ESTABILIZATION TIME FOR SUBCRITICAL SYSTEM WITH DIFFERENT EXTERNAL NEUTRON SOURCE
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1 03 Iero Nuer Coferee - INC 03 Refe PE Brz Noveer OCIÇÃO BRILEIR E ENERGI NUCLER - BEN IBN: ETBILIZTION TIE FOR UBCRITICL YTE WITH IFFERENT EXTERNL NEUTRON OURCE Bry. Fose Ferdo C. v d Zeo R. L Pror de Eehr Nuer - COPPE Uversdde Feder do Ro de Jero v. Horáo edo Ro de Jero RJ ryuff@ho.o; ferdo@o.ufrj.r; zeorod@.o Isuo de Eehr Nuer (IEN/CNEN RJ) Ru Héo de ed Cdde Uversár RJ zeo@yhoo.o.r BTRCT Ths work s sudy oe deso sp kes equos for (eeror rve yse) ype reors hrouh opuo suos. Where he euros dffuso equos re dsrezed espy y he fe dfferees e eered esh shee d e dsrezed us he Crk-Noso ehod. srezed equos used wh fed soure proe re prored FORTRN d used o sue he syse ehvor wh dffere euro soure ypes. I hs wy we yse he s of e whe he sur syse eoes sory or he e erv orrespod o he sory fu for dffere eer soures. The resu shows h s wys posse o reh syse sy where o oso s deeed eve for pused soures.. INTROUCTION The (OEC 00) s oved syse h uses fs euros soure hrouh reo eed spo. ur spo euros re ejeed fro hevy ueus d he re hh eery pre; he se eered proos h re deroed o er re sod or qud se (OEC 00). The reor s sur syse h offers rs seury he poe of r de euse he sur reor ese vods he fsso h reo whou oro; d so hs syse ury urs off he reor. I u reors he proess ur off he deve eeds o e doe hrouh oro rs. Thus de ses hs o ours d osequey whou oro fsso h reo. For he sy sur sudy we sue hrouh opuer reee reor ore Behrk (NGY 995) us he sp kes equos (URTT e HILTON 976) dsrezed spy y he fe dfferees e eered esh shee (v 007) d e dsrezed us he Crk-Noso ehod (NKUR 977).
2 I hs wy we ysed he e erv orrespod o he sory fu for dffere eer soures. Ths pper s sruured he foow wy: I seo we show he oe deso sp kes equos dsrezo for wo eery roups y he fe dfferees e eered esh shee d he e dsrezo us he Crk-Noso ehod. I seo 3 we deosre he reor ore used for suo d s uer des. I seo 4 we dspy he resus d furher dsuss for he suos. I seo 5 we prese he ousos.. PTIL KINETIC EQUTION ICRETIZTION I hs seo we show he sp kes equos d s sp dsrezos y he fe dfferees e eered esh shee (v 007) d he e dsrezo us he Crk-Noso ehod (NKUR 977). The oe deso sp kes equos d wo eery roups e represeed he foow wy: v ` ` ( ) ` J ( ) χ ν ( ) λ χ C ` R ( ) f 6 () d C ( ) f ( ) C ( ). () Where represes eer soure er. Here he uer preers re e depede d here re s preursors roups. I orde wh Fk s w we wre he urre desy s: J. (3) The oeure of hese equos d her respeve us re: = Neuros fu roup poso d e (uer of euros/.s); C = eyed euros preursors oeros for roup poso d e (ue/ 3 ); INC 03 Refe PE Brz.
3 = Fro of fsso euros eed per fsso h ppers fro h preursor roup; = ey os of h preursor roup (s - ); v = Neuro speed for roup (/s); ffuso oeffe for roup poso (); = Reov rosop ross seo for roup poso ( - ); R = Group-rsfer rosop ross seo fro roup ' o he roup ` poso ( - ); = vere uer of euros reesed per fsso uped y he fsso f rosop ross seos poso ( - ); = Neuros fsso speru for roup ; = eyed euros fsso speru for eery roup d preursor roup... p srezo The reor ore s de y reos s usred fure whh he o eh s. Fure : Core wh deso d wh reos We dsreze hs ore fure sudvd eh oe of he reos dsree e esh. The fure usres ore reor wh eer reo dsrezo. The dse ewee e eshes hve eh for y e esh reo d s ued he foow wy: f ; f. (4) f f - f Fure : Ce esh represeo eer reo INC 03 Refe PE Brz.
4 INC 03 Refe PE Brz. Now def: d (5) d C C (6) d d. (7) Fro equos e 3 we o: 6 ' ' ' ' ' ' v f C d d (8) d C C d d f. (9) I whh he oss e re so deered s: ) For d R (0) d. ()
5 INC 03 Refe PE Brz. ) For d () ) ( R (3) d. (4) ) for f d (5) ) ( R (6) d. (7) d) for f d (8) ) ( R (9) d. (0)
6 INC 03 Refe PE Brz. e) For N d N () d R N. ().. Te srezo For he e dsrezo equos 8 d 9 we used he Crk-Noso ehod (NKUR 977) o: V. (3) I whh he res e V re he r-do ok eees d hey re defed s: v v V (4) d (5) d (6) d. 6 6 f f (7) Whe he soure er equo 8 s: V. (8)
7 I whh: 6 C. (9) o o sove he equo (3) eh sep of e we use he ed Thos orhs (v 007) esdes kow sp d e euro soure. 3. BENCHRK NL B-6- PREENTTION I hs seo we show he Behrk proe used he suos doe dur he sudy of hs work. Ths Behrk ore (NGY 995) whose eoery e see fure 3 hs hree reos wh he reos d 3 hv he se er oposo d he se sze. The er reo wh 60 eh s dffere ype o for epe ore sorers. Fure 3: NL-B-6 Behrk proe eoery I hs Behrk he fu s zero erey s oudry odo. The uer des veoy d deyed euro oss re show respevey es e 3: INC 03 Refe PE Brz.
8 Te : NL-B-6 Behrk proe uer preers Cos Reo e 3 Reo ( ).5.0 ( ) R ( ) R ( ) ( ) s ( ) f ( ) f Te : NL-B-6 Behrk proe euro veoy ( / s) v Te 3: NL-B-6 Behrk proe deyed euro oss ( s ) I order o o dffere sur syses fro Behrk reov rosop ross seo vues were ered hrouh vre he ohers uer preers. The e 4 shows he reov rosop ross seo vues eh reo for he wo eery roups d he upo for ssoed. Te 4: Reov rosop ross seo ( ssoed R R R R ) d he upo for ( k eff ) R eff k INC 03 Refe PE Brz.
9 4. REULT NLYZE We show hs seo he resus oed wh he opuo suo. For he ses he dse ewee eh e esh ( ) ws y reo. Ths ozes 40 e eshes. The euro eer soure ws djused o hve euro fu order 0 5 êuros/.s es for he fs eery roup d e zero for he er roup euse we re su sur syses ke reor ype. I ses osdered he e 5 erv ewee seps of e were 0 s wh fu wys equ o zero s. The resus show re s foows; he fu szo e for he dffere sur syses d eer euro soure. oe dffere ses were osdered for hs fy: ) 4 puu soure ozed 0 e 0 euros /. s ; ) oure eered 3 3 reor ore oupy 0 eh e 0 euros /. s ; ) dsrued soure 3 hrouh he ere reor ore e 0 euros /. s. I he e suseos re show seprey he resus for he ses wh eer soure wh os d vry e esy respevey. 4.. Eer oure wh Cos Te Iesy I he es 5 6 e 7 re show he euro fu szo e for he ses e respevey wh os e soure osder he dffere sur syses. Te 5: Te szo for soure er reor ore k eff (s) Te 6: Te szo for soure eered reor ore wh eh 0 keff (s) INC 03 Refe PE Brz.
10 Iesdde (êuros/ Te 7: Te szo for soure dsrued hrouh he ere reor ore keff (s) Eer oure wh Vry Te Iesy For hs se he e shpe doped for he soure s desrped eow: T o o. (30) I whh 0 s he esy of he soure orde wh he ses e d T s he perod seods. The rph represeo of hs soure for perod T equ o 00s d fro se s show fure 4. o T=05 s 00E+00 3.s) 800E E E E E Tepo (s) Fure 4 oure esy e fuo The euro fu szo e osder he dffere sur syses for o fro he ses d respevey hey re show es 8 9 e 0. INC 03 Refe PE Brz.
11 Te 8: Te szo for soure er reor ore (s) T=00s T=000s k eff Te 9: Te szo for soure eered reor ore wh eh 0 (s) T=00s T=000s k eff Te 0: Te szo for soure dsrued hrouh he ere reor ore (s) T=00s T=000s k eff We see wh he resus show es 8 9 d 0 h he fu e szo does vry so uh ewee he posos d esy of he vry e eer soure. houh for he ses wh os e eer soures we see h he fu szo e eds o rese he ry proy. INC 03 Refe PE Brz.
12 5. CONCLUION I orde wh he resus oed y he sp kes pror (-/-G) we oude h os e eer soures he ses eed he fu szo e reses wh upo for k eff or he szo reses he ry proes. For he vry e eer soure we see h he syse rehed he szo for he perods or frequey of euro pused e d for dffere poso or esy of he euro soure. Noe oso ws deeed hese resus eve wh pused soure. We oude so h ord o he ehodooy work we were e o o euro fu szo e for sur syses wh dffere eer euro soures. I spe of fuure sudy perspeves we eed hs uer opu o ore h oe deso; use ohers eer euro soures ypes or shpes use orhs d dffere dsrezo ehques for he proess of euros dffuso equos. REFERENCE..C.. v éodos Nuéros e Eehr Nuer Ed. Cer Cur-Brs (007).. J.J. udesd d L.J. Ho Nuer Reor yss New York-U Joh Wey & os (976). 3. F. I Corse esh Nod ehod For Oe-eso p Kes Cuos. NuL Eery V. 4 No. 4 pp (997). 4. Y. Ny d K. Koysh ouo of - u-group Te-epede ffuso Equos Us The Couped Reor Theory. NuL Eery V. N.7 pp.4-40 (995). 5.. Nkur Copuo ehod Eeer d ee Joh Wey & os New York-U (977). 6. OEC-eeror-drve yses () d Fs Reors (FR) dved Nuer Fue Cyes hps:// (00). 7. T.. uo d B. N. ves ffuso Theory ehod For p Kes Cuos Proress Nuer Eery V.30 N. pp.9-8 (996). 8. R. L. Zeo pção do éodo dos Pseudo-Hrôos à Cé udeso Tese de.. COPPE/UFRJ Ro de Jero-Brs (005). 9. The Geero IV Iero Foru (GIF) hp:// (0). INC 03 Refe PE Brz.
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