Physics Basis for a Spherical Torus Power Plant Page: 4 of 71
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the surface-averaged parallel current density be the larger of the bootstrap current
density and a constant value (inside some cutoff radius) determined also by a central
q(0) constraint. The first method ensures continuity of all equilibrium profiles but
makes direct control of the bootstrap current fraction more difficult in some situ-
ations. All bootstrap current calculations use the collisionless model described in
Ref. 18 and use an accurate approximate expression for the trapped particle fraction
derived in Ref. 19.
2.3 Initial Shape and Profile Optimization
Once the equilibrium current profile is constrained to be exactly aligned with the
bootstrap current, the aspect ratio, boundary shape, density and temperature pro-
files, and q(0) completely determine the equilibrium. For analyzing the stability
of these equilibria, the codes BALLOON [20, 21] and BALOO [10] were used for
high-n ballooning modes, and the PEST-II [22] and GATO [23] codes were used
for computation of both marginal values and the marginal wall position which
stabilizes low-n kink modes. The functional forms used for the shape and pressure
and temperature profiles in the following analysis are described in Refs. 4 and 5 and
are not repeated here.
For most of the results discussed below, systematic ballooning stability opti-
mization was performed prior to kink optimization because kink stability analysis
is comparatively computationally expensive and time consuming. In this optimiza-
tion, it is important to span a reasonable range of shape and profile combinations
to be confident that one is truly approaching an optimal configuration. Further, the
aspect ratio with the highest 3 is not necessarily optimal from a power production
stand-point, so determining stability limits for a range of aspect ratios is essential
for reactor optimization.
The starting point for the ARIES-ST stability optimization is essentially sum-
marized in Fig. 1 whose data is taken from Figs. 15 and 16 of Ref. [4]. The diamonds
in the figure show the optimal ballooning stable N and / for near 100% bootstrap
fraction equilibria with q(0)=3 and S = 0.45 for a range of aspect ratios and elonga-
tion. The first important point of this figure is that increasing r actually leads to an
increase in the marginal /N which together lead to rapidly increasing /. The second
important point is that A > 1.4 is optimal for stability when the high bootstrap
fraction constraint is enforced. Since the TF dissipation decreases with increasing
aspect ratio, the optimal reactor configuration will also have A > 1.4.
The squares in the figure represent the corresponding optimal /N and / taken
from Fig. 4 of Ref. 5 for r=2.8 and A=1.4 and show a roughly 10% higher / due
either to small numerical differences between the codes or to the profile functional
forms used by Miller being somewhat better suited for ballooning stability optimiza-
tion. The very similar optimal pressure profiles found by the two authors are shown
in Figure 2. As seen in the figure, broad pressure profiles with large gradients near
the plasma edge and smaller but finite gradients in the core are optimal with respect4
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Kessel, C. E.; Menard, J.; Jardin, S. C. & Mau, T. K. Physics Basis for a Spherical Torus Power Plant, report, November 1, 1999; Princeton, New Jersey. (https://digital.library.unt.edu/ark:/67531/metadc625889/m1/4/: accessed April 24, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.