AAWSAP DIRD, Inertial Electrostatic Confinement Fusion, March 2010

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exponents greater than 2. The first suggestion of th ils was By R. W. Bussard based on
theoretical arguments (see Section 1). Later, PIC studies by M. Ohnishi at Kyoto
University (now at Kansai University) also showed such strong scaling (not covered
here- but see M. Ohnishi in Proceedings of 16th IEEE/NPSS, vol. 2, pp. 1468-1471). The
unanswered question is at what current level this occurs. Future simulations should
address that issue and also examine low angular momentum spread and higher ion
injection energies.
In summary, this study by Tzonev et al. is very encouraging for formation of deep wells
in IEC devices designed for reactors using beam-beam dominated fusion. However,
much more work needs to be done along these lines to fully identify the optimal ion
injection strategy for deep wells with minimum power input. As stressed earlier, the
potential well parameters must also be combined with a consistent calculation of the
energy gain (Q) following the methods of L. Chacon et al. to establish a complete
picture of energy gain possible in a power type IEC.
MOMOTA ET AL. - STUDY OF VIRTUAL ELECTRODE STRUCTURE
In another related study, Momota and Miley (Reference 4.5) used an analytic solution
to examine the angular momentum effects. "Double-well" potential structure (virtual
cathode formation) was studied in a stationary spherical IEC using the nonlinear
Poison's equations and particle densities derived from kinetic theory. A novel method to
obtain a spherica lly symmetric stationary distribution function is introduced and an
integral-differential equation is simplified by applying a relevant approximated formu la
for an integral. Electron and ion beams are collision-free, and their velocities are
roughly aligned toward the spherical center, but with a slight divergence. Analyses
show that the angular momentum of ions and the smaller one of the electrons create a
virtual cathode, i.e., a double-well structure, of the electrostatic potential on a potential
hill near the center. The density limit of an !EC well was found and the conditions
relevant to form a deep potential well was presented.
These results show trends roughly similar to the numerical studies of Tzonev, et al.,
and may be useful to persons wanting to study the effects analytically.
KIM - STABILITY ANALYSIS
In addition to achieving adequate potential well trapping for net energy production, the
question of stability of the non-Maxwellian plasma in the well must be considered.
(Note that "stability" is a separate question from the thermalization of the beam-like
distribution in the IEC discussed earlier. However, they are coupled nonlinear problems
due to the fact that the distribution function used for both calculations should be
consistent). N. Krall did some earlier studies to show that the distribution in the R.W.
Bussard type Polywell IEC are stable against key instabilities such as two-stream. These
studies however, were internal company reports and not openly published . Some
information is given, however, in Reference 1.7. More recently, H.J. Kim, in his thesis
done with G. Miley, did an in-depth study of two stream-like instabilities in the ion­
injected type IEC (see Reference 4.6). His work is very encouraging in that he identifies
a possible "window of stability" which depends on the injected energy distribution and
angular velocity spread. This result is summarized in Figure 4.10. The analysis is briefly
described as follows.
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