- 1 - Reactivity Monitoring in ADS with Neutron Fluctuation Analysis I. Pázsit and Z. F. Kuang 1 Department of Reactor Physics, Chalmers University of Technology SE-412 96 Göteborg, Sweden ABSTRACT This paper gives an overview of the statistical methods with which the reactivity in a source-driven subcritical system can be determined as well as giving several new results. These methods are based on measurement of the variance-to-mean (Feynman-alpha) or the correlations (Rossi-alpha) of the detector counts. In the traditional method a simple radioactive source is used which emits one neutron at a time, and whose source intensity is constant. In a future ADS the source will be either a spallation source, producing several correlated source neutrons for each incoming proton, or a neutron generator with a time-varying source intensity due to pulsed mode of operation. We give here the Feynman-alpha formula for both traditional and spallation sources as well as the Feynman-alpha formula for pulsed neutron generator sources. The formal solution for a randomly pulsed system is also given but is not evaluated. The results concerning the pulsed system are new. 1. INTRODUCTION It is well known that neutron fluctuations in a subcritical reactor, driven by an extraneous source, can be used for determination of subcritical reactivity. The application area is measuring the reactivity during start-up of a traditional research or power reactor. The two most common such methods are the variance-to-mean or Feynman-alpha and the correlation or Rossi-alpha methods. These methods have received a renewed interest lately in connection with ADS (accelerator driven systems). An ADS is also a subcritical system with a source, in which monitoring of the reactivity with fluctuation analysis is both possible and desirable. Nevertheless the underlying theory needs to be developed further, because the source has statistical properties that are different from those of the traditional systems, which use a radioactive source. The differences are of two basic types. In a future full- scale ADS, the source will be a spallation source. Such a source will emit several neutrons for each impinging proton, in contrast to the radioactive source that emits only one neutron at a time. Thus instead of simple Poisson statistics, a spallation source has a so-called compound Poisson statistics (to a good approximation). Second, in planned pilot experiments such as the European Union-sponsored MUSE project, the source will be an ordinary neutron generator (one neutron per incident deuterium ion), but the source will be pulsed periodically. Thus here the source has Poisson statistics with a time-dependent parameter. With periodic pulsing, the source (and thus the detector count) will not be stationary. The process can be made stationary by adding a random shift to the time scale (i.e. not synchronising the pulsing with the detector time gate). In that case the source will be a doubly random Poisson process. This paper gives Feynman-alpha formulae which are elaborated by the theory of backward master equations assuming the above types of sources. The case of compound Poisson distribution, applicable for continuous spallation sources, has been elaborated earlier by us, and both analytical and quantitative results are available. These will be briefly listed in Section 3. The case of periodic pulsing, i.e. a Poisson process with a deterministic time-dependent (periodic) intensity, has been elaborated in this paper and the results will be given in Section 4. The case of random periodic pulsing (which occurs if the pulsing and data acquisition are not synchronised), corresponding to the doubly random Poisson source, has also been considered. The formal solution is given in Section 5, however the concrete evaluation will be given in a later communication. 2. GENERAL THEORY AND FORMULAS IN TRADITIONAL SYSTEMS The inherent neutron noise in a static low power reactor driven by an external source can be calculated by the master equation approach 1-3 . The theory is quite straightforward, since the transition probabilities of the process can be given by the macroscopic cross sections of the neutron reactions. One usually seeks a second moment, either the relative variance or the (temporal) two-point correlations of the neutron number or detector counts. These can be obtained from the starting master equation. 1 Permanent address: China Institute of Atomic Energy, Beijing, China