Alfvén Eigenmodes in “Advanced Tokamak” Plasmas
We now consider another type of AEs, different than TAE or other gap modes, with their frequencies locked to the equilibrium. These AEs were observed in discharges with reversed magnetic shear and were first called “Alfven cascade” (AC) eigenmodes [9.1-9.3] due to special clustering of toroidal mode numbers of these excited modes. After theoretical identification of the modes and development of relevant models, the modes were also called reversed-shear AEs (RSAEs) [9.4]. We will be using both AC and RSAE abbreviations for these modes to reflect different papers published on this subject in the last 20years.
A spontaneous improvement in fusion performance was observed in JET from the very first observations of ACs [9.5]. Figure 9.1 shows an example of such a case w'here the neutron rate in JET discharge was constant for about 1 s at fixed power of NBI and ICRH. However, this neutron yield almost doubles suddenly at f«7s without a change in either NBI or ICRH power. Simultaneously, a set of six AEs was detected with Mirnov coils starting at about f«7s. The modes start mostly at a frequency of «90kHz, well below TAEs seen at -180-240kHz, and sweep in frequency up to «140-250 kHz, each branch having its own slope of df/dt and ending at its own frequency. The sweeping rate of the modes is rather slow indicating that it is likely to be associated with equilibrium change, for example, with ^-profile evolution than with the non-linear wave-particle phenomena described in Chapter 8. Two questions arise: is the correlation between the improvement of fusion performance and the AEs observed just a coincidence? If not, can we use such correlation for scenario development? A sudden doubling of the neutron rate definitely deserves an investigation!
FIGURE 9.1 Left: Neutron yield, NBI and ICRH power in JET discharge #40410 with magnetic field Br=3.4 T and plasma current Ip =3 M A. Right: ACs seen at the time of neutron rate increase.
ADVANCED TOKAMAK SCENARIOS AND INTERNAL TRANSPORT BARRIERS
Advanced tokamak (AT) scenarios aim at obtaining a high fusion performance plasma at significantly reduced inductive current while maximising off-axis bootstrap current and using current drive systems [9.6—9.8]. The AT scenarios often trigger internal transport barriers (ITBs), which are rather narrow' radial regions in the plasma core, across which transport of plasma heat and/or mass are suppressed. The central region inside an ITB could deliver a very high fusion performance. In particular, the record in D-D neutron rate, that is, Sn~5.5x I0l6s_l (pulse #40554), the JET record ion temperature, T;(0)«40 keV, and the ion temperature and pressure radial gradients, =150 keV/m and =106 Pa/m (pulse #42940), were achieved in ITB discharges on JET with carbon wall [9.9]. To develop an ITB, the main heating pow'er is applied during the inductive current ramp-up, as shown in Figure 9.2, before the current flat top is achieved. On JET, low hybrid current drive (LHCD) and/or low-power ICRH are often used additionally in the early ramp-up phase of discharges to adjust the ^-profile if required.
When main NBI heating power is applied to the same AT scenario, but at different times in different discharges, for example, at /,,..., t4 each of these times corresponds to a different inductive current, as showm in Figure 9.2.
In accordance with the diffusion of inductive current and current drive applied early, the safety factor evolves through a series of profiles q(r,t) in the early pre-heating phase, so different “target” ^-profiles correspond to different times /,,..., t4 as Figure 9.3 illustrates.
FIGURE 9.2 Schematic figures showing (a) the inductive current ramp-up in time, and (b) main NBI heating power applied at different times.
FIGURE 9.3 Schematic illustration of «/(/J-profiles corresponding to different times f,,..., t4 of the current ramp-up phase shown in Figure 9.1.
When the main NBI heating is applied, plasma temperature increases strongly, so the resistive diffusion time increases and the evolution of q(r, t) becomes slow. Essentially, this means that by selecting the time of main heating one picks up a “target” «/-profile to be further explored for ITB development.
An ITB could spontaneously arise in AT plasmas with both positive and negative magnetic shear. However, triggering of an ITB in plasma with positive shear has a threshold in the input power, while triggering of an ITB in reversed-shear plasma has a very little or no threshold in the input power, and is much easier to develop. On JET, LHCD of low power (<2 MW) was often employed before the main heating to obtain a reversed-shear (non-monotonic «/-profile) magnetic configuration for further ITB development. Although LHCD applied was of low power, it was sufficient enough to affect significantly the early “embryo” state of the plasma in the very beginning of a discharge formation.
The ITB triggering has a very interesting and important correlation with integer values of the safety factor q [9.10,9.111. In particular, ITBs are most often formed and sustained at the q = 2 or min (1) passes an integer value, which is most often qm[n=2.
