AAWSAP DIRD, Inertial Electrostatic Confinement Fusion, March 2010

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of various loss channels such as hitting the grid, charge exchange, or up-scattering in
energy, the ions would be prematurely trapped in the potential well until they fused.
The conventional requirement for fusion confinement is given in terms of the
confinement parameter, nt, where n = the ion density and t is the confinement time.
Also the ion energy (or temperature T) must be in the 20 or more keV range assuming
D-T fuel. For breakeven, J. Lawson developed his famous "criterion" nt = 1014 cm·3-sec
at T > 15 keV for DT fusion. Here t = energy confinement time, sec; n = ion density,
cm·3 and T = ion "temperature" or average energy.
The Lawson criterion is independent of the confinement method, but does depend on
the fuel via the selection of cross sections in the derivation. Magnetic confinement is
generally limited to n ~ 1014 cm·3 by pressure balance. Then a confinement time • of~
1 sec is required. For Inertia Confinement Fusion (ICF) or "laser fusion", compression of
targets can achieve n N 1024, so a confinement time of only 10-10 sec is need
(corresponding to the disassembly time of the compressed target). (For a general
review of energy breakeven requirement for D-T fusion and other fuels like D-3He and
p- 118, the reader referred to: G. Miley, Fusion Energy Conversion, American Nuclear
Society, La Grange, IL 1973).
Now consider the IEC. In principle, the ions focused on the center of the IEC can
achieve a density of n ~ 1016, giving a required confinement time of 10-2 sec for DT
fusion breakeven. This time can be restated in terms of the number of ion recirculations
in the IEC potential well by dividing the well diameter by the average velocity of the
recirculating ion. In later cases discussed in this report, this number is typically quite
large, usually N1000 recirculations. Achievement of this large number of recirculations
requires strong reduction of all of the loss channels noted earlier. Grid losses can be
reduced by STAR mode operation discussed later where the recirculating ions possess
beam-like trajectories passing through the center of the grid opening. The ideal,
however, is the elimination of the grid altogether which can be done via formation of
virtual potential structures, originally proposed by Farnsworth and discussed in
following sections. The temperature requirement also leads to a fundamental difference
in the IEC physics vs. other confinement approaches. (Note that "temperature" is not a
proper term here since it implies an equilibrium distribution while the IEC is far from
that with its beam-like ions. Thus, the reader should view "temperature" as meaning
average energy of the ions. In doing that, however, it is assumed that the ion energy
distribution is known so that averaging is possible). Most ions in the IEC are born near
the chamber wall so are accelerated to an energy close to the applied voltage on the
grid during the extraction process. A reasonable estimate is that the ions reaching the
fusion region in the center have an energy near 80 percent of the grid voltage on
average. Thus it becomes relatively easy to achieve the Lawson D-T requirement by
applying a voltage of~ 25 kV. In fact most IEC neutron sources discussed later operate
at voltages > 80 kV to get into an energy range giving a higher fusion cross section. In
sharp contrast, magnetic fusion devices struggle to obtain a temperature in the 10 keV
range since the entire plasma population must be heated (vs. direct ion acceleration in
the IEC) due to the equilibrium distribution maintained in these plasmas. Another very
important point is that Lawson assumed that the ions and electrons were in thermal
equilibrium, at the same temperature, T. This is a reasonable approximation for
magnetic confinement, but not so for the IEC. In the latter, the electrons form a
"distorted" Maxwellian distribution at an effective temperature well below that of the
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