5.2 Brightness of the Trinity Explosion
183
street lights to fail in Hawaii, some 1400 km away. Readers interested in exploring the
effects of nuclear weapons are encouraged to consult the extensive and authoritative
volume prepared by Glasstone and Dolan (1977).
5.3 A Model for Trace Isotope Production in a Reactor
In Sect. 3.3, we examined the production of
239 Pu in a reactor via calculations that
involved only the isotopes
235 U,
238 U, and
239 Pu; no account was taken of other
isotopes that are produced along with
239 Pu. In Sects. 4.2 and 4.3, however, we saw
that even a small amount of
240 Pu in a bomb core can lead to significant predetonation
issues because of its high spontaneous fission rate. It was remarked in that section that
formation of
240 Pu in a reactor is inevitable on account of neutron capture by alreadysynthesized nuclei of
239 Pu. In this section, a numerical simulation is developed to
approximately quantify the rate of production of
240 Pu.
The idea here is to simulate the time-evolution of the abundances of a few key
isotopes in a reactor of given thermal power output and fuel load. Reactor engineering
is an extremely complex discipline, so a number of simplifying assumptions have to
be made for the purpose of a pedagogical model. The simulation is encoded in the
spreadsheet Reactor.xls.
In developing any reactor simulation, the first issue to decide is what isotopes are
to be tracked. Figure 5.3 flowcharts reactions considered in the present case.
236 U can
be formed from neutron capture by
235 U.
236 U has a small thermal neutron-capture
cross-section of its own, but as this is only about 5 barns it is neglected;
236 U is
assumed to accumulate as an end product. As in Sect. 3.3, I assume that the creation
of
239 Pu via neutron capture by
238 U is an instantaneous process; no account is taken
of the intermediate
239 U and
239 Np nuclei. The neutron capture cross-sections for
239 Pu,
240 Pu, and
241 Pu are all fairly large, so these species are tracked;
242 Pu is
assumed to accumulate like
236 U as an end product.
235 U,
239 Pu, and
241 Pu all have
appreciable fission cross-sections, so those processes must be tracked as well; of
course, the vast majority of the energy generated comes from fission of
235 U.
The simulation is predicated on a constant number of atoms within the reactor’s
fuel load, so I assume that when a nucleus fissions, it gives rise to a single nucleus of
“fission product.” The simulation is programmed to track two fission products should
the user desire, with provision for assigning a neutron-capture cross section for the
generation of fission product “2” from fission product “1”. The results discussed
below assumed zero-cross section for this process, but this can easily be changed by
the user. In reality, most fission products have half-lives of but a few hours and so
decay quickly.
I also assume that no fresh fuel is loaded into the reactor during the span of
the simulation. Some smaller cross-sections, such as that for fission of
238 U, are
neglected, and no decay processes are presumed to occur.
To formulate the simulation, we can begin with the logic advanced in Sect. 3.3:
That if P t is the thermal power generated by the reactor and E f is the average energy
183
street lights to fail in Hawaii, some 1400 km away. Readers interested in exploring the
effects of nuclear weapons are encouraged to consult the extensive and authoritative
volume prepared by Glasstone and Dolan (1977).
5.3 A Model for Trace Isotope Production in a Reactor
In Sect. 3.3, we examined the production of
239 Pu in a reactor via calculations that
involved only the isotopes
235 U,
238 U, and
239 Pu; no account was taken of other
isotopes that are produced along with
239 Pu. In Sects. 4.2 and 4.3, however, we saw
that even a small amount of
240 Pu in a bomb core can lead to significant predetonation
issues because of its high spontaneous fission rate. It was remarked in that section that
formation of
240 Pu in a reactor is inevitable on account of neutron capture by alreadysynthesized nuclei of
239 Pu. In this section, a numerical simulation is developed to
approximately quantify the rate of production of
240 Pu.
The idea here is to simulate the time-evolution of the abundances of a few key
isotopes in a reactor of given thermal power output and fuel load. Reactor engineering
is an extremely complex discipline, so a number of simplifying assumptions have to
be made for the purpose of a pedagogical model. The simulation is encoded in the
spreadsheet Reactor.xls.
In developing any reactor simulation, the first issue to decide is what isotopes are
to be tracked. Figure 5.3 flowcharts reactions considered in the present case.
236 U can
be formed from neutron capture by
235 U.
236 U has a small thermal neutron-capture
cross-section of its own, but as this is only about 5 barns it is neglected;
236 U is
assumed to accumulate as an end product. As in Sect. 3.3, I assume that the creation
of
239 Pu via neutron capture by
238 U is an instantaneous process; no account is taken
of the intermediate
239 U and
239 Np nuclei. The neutron capture cross-sections for
239 Pu,
240 Pu, and
241 Pu are all fairly large, so these species are tracked;
242 Pu is
assumed to accumulate like
236 U as an end product.
235 U,
239 Pu, and
241 Pu all have
appreciable fission cross-sections, so those processes must be tracked as well; of
course, the vast majority of the energy generated comes from fission of
235 U.
The simulation is predicated on a constant number of atoms within the reactor’s
fuel load, so I assume that when a nucleus fissions, it gives rise to a single nucleus of
“fission product.” The simulation is programmed to track two fission products should
the user desire, with provision for assigning a neutron-capture cross section for the
generation of fission product “2” from fission product “1”. The results discussed
below assumed zero-cross section for this process, but this can easily be changed by
the user. In reality, most fission products have half-lives of but a few hours and so
decay quickly.
I also assume that no fresh fuel is loaded into the reactor during the span of
the simulation. Some smaller cross-sections, such as that for fission of
238 U, are
neglected, and no decay processes are presumed to occur.
To formulate the simulation, we can begin with the logic advanced in Sect. 3.3:
That if P t is the thermal power generated by the reactor and E f is the average energy