How to calculate critical atom density of a slab reactor?

[dss91]

I am given a critical bare slab reactor 150cm thick (a0=150cm) consisting of a homogenous mixture of U235 and graphite.

I am stuck on the part which asks me to calculate the critical atom dennsity. I have solved for the mass of the fuel in terms of the mass of the moderator. I would solve for the mass of the moderator by multiplying the volume of the reactor by the density of graphite and then plug that into the relation I have found for the mass of the moderator and the mass of the fuel, however since a slab reactor is defined only in width, I'm not sure how to find the volume of the reactor.

Thanks for any help.

 

[Astronuc]

Is one to assume a semi-infinite reactor. The there would be no leakage of neutrons in the lateral directions. One only needs to consider leakage in the normal direction (normal to the slab).

Criticality is usualy defined in terms of Ʃ (macroscopic cross-sections) which are simply products, Nσ.

 

[geddo]

Usually, the semi-infinite reactor parameters are calculated per unit infinite length. But i think that u should give us the problem for more help

 

[QuantumPion]

You want to solve for critical buckling, so that $B^{2}_{M}=B^{2}_{G}$.

$B^{2}_{M}=\frac{\nu\Sigma_{f}-\Sigma_{a}}{D}$

You are assuming no leakage in the lateral directions so the geometric buckling for a 1-D slab is simply:

$B^{2}_{G}=(\frac{\pi}{a})^{2}$

where a is the slab thickness.

 

[alphy]

To calculate the critical atom density of a slab reactor, you will need to use the concept of neutron balance and the criticality condition. This condition states that the number of neutrons produced in a reactor must be equal to the number of neutrons lost in order to maintain a stable chain reaction.

First, you will need to determine the critical mass of the reactor, which is the minimum amount of fissile material required for a self-sustaining chain reaction. This can be calculated using the criticality condition and the neutron multiplication factor, which takes into account the number of neutrons produced per fission and the number of neutrons lost due to absorption and leakage.

Once you have calculated the critical mass, you can then determine the critical atom density by dividing the critical mass by the volume of the reactor. In the case of a slab reactor, the volume can be calculated by multiplying the width of the slab (150cm) by its length and height.

It is important to note that the critical atom density will depend on the composition of the reactor, so you will need to take into account the percentage of U235 and graphite in the mixture. You can use the mass of the moderator and fuel that you have already calculated to determine the percentage of each component.

In summary, to calculate the critical atom density of a slab reactor, you will need to use the criticality condition, the neutron multiplication factor, and the volume of the reactor. It is also important to consider the composition of the reactor when determining the critical atom density. I hope this helps!