2.4 Critical Mass: Tamped Composite Core
77
Fig. 2.13 Conceptual sketch
of composite core with
tamper. The inner and outer
cores are presumed to be
made of fissile material; the
tamper is non-fissile. This
sketch is purely schematic
cores been used at that time, the more efficient implosion-based Fat Man design
would have been employed, and this is what is assumed here. The first compositecore weapon was tested in Operation Sandstone in 1948, and a detailed study of the
World War II situation can be found in Reed (2020a). The key physics question of
interest here is: How does the critical mass of a composite core bomb, under, say, a
compression ratio of Trinity’s 2.5, compare to that for a
239 Pu-only bomb?
The physics of this situation can be analyzed with the solutions of the diffusion
equation and the boundary conditions developed in the preceding two sections. The
analysis is restricted to threshold criticality, that is, where the exponential growth
parameter α = 0.
For the inner core (subscript “1”), the neutron density N 1 (r) is given by (2.28)
without the r = 0 divergent cosine term:
N 1 (r ) = A
d 1
r
sin
r
d 1
,
(2.58)
where d 1 is the characteristic length scale of (2.25), with values appropriate to this
material:
d 1 =
λ
f iss
1
λ
tran
1
3(ν 1 − 1)
.
(2.59)
For the outer core (subscript “2”), both terms in (2.28) are retained:
N 2 (r ) = B
d 2
r
sin
r
d 2
+ C
d 2
r
cos
r
d 2
,
(2.60)
with
d 2 =
λ
f iss
2
λ
tran
2
3(ν 2 − 1)
.
(2.61)
77
Fig. 2.13 Conceptual sketch
of composite core with
tamper. The inner and outer
cores are presumed to be
made of fissile material; the
tamper is non-fissile. This
sketch is purely schematic
cores been used at that time, the more efficient implosion-based Fat Man design
would have been employed, and this is what is assumed here. The first compositecore weapon was tested in Operation Sandstone in 1948, and a detailed study of the
World War II situation can be found in Reed (2020a). The key physics question of
interest here is: How does the critical mass of a composite core bomb, under, say, a
compression ratio of Trinity’s 2.5, compare to that for a
239 Pu-only bomb?
The physics of this situation can be analyzed with the solutions of the diffusion
equation and the boundary conditions developed in the preceding two sections. The
analysis is restricted to threshold criticality, that is, where the exponential growth
parameter α = 0.
For the inner core (subscript “1”), the neutron density N 1 (r) is given by (2.28)
without the r = 0 divergent cosine term:
N 1 (r ) = A
d 1
r
sin
r
d 1
,
(2.58)
where d 1 is the characteristic length scale of (2.25), with values appropriate to this
material:
d 1 =
λ
f iss
1
λ
tran
1
3(ν 1 − 1)
.
(2.59)
For the outer core (subscript “2”), both terms in (2.28) are retained:
N 2 (r ) = B
d 2
r
sin
r
d 2
+ C
d 2
r
cos
r
d 2
,
(2.60)
with
d 2 =
λ
f iss
2
λ
tran
2
3(ν 2 − 1)
.
(2.61)