K. Kobayashi and S. Tsumura

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The denominator of the right hand side of Eqs.(77) is written as 1 ω = m1 − m2 2 + p1ω + p2 q0ω3 + q1ω2 2 ck = + q2ω + q3 k=0 ω − ωk where p1 = λI + λX(1 + η1), p2 = λIλX(1 + η1) (93) q0 = l1, q1 = ∆1 + ∆12 + l1(λI + λX(1 + η 1) q2 =(∆1 + ∆12)(λI + λX(1 + η1)) + λX (ˆγ I − β1)η (94) G 1 + l1λI(1 + η1) q3 = λIλX (∆1 + ∆12)(1 + η1)+(ˆγ I +ˆγ X − β1)η (95) G 1 , (96) c0 = ω 2 0 + p1ω0 + p2 l1(ω0 − ω1)(ω0 − ω2) , c1 = ω 2 1 + p1ω1 + p2 l1(ω0 − ω1)(ω2 − ω1) , ω c2 = 2 2 + p1ω2 + p2 , l1(ω0 − ω2)(ω1 − ω2) and ωk, k=0, 1, 2 are the roots of the cubic equation of the denominator of Eq.(92), (97) q0ω 3 + q1ω 2 + q2ω + q3 =0. (98) The approximate roots of ω1 and ω2 are given by Eq.(83). Using Eq.(92) in Eq.(77), we obtain δ¯s1(ω) =−α Cφ 2 ck 1 δ ω − ωk k=0 ¯ Σ C G1 (ω), from which we obtain a solution by the inverse transformation, (99) δs1(t) =−α Cφ 2 t 1 ck e k=0 0 ωk(t−t ′ ) C δΣG1 (t ′ )dt ′ . (100) For iodine, from Eq.(66) we obtain δIm(t) =ˆγ I t For xenon, Eq.(67) can be written as where δ ¯ Xm(ω) = 0 d1 (92) e −λI(t−t ′ ) δsm(t ′ )dt ′ , m =1, 2. (101) ω + λI + d2 δ¯sm(ω), (102) ω + λX(1 + ηm) ˆγ IλI d1 = − λI − λX(1 + η1) , d2 =ˆγ X + λI(ˆγ I − β1)+λXβ 1(1 + η1) . (103) λI − λX(1 + η1) The inverse transformation of Eq.(102) gives the solution δX1(t) =d1 t 0 e −λI(t−t ′ ) δs1(t ′ )dt ′ + d2 12 t e 0 −λX(1+η1 )(t−t ′ ) δs1(t ′ )dt ′ . (104)
2..6 CONTROL OF XENON OSCILLATIONS We consider the cases that the xenon oscillation initiated by the first movement of the control rods and is terminated by their second movement. In the present work, the control of the xenon oscillation by the simple bang-bang control method which was discussed by Shimazu 10) is investigated, namely, the control rods are moved according to the following equation; δΣ C G1 (t) = ⎧ ⎪⎨ ⎪⎩ 0, t < t1 δΣ C1 , t1 ≤ t ≤ t2 0, t2
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: which can be written in a form wher
Page 15 and 16: where κi = Σai/Di, i = c, r and
Page 17 and 18: Importance Function G1(x) G1(x) 1 0
Page 19 and 20: AOI-AOX 0.002 0 -0.002 B C A D E -0
Page 21: CONCLUSIONS It has been shown that

K. Kobayashi and S. Tsumura

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