Using the same one-group point-kinetics data as usual ( , , )

PHYSICS · Multi-part · Fermi University Physics · Nuclear Physics · Fission, fusion and nuclear energy · Fission, fusion and nuclear energy

Energy from Physics, Ch Running a reactor: kinetics, heat removal, feedback, burn-up and the fuel cycle

Problem

Using the same one-group point-kinetics data as usual (

\beta = 0.0065

\lambda = 0.0767\,\mathrm{s^{-1}}

\Lambda = 2\times10^{-5}\,\mathrm{s}

), a reactivity step

\rho_0 = 0.009

is inserted, which is above the delayed-neutron fraction

\beta

(prompt critical). ((a)) Starting from the inhour relation

\rho = \Lambda/T_{\rm p} + \beta/(1+\lambda T_{\rm p})

, show why for a step above prompt critical the stable period is dominated by the prompt term alone, and derive the simplified relation for

T_{\rm p}

in this limit. ((b)) Evaluate

T_{\rm p}

for this step, and find the time for the power to rise a hundredfold, treating the growth as a clean exponential

n(t) = n_1 e^{t/T_{\rm p}}

and measuring time from the moment the growth has become that clean exponential.