Stabilized Spheromak Fusion Reactors Page: 6 of 21
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drive, though electrostatic current drive by a coaxial gun is also being explored on NSTX.
As in all tokamaks, it is the toroidal field in NSTX that accounts for its inherent stability.
The disadvantage of spheromaks is the possibility of residual MHD instability
that disturbs flux surfaces, even for the "stabilized" case, and additional current drive
power that would be needed if stabilization is required at the edge in order to maintain a
Taylor state everywhere. On the other hand, if a spheromak can be made as stable as
already appears to be the case in SPPX, any reactor designer would opt to omit the
central column, in order to simplify the divertor and above all to simplify blanket and
neutron shielding design.
It may or may not be necessary to stabilize the edge, as discussed in Section 4,
and in any case the additional current drive power required to stabilize the edge is only a
factor 2 or so greater than that for the tokamak-like stable case. To see this, we average N
T32 over the temperature profile giving:
N = NS foa (2rdr/a2)j(x)/ j(0) (1 - x2)32 (4)
Here T c (1 - x2) with x = r/a giving N = NS(1 - x2)]32; and we have weighted the integral
by the current density j being driven by the beam. For a current density peaked on axis,
as in a tokamak or the potentially stable spheromak discussed in Section 4, N = Ns giving
Eq. (2) above. For the parabolic temperature profile and constant j, the average <N> >
2/5Ns even if j is roughly uniform as in a Taylor state.
3. Power Balance in Stabilized Spheromak Reactors
We shall first discuss a spheromak maintained in a stable Taylor state with flat X
profile, as in present SSPX experiments, where = [j/B is proportional to the current
density j. The possibility that stability may allow a X profile that is "sagging" toward the
separatrix is discussed in Section 4 and Appendix A.
To illustrate, we consider the steady state spheromak reactor design of Hagenson
and Krakowski [5], reviewed in Ref. [6]. Using the numbers in Refs. [5] and [6], we find
for the Hagenson-Krakowski design:4
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Fowler, T. Stabilized Spheromak Fusion Reactors, report, April 3, 2007; Livermore, California. (https://digital.library.unt.edu/ark:/67531/metadc883105/m1/6/: accessed July 16, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.