[ RadSafe ] shutdown Rx n flux

[Philip Simpson]

Mike,

According to this CANDU reactor educational site, http://canteach.candu.org/library/20040706.pdf, the gamma energy threshold for the deuterium gamma,n photo-neutron reaction is 2.22 MeV. 

For those who are interested, here is some information on the shutdown neutron flux in the University of Michigan's now decommissioned Ford Nuclear Reactor (FNR).

The effective neutron multiplication factor, keff, of the FNR core was approximately 0.97 when fully shutdown. Sub-critical multiplication is a property of any neutron multiplying media such as a shutdown reactor or sub-critical assembly. Sub-critical multiplication is given as M = S/(1-keff), where M is the multiplied neutron strength  and S is the neutron source strength.  The FNR had a heavy water reflector tank on one face of the reactor.  This provided a substantial source of deuterium (gamma,n) photo-neutrons that then got multiplied by a factor of 33 in the core, 1/(1-0.97). This is why there was always some low level of neutron induced fissioning going on even when the reactor was fully shutdown.  This level is directory proportional to the strength of the neutron source in a neutron multiplying medium.  

The FNR's average neutron flux at full power, 2Mw thermal, was a bit above 1e13 n/cm^2/s.  The shutdown neutron flux was approximately 8.5 decades below the full power level at about 5e4 n/cm^2/s. This was easily measured with the FNR's movable fission chambers. In fact, determining the shutdown power level of the FNR was one of the undergraduate Reactor Laboratory, NE445 course experiments until the FNR's permanent shutdown in 2003.

A "back of the envelope" calculation of the FNR's shutdown neutron generation rate from spontaneous fission and total shutdown neutron generation rate follows.

The Wikipedia spontaneous fission page gives the U-235 spontaneous fission rate as 1.0e-5/g/s and neutrons per fission as 1.86 on average. The U-238 spontaneous fission rate is given as 0.0136/g/s and an average of 2.07 neutrons per fission. The FNR had about 8 kg of U-235 and 32 kg of U-238 in the typical core. Doing the math gives 901 neutrons per second from spontaneous fission. Factor in sub-critical multiplication and we get 3.0E4 neutrons per second for the entire core. Note that the U-235 spontaneous fission rate at less than 1 neutron/s is completely insignificant for the FNR.

We can calculate the approximate total shutdown fission rate as R = Total U-235 atoms x average reactor spectrum U-235 fission cross-section x average neutron flux.  For the FNR, with 8 kg of U-235 and a fission cross-section of 582 barns the fission rate, R = 2.05e25 atoms x 582e-24 cm^2 x 5e4 n/cm^2/s = 5.96e8 fissions/s. When we consider that 2.4 neutrons are given off for each U-235 thermal fission and we get a neutron generation rate of 1.43e9 neutrons/s for the shutdown FNR reactor. Dividing by M (33.3), the sub-critical multiplication factor for the FNR, gives the total neutron source strength which is 4.3e7 neutrons/s. Compare this to the 901neutrons/s from spontaneous fission. 

Note that while 6e8 fissions/s appears to be a lot, converting to power puts things into perspective, 6e8 fissions/s x 240 MeV/fission = 1.44e11MeV/s x 1.602e-13 W/MeV/s = 0.0231W.

I believe the FNR's shutdown flux was higher than that at most research reactors and light water moderated power reactors because of the heavy water reflector tank. Still, this gives some idea of the relative contribution of deuterium photo-neutrons as compared to spontaneous fission neutrons in a shutdown reactor.

Other research reactors often used Sb-Be neutron sources as start-up sources. We had one but used it only once in the time I was at the reactor. That was when we switched from 93% enriched HEU to19.5% enriched LEU fuel in 1980. This was a completely new core and we were concerned there would not be enough deuterium photo-neutrons with the new fuel.

I would be interested to hear from other research reactors or power reactors as to their shutdown flux level.

Phil Simpson
Assistant Reactor Manager, (Ret.)
University of Michigan
Ford Nuclear Reactor

On Apr 1, 2011, at 5:53 PM, McNaughton, Michael wrote:

> Phil
> 
> Thank you for the valuable comments.
> 
> What minimum gamma energy is required to produce photo-neutrons from deuterium? The higher-energy gammas are mostly from the shorter-lived radionuclides. Most of the remaining fission products emit lower-energy gammas. Do these have sufficient energy?
> 
> mike