Chapter 12
Theory of Power Spectral Density
and Feynman-Alpha Method in AcceleratorDriven System and Their Higher-Order
Mode Effects
Toshihiro Yamamoto
Abstract 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.
Keywords ADS • Feynman-α method • Higher-order mode • Monte Carlo •
Neutron noise • Power spectral density
12.1 Introduction
In accelerator-driven systems (ADS), fission chain reactions are driven by spallation neutrons emitted from a proton beam target. An ADS is quite different from
an ordinary nuclear reactor in that it is always operated at a subcritical state. Thus,
the safety requirements for reactivity control can be eased in ADSs. The
T. Yamamoto (*)
Kyoto University, Research Reactor Institute, 2-1010 Asashiro Nishi,
Kumatori-cho, Sennan-gun, Osaka 590-0494, Japan
e-mail: tyama@rri.kyoto-u.ac.jp
© The Author(s) 2015
K. Nakajima (ed.), Nuclear Back-end and Transmutation Technology for Waste
Disposal, DOI 10.1007/978-4-431-55111-9_12
119
Theory of Power Spectral Density
and Feynman-Alpha Method in AcceleratorDriven System and Their Higher-Order
Mode Effects
Toshihiro Yamamoto
Abstract 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.
Keywords ADS • Feynman-α method • Higher-order mode • Monte Carlo •
Neutron noise • Power spectral density
12.1 Introduction
In accelerator-driven systems (ADS), fission chain reactions are driven by spallation neutrons emitted from a proton beam target. An ADS is quite different from
an ordinary nuclear reactor in that it is always operated at a subcritical state. Thus,
the safety requirements for reactivity control can be eased in ADSs. The
T. Yamamoto (*)
Kyoto University, Research Reactor Institute, 2-1010 Asashiro Nishi,
Kumatori-cho, Sennan-gun, Osaka 590-0494, Japan
e-mail: tyama@rri.kyoto-u.ac.jp
© The Author(s) 2015
K. Nakajima (ed.), Nuclear Back-end and Transmutation Technology for Waste
Disposal, DOI 10.1007/978-4-431-55111-9_12
119