# Nuclear Criticality in a Homogeneous Slab

## 1. Is the slab critical, subcritical, supercritical? Justify

What is the criticality state of the homogeneous slab and why?

## 2. Give an expression for the scalar flux in the slab as a function of position. Define each new symbol that you introduce.

Provide the formula for the scalar flux in the slab and explain any new symbols used.

## 3. What is the net leakage rate out of the slab?

Calculate the net leakage rate from the homogeneous slab.

## 4. What is the source rate in the slab?

Determine the source rate within the slab.

## 5. What is the absorption rate in the slab? The fission production rate in the slab?

Find the absorption rate and fission production rate within the slab.

## Answer:

1. The slab is subcritical since the kinf value is equal to 1, which is less than the critical value of 1.5.

2. The scalar flux in the slab as a function of position can be expressed as φ(x) = φ0 + Σi(Qi/4πDi), where φ0 is the flux at the center of the slab, Qi is the volumetric source rate, Di is the diffusivity of the material making up the slab, and Li is the extrapolated distance of the material.

3. The net leakage rate out of the slab is equal to φ0*2L.

4. The source rate in the slab is equal to the volumetric source rate (Qi).

5. The absorption rate in the slab is equal to the fission production rate (which is equal to the volumetric source rate).

When analyzing the criticality of a homogeneous slab in a vacuum, it is crucial to understand the key parameters involved in nuclear physics. The kinf value for the material making up the slab is a critical factor in determining the criticality state. In this case, with a kinf value of 1, the slab is considered subcritical as it is below the critical value of 1.5.

The expression for the scalar flux in the slab provides a mathematical representation of the flux at different positions within the slab. New symbols introduced in the expression, such as φ0, Qi, Di, and Li, represent specific parameters related to the volumetric source rate, diffusivity of the material, and the extrapolated distance.

The net leakage rate out of the slab is the total flux leaving the slab boundaries, which can be calculated as the product of the flux at the center of the slab (φ0) and the slab thickness (2L).

Moreover, the source rate in the slab corresponds to the volumetric source rate, denoted as Qi. The absorption rate in the slab is equivalent to the fission production rate, both of which are equal to the volumetric source rate.