AAWSAP DIRD, Inertial Electrostatic Confinement Fusion, March 2010

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plasma. When an ion beam is hot, the waves excited by the instability are ion acoustic
type waves. Then one observes that a certain temperature ratio is required before the
wave will go unstable.
He also developed a two-dimensional perturbative (~f) particle-in-cell algorithm to
simulate the electrostatic interaction of electrons and ions in spherical inertial
electrostatic confinement. of scheme is applied, because the noise level in of algorithm
is significantly reduced, compared with conventional particle-in-cell simulation. Since a
particle-in-cell simulation in two or three-dimensions is very computationally and
memory intensive, it is necessary to seek computational methods and options which
lead to solutions in a reasonable amount of time. A distributed computing approach is
implemented by using parallel libraries. Applying a uniform grid spacing in spherical
coordinates may lead to a stability problem due to singularity at the spherical center. In
order to avoid the singularity issue, a two-dimensional rectangular domain and an
immersed boundary method are applied so that a spherical domain inside the cathode
gird of spherical electrostatic confinement is simulated by r-z coordinates. It is evident
from the result that the growth rate of instability, a ,decreasing function of the
longitudinal energy spread of ion distribution function, becomes reduced because the
large energy spread induces strong Landau damping by parallel kinetic effects. Besides
the effects of longitudinal Landau damping by the barn ions, a more monoenergetic
beam is able to stabilize the instability because a growth rate of instability can be
reduced for a higher beam density when the beam speed is fixed and located on the left
hill in the diagram of growth rate versus beam speed. The growth rate does not change
dramatically as a mode of angular perturbation increases.
The results summarized in Figure 4.10 indicated that the two-stream instability is
stabilized if the angular momentum spread of the beam ions is small enough, due to
enhanced ion densification at the center of the device. This is very encouraging for
future IEC development. However, an experimental study should be performed to verify
this result.
RIDER - ENERGY BALANCE STUDY
Todd Rider in Reference 4. 7 reports a quite different type of energy balance analysis.
While the prior papers used various methods to concentrate on up-down scattering in
various potential well configurations, Rider considered a "block diagram" type energy
flow balance to determine the net gain from a power unit. In such an analysis t he
reaction and scattering rates, plus the electron-ion equilibration rates, enter as (<av>)
averaged over the distribution functions for ions and electrons. Thus, the distribution
functions were not calculated explicitly in Rider's analysis. In addition to the base
function, any spatial variations in the distribution, such as pointed out by Tzonev et al.,
must be envisioned via the assumed distribution function. In traditional magnetic
confinement analyses a Maxwellian distribution function has generally been assumed.
In prior Tokamak studies, this technique has been widely used with reasonable
accuracy since such systems are indeed near thermal equilibrium. In sharp contrast, as
stressed repeatedly here, the IEC is not.
This uncertainly in <av> makes an analysis of the type attempted by Rider very
challenging, and leaves it open for possible criticism. In fact, it appears that Rider used
Maxwellian key averages and critics generally cite this as the cause for his pessimistic
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