Page 6 - Characterization and calibration of the Thomson scattering diagnostic suite for the C-2W field-reversed configuration experiment

Nucl. Fusion 58 (2018) 126026
B.H. Deng et al
Figure 13. Relative line integral density fluctuation measured
by the central chord FIR interferometer during shots of the same plasma discharge settings but with different neutral beam energies. Each spike is a micro-burst. The dashed exponential curves are plotted as bench marks for comparing the two data sets.
Figure 14. Time traces of excluded flux radius under identical plasma operation conditions with NBI beam energy scan.
n = 1 wobble mode and n = 2 rotational mode. The micro- burst caused step drops are most clearly seen with 12keV NBI, while with 8 keV NBI the curve is smooth and no clear micro burst is observed. With 10keV beam energy, small step drops are only seen in the later phase (>5 ms) of the dis- charge. Therefore the collection of the experimental data sug- gests that the micro-burst is most easily destabilized when the beam energy is near 12 keV for typical equilibrium profiles of C-2U plasmas.
3. Discussion
3.1. Comparison with known fast ion driven bursting instabilities
The micro-burst is a new type of fast ion driven instability which has not been reported in previous FRC experiments as the early FRC experiments did not have the necessary plasma
Figure 15. A sample fast ion (proton) orbit in the toroidal plane with beam energy of 12.5 keV in the C-2U equilibrium magnetic field showing n = 2 structure rotating (azimuthal precession) in the ion diamagnetic direction. O is the projection of the machine axis. The orbit is bouncing radially between a minimum radius of 0.08 m and a maximum radius of 0.51 m. The black circle represents the vacuum vessel wall. The plasma excluded flux radius is 0.32 m (dashed circle).
lifetime and good bulk plasma and fast ion confinement prop- erties. The bursting chirps have some similar characteristics with that of the tokamak fishbone instabilities [10]: frequency down chirping; the burst interval, the growth rate, and the chirping rate in the growing phase (t < tp) all scale linearly with the bursting amplitude; lack of correlation between the bursting amplitude and the damping rate and chirping rate at t > tp; and the existence of preferred directions. However, the physical mechanisms leading to micro-bursts in FRCs and tokamak fishbone instabilities are different. In tokamaks the fishbone instabilities are kink modes with both the poloidal and toroidal mode number of 1 [11, 12]. Kink modes do not exist in FRC plasmas. Coppi’s theory [11] can explain the fluid type of tokamak fishbone instability as being driven unstable by bulk plasma pressure gradients and can lead to flattening of core temperature and density profiles. On the contrary the density profile is more peaked after each FRC micro-burst as shown in figure 12. This observation excludes the applicability of Coppi’s theory, with the caveat that the ion and electron temperature profile measurements have large error bars of ~30%.
Chen’s fishbone theory [12] developed to explain the kinetic tokamak fishbone instability does not apply to micro- bursts in FRC either, because the n = 2 and kz = 0 mode structure of micro-bursts is different from the m = 1 and n = 1 kink mode in tokamak plasmas. Also the fast ion pre- cession motion described by Chen and commonly discussed in the literature is the drift motion of the guiding centers of fast ion orbits, which does not apply to fast ions in FRC plasmas. In C-2U, the fast ion orbit size is comparable to the vacuum vessel radius and larger than the bulk plasma radius, the guiding centers of fast ion orbits are nearly localized to the center of the plasma (figure 15), and therefore, there is no guiding-center drift related instability. In the calculation of the particle orbit shown in figure 15, realistic equilibrium
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