Appendix D: Diagnostics of Alfvén Eigenmodes Excited by Energetic Particles

Because energetic particles excite instabilities via wave-particle resonances, excited shear Alfven eigenmodes have their frequencies close to the poloidal and toroidal characteristic frequencies of drift orbits of the energetic particles driving the modes. For present-day tokamaks, AEs of various types, from the fishbones to EAEs and NAEs, cover the frequency range from ~10 to ~500 kHz in the plasma reference frame. The best tested and most common instrument for detecting electromagnetic modes in this frequency range is a magnetic sensor, most often a Mirnov coil, measuring time-dependent magnetic flux just outside the plasma. A set of toroidally and poloidally separated Mirnov coils can also provide information on the mode numbers and the directivity of propagation of unstable AEs. For an in-depth study of any particular type of AE, and especially for using AEs detected as MHD markers for providing information on plasma equilibrium properties (Alfven spectroscopy discussed in Chapter 10), a knowledge of some specific properties of AEs is required. In this Appendix, we consider in detail the properties of TAE and describe, as an example, the set of Mirnov coils on JET.

However, the use of magnetic sensors in future burning DT plasma experiments, such as ITER, could be difficult [D.l]. To be protected in the harsh environment with high flux of DT neutrons, the magnetic sensors must be hidden well, for example, behind a thick blanket. Moreover, the plasma itself will be much larger, and detection of AEs deep in the plasma core cannot be guaranteed. Therefore, alternative techniques of AE detection, which are more compatible with DT operation, are required.

Microwave diagnostics, reflectometry, and interferometry measuring fluctuations of plasma density associated with AE are described in this Appendix as the possible avenues for development in view of a large-scale DT plasma. In particular, X-mode reflectometry was used successfully for detecting alpha particle-driven AEs in TFTR [D.2], which has recently shown its potential in obtaining information on q(R, t) from the positions of AEs [D.3], while the FIR interferometry with vertical line-of-sight through the magnetic axis has become the most reliable diagnostic technique for detecting AEs on the magnetic axis of JET [D.4].

Diagnostics measuring fluctuations of electron temperature associated with AE, ECE, and soft X-ray (SXR) are other options to consider. Excellent performance of ECE diagnostics on present- day machines, especially on DIII-D [D.5] and ASDEX-Upgrade [D.6], has led to top-quality internal measurements of AEs, providing an opportunity for a complete theory-to-experiment successful comparison [D.7].

We note here that (1) magnetic sensors do not provide information on the amplitude of an AE perturbation inside the plasma, while X-mode reflectometry and ECE do, and (2) toroidally and/or poloidally separated magnetic sensors provide information on the mode numbers, while interferometry, reflectometry, ECE, and SXR do not, and even the directivity of the wave propagation, which comes naturally from the magnetics requires special arrangements for reflectometry. The diagnostics above are complementary to each other, and when they are used on present-day machines in a combination, see, for example, [D.8], they can provide all the information on AEs needed for further interpretation and modelling. The problem now is to extend such complementarity options to DT burning plasma experiments.

D.1 PROPERTIES OF ТАЕ

The frequency gap in the Alfven continuum appears in toroidal geometry at frequency so that at the radius associated with TAE-gap we have that is

Expression (D.3) shows that at the TAE-gap the safety factor is related to TAE toroidal and poloidal mode numbers via

By substituting this value of TAE-specific safety factor in (D.l), we obtain the characteristic frequency of the TAE-gap,

where r0 is the radius of the TAE-gap. It is important to note here that TAE-gap frequency (D.5) does not depend on either toroidal or poloidal mode numbers of TAE.

The relation (D.4) implies that the very existence of a TAE-gap (and relevant weakly damped TAE-mode inside it) in toroidal plasma depends on whether a magnetic flux surface with the relevant value of q exists in the plasma. Table D.l shows the values of q required for TAEs with poloidal and toroidal mode numbers within 1.....6.

We now estimate from (D.5) the characteristic frequencies of TAE-gap for typical JET parameters 5о=ЗГ; n, =5xl019 rrf3;/?г, =m0, giving VA =6.6x106 m/s. For typical value of q = 1.1 we obtain the frequency estimate:

This frequency is estimated for the plasma reference frame. However, plasma often rotates, and a proper correction for the relevant Doppler shift of the mode frequency is needed. For example, unidirectional NBI on JET shown in Figure D.l spins up the plasma toroidally, and the toroidal plasms

TABLE D.1

q-values of TAE-Gaps Determined by (D.4) for 0.5 < q < 6.5

m=1

m=2

m=3

m=4

m=5

m=6

/1=1

1.5

2.5

3.5

4.5

5.5

6.5

n=2

0.75

1.25

1.75

2.25

2.75

3.25

/1=3

0.5

0.83

1.167

1.5

1.83

2.167

/1=4

0.625

0.875

1.125

1.375

1.625

//=5

0.5

0.7

0.9

1.1

1.3

//=6

0.583

0.75

0.917

1.083

rotation may be about /го1 (г) ~ Юн-25 kHz (maximum achieved was ~40 kHz) depending on the power of NBI. Frequencies of AEs with mode number n in laboratory reference frame, /Н1ЛВ, and in the plasma, /„°, are related through the Doppler shift nfml (r):

In the case of several TAEs with neighbouring toroidal mode numbers excited at once in toroidally rotating plasmas, the frequency separation between them is approximately fM (/'):

where we used the independence of TAE-gap frequency (D.5) on n,

D.1 Geometry of NBI injection system on JET (view from the top of the machine)

FIGURE D.1 Geometry of NBI injection system on JET (view from the top of the machine).

 
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