在某些情況下，沸水式電廠會發生中子/熱水力學等不穩定性情況發生。這些由週期爐心功率與水力學振盪所造成的不穩定性，會影響到燃料安全極限的建立。目前在商轉的沸水式電廠中，發現的不穩定性有兩種：A 泛爐心反應度不穩定性；B異相不穩定性。這兩種反應度不穩定性，皆由中子功率與入口通道流量形成回饋進而產生的密度波機制來造成。
我們用來計算沸水式電廠不穩定性分析的工具，係由Oak Ridge國家實驗室所研發出來的電腦程式LAPUR5。它使用中子動力學的多節點分析，伴隨著爐心熱水力學參數模型，在穩態小擾動的情況下，於頻域中計算BWR與空間相關的動態。LAPUR5程式包含兩個部份，LAPURX及LAPURW。LAPURX是解冷卻劑和燃料在穩態下的統一方程式；LAPURW則是在頻域中解冷卻劑、燃料以及中子場的動態方程。穩定性的指標則以Decay Ratio表示。
現今由於個人電腦普及並且運算能力可謂日新月異，我們希望將這些繁複並重複性的工作，例如穩定性參數測試等，派工給電腦去運行。在此篇論文中，我們將一些程式的技巧以及迴圈的觀念使用在LAPUR DR的計算上，希望能藉由這樣的程式來達到節省人力、減少人為誤差的功效。我們同時也希望這樣子的工具能提供那些致力於穩定性參數研究的人員，能夠簡單並且有效率地得到大量可信度高的資料。

Under certain conditions, boiling water reactors (BWRs) are susceptible to coupled neutronic/thermal-hydraulic instabilities. Such instabilities, which are characterized by periodic core power and hydraulic oscillations, can compromise established fuel safety limits. There are two types of reactivity instabilities have been observed in commercial BWRs: A. Core-wide reactivity instabilities; B. Out of phase instabilities. In both cases, the reactivity instability is caused by the density wave mechanism, which is reinforced by feedbacks from neutronic power and channel inlet flow.
LAPUR is a computer code developed at Oak Ridge National Laboratory for the calculation of BWR core stability parameters. It uses a multinodal description of the neutron dynamics, together with a distributed parameter model of the core thermal hydrodynamics to produce a space-dependent representation of the dynamics of a BWR in the frequency domain for small perturbations around a steady state condition. The LAPUR program consists of two autonomous modules, LAPURX and LAPURW, which are linked by means of an intermediate storage routine. The first module, LAPURX, solves the governing equations for the coolant and the fuel steady state. Map of the core steady state are generated and stored in data files for subsequent utilization by LAPURW. The second module, LAPURW, solves the dynamic equations for the coolant, fuel, and neutron field in the frequency domain. A set of open-loop transfer functions are generated and the stability index (decay ratio), is estimated from the closed loop reactivity to power transfer function.

Today, personal computers are cheaper and powerful. With its faster and faster computing ability, we can dispatch PC to calculate the routine work, like the repeating parameter testes. In this paper, we use programming skills and loop concepts on LAPUR DR calculation, in order to saving human power on parameter testing. We expect that this method can provide a simple way to those who concentrate on parametric studies, and get a large mount, more and more reliable data easily.

1. A. Escriva and J. March-Leuba, “LAPUR5.2 Verification and User’s Manual”, ORNL/TM-2000/340, Oak Ridge National Laboratory, November 2000.
2. J. March-Leuba, P. J. Otaduy, “A comparison of BWR stability measurements with calculations using the code LAPUR-IV”, NUREG/CR-2998, ORNL/TM-8546, Dist. Category AN, 1983.
3. J. March-Leuba, “LAPUR benchmark against in-phase and out-phase stability tests”, NUREG/CR-5605, ORNL/TM-1162, 1990.
4. Tim H J. J. VAN DER HAGEN, “Methods for the determination of the in-phase and out-of-phase stability characteristics of a BWR”, Chalmer University of Technology Department of Reactor Physics, January 28, 2003.
5. J. March-Leuba and E. D Blakeman, “A mechanism for out-of-phase power instabilities in boiling water reactor”, Oak Ridge National Laboratory, January 30, 1990.
6. R. Miro, D. Ginestar, D.Henning, G.Verdu, “On the regional oscillation in BWR, Nuclear Energy, vol.36, No2, pp.189-229, 2000.
7. J.A. Turso, J. March-Leuba and R. M. Edwards, “A modal-based reduced-order model of BWR out-of-phase instabilities”, Annals of Nuclear Energy, Vol. 24, No.12, pp.921-934, 1993.

8. J.L. Munoz-Cobo, R. B. Perez, D. Ginestar, A. Escriva, G. Verdu, “Non linear analysis of out of phase oscillations in BWRs ”, Annals of Nuclear Energy, Vol. 23, No.16, pp.1301-1335, 1996.
9. Kengo Hashimoto,“Linear modal analysis of out-of-phase instability in BWR cores”, Annals of Nuclear Energy, Vol. 20, No.12, pp.789-797, 1993.
10. J. L. Munoz-Cobo, S. Chiva, A. Sekhri, “A reduced order model of BWR dynamics with subcooled boiling and modal kinetics : application to out of phase oscillation”, Annals of Nuclear Energy 31 1135-1162, 2004.
11. J. L. Munoz-Cobo, O. Rosello, R. Miro, A Escriva, D. Ginestar, G Verdu,“Coupling of density wave oscillations in parallel channels with high order modal kinetics : application to BWR out of phase oscillations”, Annals of Nuclear Energy 27 1345-1371, 2000.
12. Hao-Tzu Lin, Jong-Rong Wang, Chang-Lung Hsieh, Chun-kuan Shih, Show-Chuyan Chiang, Tong-Li Weng, “KUOSHENG BWR/6 STABILITY ANALYSIS WITH LAPUR5 CODE” , Annals of Nuclear Energy, 2005.
13. Chang-Lung Hsieh, Hao-Tzu Lin, Jong-Rong Wang, Chun-kuan Shih, “BWR parametric sensitivity effect of regional mode instability on stability boundary”, 15th International Conference on Nuclear Engineering, 2007.
14. Hao-Tzu Lin, Chang-Lung Hsieh, Jong-Rong Wang, Chun-kuan Shih,“In-phase and out-of-phase mode instability analysis with LAPUR5 for CHINSHAN”, 15th International Conference on Nuclear Engineering, 2007.
15. 林浩慈、黃國修、陳昱中、陳佩琪、羅芳琪、施純寬、謝昌倫、邱茗秀、林紋仕、江授全、翁烔立、周鈴曜，“沸水式反應器穩定性拉普(LAPUR)分析技術發展與應用”,中華民國九十三年六月, INER.
16. 吳坤隆,“BWR 穩定性與 LAPUR 方法論”，中華民國九十三年二月，核能研究所.
17. 林紋仕,“功率提昇下對核能電廠的穩定性分析”, 中華民國九十五年七月, 碩士論文, 國立清華大學工程與系統科學研究所.
18. 楊宗學, “沸水式反應器異相位不穩定分析”, 中華民國九十六年七月, 碩士論文, 國立清華大學工程與系統科學研究所.