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This chapter discusses the theory of higher-order modes in the Feynman Y function and cross-power spectral density (CPSD) in an accelerator-driven system (ADS) where pulsed spallation neutrons are injected at a constant time interval. Theoretical formulae that consider the higher-order modes of the correlated and uncorrelated components in the Feynman Y function and CPSD for an ADS were recently derived in a paper published by the author. These formulae for the Feynman Y function and CPSD are applied to a subcritical multiplying system with a one-dimensional infinite slab geometry in this chapter. The Feynman Y functions and CPSD calculated with the theoretical formulae are compared with the Monte Carlo simulations of these noise techniques. The theoretical formulae reproduce the Monte Carlo simulations very well, thereby substantiating the theoretical formulae derived in this chapter. The correlated and uncorrelated components of the Feynman Y functions and CPSD are decomposed into the sum of the fundamental mode and higher-order modes. This chapter discusses the effect of subcriticality on the higher-order mode effects.

Theory of Power Spectral Density and Feynman-Alpha Method in Accelerator-Driven System and Their Higher-Order Mode Effects