الفهرس 
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Abstract
The fission product short term effects on reactor kinetics (namely xenon .induced oscillation phenomenon) in reaotors prese¬nts. a serious problem_ Among the number of reactprs now in opera¬tion in the world, some reactors display tbe spatial effects of this phenomenon _ Experi.men tal data in this field are very limit¬ed. Meanwhile, j.ntensive theorl:)tical works are underway in order to understand and predic”u the behaviour of high flux large size (dimension) reactors when this phenomenon is liable to manifest itself. For economic reasons it is more advantageous to build
large r~actorsb The cost of nuclear power goes down as the size of the producing unit goes up. Studies on the subject of nuclear desal\nation and the so called Agro~Industrial Complexes are bas-
. ad on the gainj.ng of economic advantage by postulating large size
nuclear reactors ~
The fission products,affect the reactor kinetics due to the change of the fission produ.cts concentratior.i. during the reactor operat1.on. The xenon ... l’~ is the fission product Which must be taken into consideration when dealing Wi~l relatively short dura¬tion changes. This is due to its high absorption cross section f~r thermal neutrons and its relatively wide fluctuations of conc-
entration.
The nature of format.ion and distruction of xenon-l’5 as
fission product leads to instability ~ both gross power as well a.e spatial ”power distribu.tion specially in large siiZe high flux power reactors
The stability of a reacto r in the presence of xenon is stro¬modified by the power c~efficient of reactivity which has a: -stabilizing effect. In operating reactors the power coefficient of reactivity is associated with certain delay constant due to the
lagg:Lng in heat transfer from the heat generating medium. to that
whioh is mainly responsible for the power coefficient of reactivi-
ty ( mvderator, coolant or fuel ).
The present work gives a general theory for the reactol s-Gabili ty in the presence of xenon-l;5 as a fission product and
a ~;:lme lagging power coefficient of reactivity. We use the spa¬tial• model in which the variables (neutron flux~ xenon and iodine concentrations and temperature distributiOlf) are functions of
spaoe a,’:ld timec The neutron flux is described by a one-group
energy model 0 The time lagging power coefficient of reactivity is described by Newtons law of cooling~ A linearized system for small perturbation about the steady state is considered in the 8,;.’lalysis<> The perturbed flux is expanded in the eigenfunctions of the wave equation associated with the reactor geometry with expansion expansion co efficients that have an exponential time dep endenca. This time dependence is then examined in details-to determine the regions stability of the perturbed flux.
The general theory that we have developed can be used to obtain the stability conditions of gross power as well as spatial
pC’Nor tiistribu•tion f’oI’ bar-’-\ and perfectly reflected reactors.