What is reactor kinetics? Reactor reaction on reactivity changes (whatever are the reasons of changes) Generally not possible HT2005: Reactor Physics T11: Reactor Kinetics

Principles of a Nuclear Reactor Leakage N2 2 MeV N1 Fast fission Energy n n/fission Slowing down Resonance abs. ν ≈ 2.5 Non-fissile abs. Non-fuel abs. 1 eV Fission 200 MeV/fission Leakage HT2005: Reactor Physics T:Reactor Kinetics

Homogeneous infinite reactor HT2005: Reactor Physics T:Reactor Kinetics

Fraction of total fission neutrons, bi Group Half-life T1/2(s) Mean life tmi (s) Decay constant li (s-1) Fraction of total fission neutrons, bi 1 55.7 80.2 .0124 .000215 2 22.7 32.7 .0305 .001424 3 6.2 8.9 .111 .001274 4 2.3 3.3 .301 .002568 5 .61 .88 1.14 .000748 6 .23 .33 3.01 .000273 HT2005: Reactor Physics T:Reactor Kinetics

Kinetic Equations HT2005: Reactor Physics T:Reactor Kinetics

Solution of Kinetic Equations HT2005: Reactor Physics T:Reactor Kinetics

Delayed neutrons ignored n(t)/n(0) ρ0 > 0 C(t)/C(0) ρ0 < 0 ρ0 Time HT2005: Reactor Physics T:Reactor Kinetics

Inhour Equation Unit “inverse hour” = inhour 1 inhour = amount of reactivity needed to make the reactor period equal to one hour 1 pcm (per cent mille) = 10-5 of Δk/k 1$ is equal to ρ = β HT2005: Reactor Physics T:Reactor Kinetics

HT2005: Reactor Physics T:Reactor Kinetics

Special Cases HT2005: Reactor Physics T:Reactor Kinetics

HT2005: Reactor Physics T:Reactor Kinetics

HT2005: Reactor Physics T:Reactor Kinetics

ρ0 = –0.5% ρ0 = –5% ρ0 = –10% n(t)/n(0) HT2005: Reactor Physics T:Reactor Kinetics

The END HT2005: Reactor Physics T:Reactor Kinetics

HT2005: Reactor Physics T:Reactor Kinetics

HT2005: Reactor Physics T:Reactor Kinetics

HT2005: Reactor Physics T:Reactor Kinetics

Graphite-moderated: lp = 10-3 Water-moderated: lp = 10-4 Fast reactors: lp = 10-7 HT2005: Reactor Physics T:Reactor Kinetics