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Subcritical multiplication

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0 k 1.0 - p 0. Rod withdrawal. Fuel addition. Predicting criticality ... k. Value. Parameter. Sub-critical. Fuel addition. Rod withdrawal. Critical. One more example ... – PowerPoint PPT presentation

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Title: Subcritical multiplication


1
Sub-critical multiplication
  • How to count neutrons when k is not 1

2
Reactivity
k1, r0
Power
k lt1, r -
k gt1, r
Time
3
Definition
  • Sub-critical multiplication is the increase in
    neutron population in the reactor core by
    positive reactivity additions by the withdrawing
    the control rods while the reactor is sub-critical

4
The thought experiment
  • All reactors have a start-up source in the core
    used for an instrumentation
  • Source emits 1000 nts per generation
  • k0.5, what happens next

S
5
How many neutrons are in the core?
Generation (k0.5)
Total
6
  • The total number of neutrons can be written
  • CSkSk2Sk3Sk4Sk5SknS
  • CS(1k2k3k4k5kn)
  • This is the power series it can be reduced to

7
Things to remember
  • As k approaches 1 the neutron produces a larger
    sub-critical neutron population
  • As k approaches 1 it takes a longer time to reach
    steady state
  • Sometimes in theory and practice the sub-critical
    multiplication equation is approximated.

8
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9
Equations and Relationships
10
Where did. What ismc
  • Inverse multiplication

11
Linear relationship
1/M
0 k 1.0 -8
p 0
Rod withdrawal Fuel addition
12
Predicting criticality
  • As fuel is added the inverse multiplication
    factor 1/M approaches 0.
  • Mass is proportional to number of elements.
  • Lets do some examples.

13
Example
  • In a sub-critical reactor (k10.8), What new
    value of k is required to double the count rate?

14
Example Continued
15
Example 2
  • What positive reactivity insertion will cause the
    count rate to double (k0.8)

16
Summary
Critical
Sub-critical Fuel addition Rod withdrawal
17
One more example
  • You are helping to load a core
  • Here are the first 5 data points

18
Example
  • How many more rods does the core need to be
    critical?

19
1/M plot
20
Questions
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