Nuclear Reactor Kinetics

1
Nuclear Reactor Kinetics

• Craig Marianno
• NE 113

2
Effective Multiplication Factor (keff)

keff determines whether the neutron density
within a reactor will remain constant or change.
3
keff 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)

4
k 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

5
Reactivity

• When keff is close to 1.0000, ?k and ? and nearly
  the same.
• Example keff 0.98

6
Delayed 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.

7
Delayed Neutrons
8
Delayed Neutrons
9
Delayed 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!

10
Prompt 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?
11
Prompt Critical
12
Reactivity in Dollars

• From our previous example

13
Neutron 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)

14
Neutron Lifetime
15
Neutron 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

16
Effective Neutron Lifetime(delayed neutrons
included)

• ?eff effective fraction of delayed neutrons
• ?eff effective decay constant of precursors
• ? reactivity

17
Reactor 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

18
Reactor Kinetics

• Solving

19
Reactor 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.

20
Reactor 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

21
Reactor 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