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~ 1ms

Lifetime of neutron

Leak from reactor, absorbed, cause further fissions.

Neutron fates

~20,000 km s^-1

Initial speed of neutron

~2 km s^-1

Speed of moderated neutron

ΦΣ_a

Absorption rate

vΦΣ_f

Production rate

dn/dt

Rate of increase in neutron number density

∇⋅J

Rate of flow of neutrons away from the location

dn/dt = vΦΣ_f - ΦΣ_a - ∇⋅J

Balance equation

Neutrons tend to perform a net drift from regions of high flux to regions of low flux at a rate proportional to the flux gradient.

Assumption of diffusion approximation

J = -D∇Φ

Diffusion approximation (equation)

dn/dt = vΦΣ_f - ΦΣ_a + D∇^2Φ

The Diffusion Equation

size of reactor (the larger, the less significant is leakage relative to other neutron fates); amount of parasitic absorption (in structure and coolant);
amount of fuel (to cause further fissions)

Criticality depends on...

Maximum at centre, zero at edges; a cosine axially (zero at the ends, maximum in the middle); a Bessel function radially (zero at the outer radius, maximum in the middle)

Flux distribution when critical in cylindrical reactor

Cosine

Linear heat flux variation in axial coolant channels

Ability to remove the heat generated without exceeding safe coolant or structure temperatures

Limiting factor of absolute reactor power

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