K. Kobayashi and S. Tsumura

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Neutron Flux (cm –2 sec –1 ) 1×10 14 5×10 13 –a3 Reflector Core 1 Moderator Neutron Flux –a2 Xenon density 0 –80 –60 –40 –20 0 Distance from the center of the system (cm) –a1 2×10 15 1.5×10 15 1×10 15 5×10 14 Figure 2. Neutron flux and xenon density distributions for a steady state Difference of Axial Offsets 0.01 0.005 0 –0.005 –0.01 A C B Control Rod AOP–AOX AOI–AOX 0 10 20 30 Time (hours) E D F Control Rod 0 1×10 –5 0 –1×10 –5 Figure 3. Time variations of AOP − AOX and AOI − AOX for t3 = 25h 18 Xenon density (cm –3 ) Control Rod’s Cross Section (cm –1 )
AOI–AOX 0.002 0 –0.002 B C A D E –0.004 –0.01 –0.005 0 0.005 AOP–AOX Figure 4. Trajectory of axial offset for t3 = 25h 2. A point of offsets moves anticlockwise on the trajectory as a function of time. 3. A point of offsets moves quickly horizontally parallel to the horizontal axis by insertion or withdrawal of control rods. The reason responsible for item 3 is the fact that the neutron production rate changes very quickly with time constant ω0 as seen in Eq.(100), while iodine and xenon densities change very slowly. In order to terminate the xenon oscillation, t3 = 25h or t3 = 28h was put in Eq.(107), and t4 =27.6h and δΣ C2 = −1.85 × 10 −6 cm −1 or t4 =55.4h and δΣ C2 = −3.74 × 10 −7 cm −1 were obtained for the cases of Figs.3 and 5, respectively. Using these values, the xenon oscillations are completely terminated as seen in Figs.3 and 5. In Fig.4, for example, the point of offsets moved in negative direction from the origin to A almost parallel to the horizontal axis in a short time by withdrawal of a control rod, and move in positive direction quickly from point B to C by returning the control rod to the original position. At the time t3 chosen appropriately, the rod is inserted and the point moved quickly in positive direction from point D to E, and at time t4, the point moved quickly from point F to the origin and the oscillation is terminated. The distance from point F to the origin is nearly the same as that from point D to E. In Figs.3 and 5, the difference between the time t3, 25h and 28h for the insertion of control rods is 3h, however, the difference of the time t4, 27.6h and 55.4h for the withdrawal between both cases is fairly large. 19 O F
Page 1 and 2: AN ANALYSIS OF XENON OSCILLATIONS U
Page 3 and 4: We use the boundary condition that
Page 5 and 6: Using the assumption that the fissi
Page 7 and 8: 2..3 KINETICS EQUATIONS FOR IODINE
Page 9 and 10: Solving the multi-group diffusion e
Page 11 and 12: which can be written in a form wher
Page 13 and 14: 2..6 CONTROL OF XENON OSCILLATIONS
Page 15 and 16: where κi = Σai/Di, i = c, r and
Page 17: Importance Function G1(x) G1(x) 1 0
Page 21: CONCLUSIONS It has been shown that

K. Kobayashi and S. Tsumura

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