140 to 260 kHz throughout the discharge. In the early phase of the discharge, when the plasma was relatively cold, only a single TAE resonance was detected, as shown in Figure 7.6a. As the current increases and the electron temperature rises, multiple resonance peaks emerge above TAE frequency identified as a spectrum of KTAEs predicted theoretically in Refs. [6.11,6.13,6.17].

During recent years, the active TAE antenna diagnostic was significantly modified on JET. In particular, this diagnostic technique was enhanced by a digital real-time control system, which allows performing individual TAE resonance tracking. With the use of the tracking system, the AE frequencies and damping rates can be measured with high time resolution (<50 ms) throughout discharges. While the sweeping technique shown in Figure 7.3 provides the opportunity to detect multiple AE resonances within an extended fixed frequency band, the tracking technique adjusts the sweeping frequency range to a narrow width surrounding an individual TAE resonance [7.8]. Figure 7.7 (left) shows an example of magnetic spectrogram with the characteristic zigzag pattern of the launched probing wave swept up and down in frequency. Figure 7.7 (p.85) shows the peak response

B probe signals for moderate (top) and high plasma current (bottom) in the same discharge #34073. Top

FIGURE 7.6 Bpol probe signals for moderate (top) and high plasma current (bottom) in the same discharge #34073. Top: /=3.5s; Ip~2 MA; Вш~2.5 T; («,,)- 1.9x 1019nr3; Te~2.2 keV. The single TAE has/-210.5kHz, ylw -1.4%;/TAE°~200kHz. Later, at /=9.5s (bottom) multiple peaks appear, with Aflf~2%; /(,~4.1 MA; Btor~2.9 T; (/?,,)-3x 1019m~3; /,-3.2 keV;/TAE°~ 180kHz.

in the synchronous detection corresponding to a TAE resonance detected. Temporal evolution of frequency and damping of TAE, which are determined by varying plasma parameters, are tracked in time by adjusting the sweeping frequency range after every resonance measurement providing high time resolution.

In present-day JET machine, two sets of dedicated TAE antennae are installed at toroidally opposite positions [7.10]. The antennae themselves are much less extended than the saddle coils. However, they can launch waves with a prescribed phase, and can also couple to TAEs with higher mode numbers, n>2. Dedicated active TAE antenna diagnostics were also installed in Alcator С-Mod and MAST tokamaks [7.11].

Finally, JET also employed a technique of probing TAE frequency range with a beat wave from two ICRH antennae launching fast magneto-acoustic waves in the ion cyclotron frequency range of -40-50 MHz [7.12]. In JET, up to four ICRH antennae and four RF generators were individually optimised and used for the best coupling to the plasma. Under these conditions, a small but finite mismatch in the frequencies of the launched waves is always present at the level of 1% or so. This mismatch frequency is close to the TAE frequency range, and so the beat wave between two ICRH antennae matching a TAE frequency could serve as a beat wave antenna inside the plasma suitable for probing the TAE. The JET experiment was successful, but it was found later that the beat wave technique on JET generates perturbations with parallel wave-vectors varying in an uncontrollable manner, very quickly and randomly. This made the technique of TAE probing by the beat wave much less attractive than the external TAE antenna probing.

Tracking of an individual n= 1 TAE resonance in the absence of energetic particle drive in the limiter phase of a JET ohmic discharge. Left

FIGURE 7.7 Tracking of an individual n= 1 TAE resonance in the absence of energetic particle drive in the limiter phase of a JET ohmic discharge. Left: The spectrogram of the directly digitised magnetic perturbations showing the zigzag pattern of the probing perturbation launched by the TAE antenna; Right: The synchronously detected signal*.

 
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