Page 6 - Compact Toroid Injection Fueling in a Large Field-Reversed Configuration

082512-6
Lau et al.
Phys. Plasmas 24, 082512 (2017)
FIG. 5. df2 (normalized by the maximum dfe2) is plotted for the ions (upper panel) and electrons (lower panel) with respect to energy and pitch angle. For ions, curves represent the ion drift frequency; pink (cyan) corresponds to values calculated at h1⁄4p (h1⁄4p/3). For electrons, the pink (cyan) corre- sponds to the electron transit frequency (electron bounce frequency).
simulations. This is shown for the kfqs 1⁄4 1.37 case for j 4 in Fig. 3. Like the core, it is found that the FLR effect is more strongly stabilizing than the rB effect when the drive is strong. However, when the drive is marginal, as might be expected from self-organization of the plasma, both are important in the complete suppression of instability.
In the experiments, the temperature gradients can actu- ally be stronger than the density gradients. In the simula- tions presented in Sec. IV A, the gradients of the density, ion temperature, and electron temperature are equal. In order to better understand the drive of the instability for g 1⁄4 1, simulations of the kfqs 1⁄4 4.1 instability were repeated with the density gradient unchanged at jn 1⁄4 6.7 while separately varying the ion temperature gradient jTi and electron temperature gradient jTe . As shown in Fig. 6, the electron temperature gradient is destabilizing while the ion temperature gradient is stabilizing. In addition, this instability exists even when there is only a density gradient (ge 1⁄4gi 1⁄40, jn 61⁄40).
These results can be understood by looking at the elec- tron perturbed distribution functions. In the g1⁄40 case as shown in the top panel of Fig. 7, the resonant electrons are at
FIG. 6. Dispersion relation with respect to ge (gi) is plotted as the blue (pur- ple) dashed lines. The frequency and growth-rate for the g 1⁄4 1 (black) case is plotted as the solid line for comparison. The density gradient drive jn is kept constant while jTe ðjTi Þ is varied for the ge (gi) scan. Note that the mode is unstable even with only jn.
lower energy in contrast to the g 1⁄4 1 case. The electron reso- nance is also no longer dominated by the locally barely trapped electrons but still by trapped electrons. In the ge 1⁄4 1, gi 1⁄4 0 case, the frequency is comparable to the g 1⁄4 1 case but
FIG. 7. The dfe2 (normalized by the maximum dfe2 ) is plotted for ge 1⁄4 0 and ge 1⁄4 1 with respect to energy and pitch angle. When the electron temperature gradient (jTe ) is decreased (ge 1⁄4 1 ! ge 1⁄4 0), the electron resonance shifts from locally trapped to globally trapped.