The temperature coefficient in a thermal reactor can be derived by using the six-factor formula,

k TjfpsPtnl Pfnl. (1.55)

In this, k is the effective multiplication factor, n is the average number of fission neutrons emitted per thermal neutron absorbed by fuel, f is the thermal utilization factor, p is the resonance escape probability, є is the fast fission factor, and Ptnl and Pfnl are the non-leakage probabilities of thermal and fast neutrons, respectively. Recalling the definition of reactivity

(1.56)

and assuming k is close to unity, the temperature coefficient can be expressed approximately in the form of the sum of each temperature coefficient of the six factors as

dp i dk ^ 1 dk

aTi~^T~~^~dTi~~k~dTi

1 drjі 1 df 1 dp 1 dPtnl. 1 dPfnl

~ VdTt f dTi p dTi є dTi Ptnl dTi Pfnl dT

= CCpi ~~ OCti OCpt + OCpt ~~ ОСт™ь OCpfNL ‘

(1.57)

The principal temperature effects of most thermal reactors are the variation in resonance absorption (the Doppler effect) and the fuel expansion due to a change of fuel temperature, the variation in neutron spectrum and the moderator expansion due to a change of moderator temperature, and the expansion of other materials such as coolant (apart from moderator) or structure. These phenomena are discussed through n, f, and p. Since the temperature coefficients of є, PTNL, and PFNL are generally small, on the order of 10_6^k/k/K, they are omitted in the discussion.