Title: Nuclear Reactor Kinetics
1Nuclear Reactor Kinetics
2Effective Multiplication Factor (keff)
keff determines whether the neutron density
within a reactor will remain constant or change.
3keff and Power
- Power is directly proportional to neutron density
- keff 1.0000 ? critical (power constant)
- keff lt 1.0000 ? subcritical (power decreasing)
- keff gt 1.0000 ? supercritical (power increasing)
4k Excess
- Any difference between a given value for keff and
1.0000 is called the excess multiplication
factor (?k) - ?k keff - 1.0000 k excess
5Reactivity
- When keff is close to 1.0000, ?k and ? and nearly
the same. - Example keff 0.98
6Delayed Neutrons
- Single most important characteristic for reactor
control - Delayed neutrons ? decay of fission products
(precursers) - Prompt neutrons ? fission
- Fraction of delayed neutrons ?
- Delayed neutrons are more effective than prompt
because they are born at a somewhat lower
energy.
7Delayed Neutrons
8Delayed Neutrons
9Delayed Neutrons
- While it is true that they are only a small
fraction of the total neutron population, they
play a vital role in reactor kinetics. - Why?
- They significantly increase the neutron cycle
lifetime!
10Prompt Critical
If you depend on the fission neutrons ONLY to
produce further fission events, the system is
said to be prompt critical. If it takes only a
fraction of a second for the next generation of
neutrons to be produced, thermalize and produce
another fission, what do you suppose happens?
11Prompt Critical
12Reactivity in Dollars
- From our previous example
13Neutron Lifetime
- For reactor kinetics, it is important to know
the average time elapsing between the release of
a neutron in a fission reaction and its loss from
the system either by absorption of escape. This
is typically called the prompt neutron
lifetime. This time can be divided into - 1) Slowing Down Time
- 2) Thermal Neutron Lifetime (Diffusion Time)
14Neutron Lifetime
15Neutron Lifetime(infinite medium - prompt only)
- ?a total thermal macroscopic absorption cross
section - ?a absorption mean free path
- v mean velocity (2200 m s-1)
- Note - finite size reduces average lifetime due
to leakage - - ?a for a core includes all materials
16Effective Neutron Lifetime(delayed neutrons
included)
- ?eff effective fraction of delayed neutrons
- ?eff effective decay constant of precursors
- ? reactivity
17Reactor Kinetics
- We need to construct an expression for the
number of neutrons per second in the reactor
during a given neutron cycle. - We could use
- n
- k
- l
18Reactor Kinetics
19Reactor Period
- To make the previous equation easier, we can
define the reactor period (T) as T l / ?k. - The reactor period represents the length of time
required to change the reactor power by a factor
of e (2.718). This is why it is sometimes
referred to as the e folding time.
20Reactor Kinetics(Prompt Example)
- Assuming the following, what is the increase in
power for a ?k 0.0025 (0.357) at the end of
1.0 s? - ?a 13.2 cm
- v 2200 m s-1
21Reactor Kinetics(Delayed Example)
- Assuming the following, what is the increase in
power for a ? 0.0025 (0.357) at the end of 1.0
s? - ? 0.0813 s-1 ?eff 0.007
- v 2200 m s-1 l 6.0X10-5 s