Global Stability of the Field Reversed Configuration Page: 4 of 8
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0.8 \ E=2 S
E 0.6 S a -
0.2 -2 0 2 4 6 8
0 0.2 0.4 0.6 0.8 1 1.2
1 /- 5FIG.2: Scatter plot of the particle distribution
FIG.1: Variation of the normalized growth rate from linearized simulation of the n = 1 tilt
of n = 1 tilt mode with 1/s parameter mode with E = 7.2 and s = 0.8, racetrack
possible. In contrast, the stability properties of oblate FRCs are not affected significantly by the
thermal ion FLR effects even for small values of s (s - 1 - 2).
2. Linear Stability of n = 1 Tilt Mode
According to analytical estimates, finite Larmor radius (FLR) stabilization of the tilt mode
should occur when L* > yo , where w* is the diamagnetic frequency and yo is a characteris-
tic growth rate, from which an approximate stability condition s/E < 0.2-0.5 can be obtained.
In the previous kinetic calculations based on Vlasov-fluid dispersion functional approach and
using trial functions , a greatly reduced growth rate for s ~ 2 and complete stabilization at
s < 1.5 (E = 7.7) was obtained.
Our self-consistent hybrid simulations show that there is a reduction in the tilt mode growth
rate when s/E < 1, but no absolute stabilization has been found for s/E values as small as 0.1.
The difference between our results and the dispersion analysis results can be explained by the
deviation of the true kinetic eigenfunction from an assumed MHD-like trial function  in the
strongly kinetic regime (small s). The linear stability results for two family of equilibria with
E ~ 2 and E = 7.2 are summarized in Fig. 1, where the growth rate is shown for different
values of 1/s. Notice that y is only slightly reduced for s > 1.5 in the simulations with small
elongation E ~ 2. For the configurations with E = 7.2, there is a significant reduction in the
tilt instability growth rate at small values of s, however, no absolute stabilization has been found
even for s < 1.
One of the possible explanations of the instability existing beyond the FLR theory stability
threshold is the resonant interaction of the wave with ions for which the Doppler shifted wave
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Belova, E.V.; Jardin, S.C.; Ji, H.; Kulsrud, R.M.; Park, W. & Yamada, M. Global Stability of the Field Reversed Configuration, article, November 15, 2000; Princeton, New Jersey. (digital.library.unt.edu/ark:/67531/metadc721435/m1/4/: accessed February 18, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.