Page 4 - Compact Toroid Injection Fueling in a Large Field-Reversed Configuration

082512-4 Lau et al.
Phys. Plasmas 24, 082512 (2017)
Due to the neglect of radial gyro-averaging, the growth-rate of instability is expected to be higher when compared to non-local simulations. Previous work by Naitou et al.5 with fully kinetic particle dynamics also supports the expectation of strongly stabilizing FLR effects.
III. STABLE DRIFT-WAVES IN THE FRC CORE
The broad stability of the core within the C-2-like parameters may provide the basis for understanding some of the experimentally observed phenomena. Experiments observe robust fluctuations in the SOL and fluctuations of an order of magnitude smaller in the core.35 Furthermore, in the same experiments, the core spectrum exhibits a depression in the ion range (kfqs < 15) unlike the SOL spectrum.
Because our linear, local simulations do not include the stabilizing influences of fast ions and non-local effects which exist in the experiments, instabilities should be enhanced within these simulations. However, quite the opposite, the results of the simulations show the core stability to be extremely robust.
It should be noted that one element missing from these simulations may explain fluctuations in the core: the cou- pling of the SOL and core. Cross-separatrix coupling between the two regions may introduce fluctuations originat- ing from the SOL (detailed in Sec. IV) into the core which, by itself, is found to be inherently stable.
IV. DRIFT-WAVE INSTABILITIES IN THE SCRAPE-OFF LAYER (SOL)
A. Collisionless g 5 1 instability
GTC simulations were also performed for the SOL, using C-2-like parameters detailed in Table I with g 1⁄4 1. Relative to the core, the temperatures and densities of both species are lowered by a factor of 2 while the magnitude of the back- ground magnetic field is roughly stronger by a factor of 2. Under these conditions, simulations show the existence of unstable modes ranging from ion-scale to electron-scale wave- lengths. This is consistent with SOL experimental measure- ments of density fluctuations which exhibit an exponential spectrum ranging from the ion-scale to electron-scale.35
Figure 2 shows the instability frequency (xr) and growth-rate (c) over a range of kfqs for various drive strengths. xr is in the electron diamagnetic direction and the electron curvature drift direction, but opposite to the electron rB drift direction. As kfqs increases, the magnitude of xr
FIG. 2. Real frequency (xr) and growth-rate (c) for different drive strengths (j) of the collisionless SOL instability for g 1⁄4 1 are shown as solid lines. For comparison, the dispersion of the collisional SOL instability for g1⁄41 is shown as the dashed line. As the drive decreases, the instability shifts toward the shorter wavelength (kf).
Within gyro-kinetically valid regimes x qi e/<1; kk 1;
(2) (where qi is the ion gyro-radius, LB 1⁄4 1 @B is the magnetic
Xi LB T k?
B @r
field scale length, and / is the perturbed electrostatic poten-
tial) the electrostatic drift-wave is found to be stable in the
FRC core when driven by pressure gradients relevant to the
C-2 advanced beam driven FRC experiment. Simulations with
equal temperature and density gradients (gi 1⁄4 ge 1⁄4 g 1⁄4 1) and
with drive strengths up to R0 1⁄4 jn < 5 were performed. Ln
Toroidal wavelengths were scanned from ion scale to electron scale up to kfqe < 0.3. From these GTC simulations, the FRC core is found to be stable within this regime.
A. Mechanisms for core stability
To understand this surprising stability, further simula- tions based on limiting cases were studied.
From magnetohydrodynamics, the radially increasing quantity Þ dl suggests the existence of a flute instability in the
B
core. An instability can be found by suppressing particle motion in the simulation by evolving only particle weight (df) and holding particle positions and velocities fixed (i.e., initial phase space coordinates of particles are fixed). This indicates the importance of electron kinetics for stability. Work based on this instability also finds both the finite Larmor radius2 (FLR) and the rB effects to be additional stabilization effects as expected. Similar simulations turning on and off FLR and rB effects were also performed in the SOL and are detailed in Sec. IV. Simulations also find that only the electron kinetic effects need to be suppressed for the core to exhibit this instability.
In simulations of purely kk 1⁄4 0 but with the evolution of both particle weight and phase space positions, in the limit of far-from-experimental conditions (for example, tempera- ture 100 lower), stability persists when FLR effects are kept; however, when FLR effects are turned off at these lim- iting case conditions, the kk 1⁄4 0 mode can become unstable.
Additional limiting conditions further show the impor- tance of electron kinetic effects. In the limit of artificially heavy electrons (me/mp > 0.25–0.5), an unstable mode peak- ing in the outer mid-plane can exist. In the limit of artificially elongated geometry approaching a theta-pinch-like geometry (Zlim/Z0 < 5–7, where Zlim is the artificially elongated length and Z0 is the original C-2-like length), a similar unstable mode can also form in the outer mid-plane. These limiting cases suggest the electron kinetic effects, and, especially, the short electron transit time (as slower velocities or longer travel length contribute to) to be important FRC features which contribute to the core stability.