Page 9 - Tomographic imaging system for measuring impurity line emission in a field-reversed configuration

022506-9 D. C. Barnes and L. C. Steinhauer Phys. Plasmas 21, 022506 (2014)
FIG. 15. Equilibrium profiles for sheared ion rotation cases, (a) number density, (b) electron rotation rate, (c) ion rotation rate, (d) ion temperature. Separatrix is again at rs 1⁄4 0:36.
to previous cases, one notices a feature in the density profile near the rotational shear (separatrix) position. The electron rotation profile is similar to the previous case, while the ion rotation profile has been chosen to produce a strong flow shear at the separatrix, with the rotation reversing sign there as might be expected in HPF cases where the plasma gun is biased to cause the SOL to rotate counter to the natural, ion diamagnetic rotation of the main column.
An additional feature of sheared ion rotation is shown in Fig. 15(d), where the previously flat ion temperature profiles have been modified to be more experimentally relevant. A feature of rotating equilibria is that it is not possible to have an ion temperature gradient and rigid ion rotation simultane- ously. Accordingly, previous rigid rotation cases also had no ion temperature gradient, while present cases have a more re- alistic profile.
We normalize x as previously discussed and further
Mode results for ‘ 1⁄4 2 show no qualitative modification from those for previous profiles considered here. There seems to be a very small stability region for negative 0:2 < a < 0 at arbitrary k which may or may not be important practically. Otherwise there is the same nearly universal instability at small k and stabilization for a a bit less than unity for k’s corresponding to experimentally realistic lengths although somewhat larger k values are required for stability. We discuss this further in our Summary.
VI. SUMMARYANDCONCLUSIONS
We have derived a fluid plus closure model appropriate for rotationally driven modes in a long system with domi- nantly axial magnetic field and with arbitrary b. The recently derived gyro-viscous model14 is used to obtain the stress closure terms. We have assumed incompressible dis- placements and ordered the axial wavenumber small. These assumptions are not unreasonable for the equilibria and modes of interest in our applications. The incompressible assumption is justified by recent work of Freidberg,15 and a posteriori by reproducing previous published results for both non-reversed (theta pinch) and reversed (FRC) profiles. An analytic result is that only the radial derivative of the equilibrium GV coefficient enters the calculation, a result observed previously in other contexts.17 Thus, it is essential to retain this profile effect in consideration of kinetic effects on these modes.
normalize X according to the moment-of-inertia definition
used previously. Thus, hXi 1⁄4 Ð rs drr3nX= Ð rs drr3n is used 00
for comparison to previous results.
Mode results for ‘ 1⁄4 1 are remarkable in that no unsta-
ble modes are found. Thus, sheared ion rotation can com- pletely stabilize the wobble mode within our model. The import of this, of course, is that additional physics have to be considered for these modes. While a detailed consideration of these effects is beyond our present scope, we summarize some important physics effects to include in future work in our last section here.