AAWSAP DIRD, Inertial Electrostatic Confinement Fusion, March 2010

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are possible in Penning IEC devices provided that: 1) The electrostatic well is deep
enough (Eo > 100 kV); 2) Ion confinement time is long enough ( 8 > 0.01); and 3) Ion
source strength is moderate (Smax < 300). Another important effect which enters these
calculation concerns is relative to ion motion in the well. To emphasize the difference
between Q values studies from Nevins and Chacon are summarized in Table 4.1. (Here,
the BAFP calculation was done for off-optimal conditions (vs. the BAFP obtained for
beam-like cases) to compare with the Nevins' calculations).
Further, calculated Q-values from the BAFP simulation by Chacon for the beam-like
cases are about five to ten times larger than those obtained in by Nevins in Reference
4.1. This added inconsistency can be traced back to the different treatment of the D
and T ion species in the two ca lculations. Thus, while BAFP treats both species as one
with average mass, Nevins treats both species separately but assumes they follow the
same monoenergetic distribution function. This results in a finite velocity difference
between species that boosts collisionality, rendering smaller Q-values. The
inconsistency in the Q-value disappears when BAFP is compared against theoretical
estimates with a similar multispecies treatment in Table 4.1.
The BAFP calculations in Reference 4.2 eliminated most of the assumptions that limited
Q values in prior studies, plus they concentrated on conditions in parameter space
where promising Q values could be expected. These conditions include that the
electrostatic well is deep enough (Eo ~100 kV); Ion confinement time is long enough
(8 ~0.01); the ion source strength is moderate (Smax < 300), while the ion injection
energy is slightly below the potential-well maximum. (Here 8 and S max are normalized
quantities defined in Reference 4.2) .
These results again confirm that proper formation of the electrostatic well is essential to
achieve large fusion gains, and demonstrate that the distorted Maxwellian ion
distribution-neglected in previous analyses-can play a positive role in the IEC gain .
Results also show that the square well assumption, used in previous analytical
estimates by Nevins is in fact a pessimistic one. Thus, parabolic wells result in larger
density peaks at the center, yielding Q-values 3 to 5 times larger (for Eo ~150 kV) than
those obtained with square wells. Parabolic wells are also more forgiving with respect to
the source to ratio requirement. As previously noted Chacon found steady-state
distributions in which the thermalized component of the distorted ion population is
significant and can produce high gains. Such operating regimes with Q-value > 100
have been identified, as plotted in Figure 4.3. These results ignore electron
Bremsstrahlung loss however. That effect on the Q-value was addressed heuristically by
Chacon using a semi-analytic model, indicating that quite large Q-values are still
possible, provided that electron particle losses are kept small and well depths are large.
These results show that in addition to potential well shape, the source strength vs. up­
scattering losses plays a crucial role in the IEC energy gain. More insight into this can
be obtained from the distribution functions for trapp-ed ions, sketched in Figure 4.3.
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