Optimization of target irradiated by light ion beam

A proposal is given here for a method to optimize the cryogenic hollow shell target which consists of the three layers of Pb, Al and DT fuel. The target is named as “Niu target” and does a cannon type of implosion. By using a model that the ion beam deposits its energy instantaneously in the Al pusher in the target and the pusher expands adiabatically and homogeneously, the final implosion velosity U
DT
of the fuel can be obtained as a function of the beam energy E
b
, the target radius r
Al
, the fuel radius r
DT
, the thickness δ
pb
of the Pb layer, the thickness δ
Al
of the Al layer and the rate C
Al
of beam energy deposition in the Al layer. Through the empirical laws obtained by simulations, the ion temperature T
i
and the fusion parameter ρR of the fuel after the fuel collision at the target center can be derived as functions of the preheat temperature T
O
of the fuel, the effective mass M of the imploding materials (the fuel mass added by the pusher mass), the fuel mass M
DT
and U
DT
. Through T
i
and ρR, the average reaction rate Y of the fuel is estimated. Thus the output thermal energy E
f
can be obtained as functions of the particle energy e
b
, E
b
, r
Al
, r
DT
, T
O
and C
Al
(hence δ
Pb
and δ
Al
). The pellet radius must be decided by considering the instabilities in the pellet and is chosen as r
Al
=6mm. Now we choose E
b
=6MJ, T
O
=1000K and let us optimize E
f
with respect to r
DT
, e
b
and C
Al
. At last we have r
DT
=3.2mm (M
DT
=2.37×10
⁻⁵
kg), e
b
=5.1MeV, and C
Al
=87% (δ
Pb
=20.5 µm and δ
Al
=156 µm) as optimum values, and we obtain the fusion output energy of E
f
=2.46GJ.