Page 5 - Drift-wave stability in the field-reversed configuration

092518-5 Onofri et al.
Phys. Plasmas 24, 092518 (2017)
FIG. 5. Evolved total temperatures at t 1⁄4 0.2 ms in the simulations of the FRC (top) and the mirror trap (bottom). Note the change in the color scale from the FRC and the mirror plasma.
flow becomes sonic at the mirrors and supersonic beyond the mirrors, with Mach numbers much greater than unity. In both cases, the velocity at the magnetic mirrors is equal to the sound speed, so it is higher in the FRC case, which has a higher temperature. When the parallel velocity is normalized to the local sound speed, the two cases are different in the region between the two mirrors, where closed magnetic field lines exist in the FRC case. In this region, the velocity in the mirror machine is higher because the plasma flows along the open field lines, while in the FRC, the velocity is lower and
(a)
(b)
FIG. 6. Axial velocities Vz for the FRC and the mirror plasmas at r 1⁄4 0 in m/ s (top) and Vz =Cs normalized to the local sound speed (bottom) at t 1⁄4 100 l s. The outflow speeds of the FRC and mirror show one universal axial profile outside the mirror throat.
FIG. 7. Axial velocities Vz and Vz=Cs from 10 simulations with different ion temperatures. When normalized to Cs, all behaviors nearly converge to a universal curve.
is directed towards the midplane due to the contraction of the FRC length. Beyond the mirror points, the velocity is supersonic in both cases, and when normalized to the local sound speed, we find, to our surprise, that it is the same for the FRC and the mirror machine, even though the absolute value of the velocity is different in the two cases. The univer- sality of the normalized parallel flow velocity beyond the magnetic mirrors has been confirmed by a parameter scan where several simulations have been done with different ini- tial conditions, varying the ion temperature from 100 eV to 1000eV. The axial velocity is different in each simulation (higher for higher temperatures), but we find that when it is normalized to the sound speed, all the curves collapse onto a universal curve (Fig. 7). It is interesting to point out that while this universality of the normalized parallel velocity profile is found, we see sharply different radial density pro- files for the FRC and the mirror, as seen in the next paragraph.
The different evolution of the density profiles in the FRC and the mirror machine may be useful to infer the pres- ence of closed field lines in experiments where the density profiles can be measured, but the magnetic topology is not known. Figure 8 shows the 2D density contours at t 1⁄4 100 ls and the radial density profile at z1⁄40 at different times for the FRC and the mirror configurations. In the FRC case, the initial equilibrium has a thick SOL, but the fast parallel flow along open field lines reduces the density in the SOL, while closed field lines confine the plasma in the core. At the same time, the FRC contracts radially and axially and a sharp den- sity gradient develops and increases with time. On the other hand, in the mirror configuration, the density decreases everywhere, and we do not see the formation of steep density