MadSci Network: Physics

Re: Nuclear reactor multiplication factor below 1.0000?

Date: Thu Jun 10 13:32:47 1999
Posted By: Bernadette Baca, Health Physicist, Uranium Licensing Project, Texas Dept of Health-Bureau of Radiation Control
Area of science: Physics
ID: 927824631.Ph


The multiplication factor is simply the ratio of what neutrons are 
introduced to create a fission reaction to those resulting or produced from 
the fission reaction which then they are available to create the next 
fission.  When the multiplication factor is 1.0, the ratio of neutrons 
going into a fission reaction is the same as those produced or emitted from 
the fission and are "available" to create the next fission reaction.  There 
are always losses of neutrons in the overall reactor system in which 
neutrons either introduced or produced are being absorbed by the fuel 
cladding, moderator, etc. 

We take the ratio of one neutron creating a fission reaction to one 
produced neutron that will create the next fission reaction to be the 
multiplication factor of one (1.0). This ratio of 1 allows for better 
control and precision in operating a nuclear reactor.  The rate of 
operation for the reactor is then at a steady, or constant, state of 
operation. This also means  the nuclear or fission chain reaction is self 
sustaining.  No other sources for neutrons are needed to make another 
fission occur.  This state is termed the critical state for a reactor.

When the multiplication factor is less than 1.0, this means less neutrons 
are produced from fission reactions and available for ...than are put into 
them.  This is termed subcritical.  When the multiplication number is less 
than 1.0, the nuclear chain reaction can not sustain itself and will 
eventually, as we say, die out to a great degree.  Additional neutrons 
would then be needed in order to get reactions going again.

In a reactor when conditions are subcritical, the reactor in a sense will 
not start.  Somewhat similar to trying to start a car with too little fuel. 
 It may try to start, but never really get going and get you where you need 
to go.  More neutrons are needed to get the reactor running and generating 
enough heat to turn into electricity.  Even though at subcritical states, 
fission reactions are going on but not enough to make the reactor system 
self sustaining.

When the multiplication factor is greater than 1.0, this means more 
neutrons are being produced from the fission reactions than introduced.  
This is termed supercritical.  This just simply means that there are more 
than enough neutrons to sustain a chain reaction for the reactor.  When in 
a supercritical state more energy is released through the increased number 
of fissions.

In a reactor when conditions are supercritical, more fuel is being consumed 
than desired.  The temperatures rise with the increased energy output from 
the fissions.  However, it is not necessarily an unsafe condition with many 
reactors.   In water cooled reactors, there is a built in safety feature 
that if the water gets too hot, the reactor shuts itself down.  The 
neutrons in some sense are moving too fast to be absorbed by the fuel and 
produce more fissions.  This in a sense slows the reactions or reactor down 
again to a safe level.  The only time that an unsafe condition might occur 
is if there was no water or other moderator to cool and moderate the 
reactor.  A moderator is a substance or medium used to slow neutrons down 
slow enough to be absorbed by the fuel for a fission reaction.

Just because there exists subcritical and supercritical states, does not 
mean a reactor can not be used or is not operational.  Several experimental 
reactors often operate at subcritical states for a variety of experiments 
and other operations which require a lower temperature than operating at a 
critical state.  Some reactors operate at supercritical states in order to 
raise temperatures at a faster rate or burn off certain impurities in the 

If there are any additional questions, please let me know and I'll see what 
I can do to help answer them.

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