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Perturbation Theory and Importance Functions in Integral Transport Formulations

E. Greenspan

Nuclear Science and Engineering / Volume 61 / Number 2 / Pages 170-180

October 1976

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Perturbation theory expressions for the static reactivity derived from the flux, collision density, birth-rate density, and fission-neutron density formulations of integral transport theory, and from the integro-differential formulation, are intercompared. The physical meaning and relation of the adjoint functions corresponding to each of the five formulations are established. It is found that the first-order approximation of the perturbation expressions depends on the transport theory formulation and on the adjoint function used. The approximations of the integro-differential formulation corresponding to different first-order approximations of the integral transport theory formulations are identified. It is found that the accuracy of all first- order approximations of the integral transport formulations examined is superior to the accuracy of first-order integro-differential perturbation theory.

 
 
 
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