伴隨函數用於蒙地卡羅計算法變異數降低技巧之建立與應用

Implementation and Application of Adjoint Function Methodology in Variance Reduction of Monte Carlo Calculation

陳昂佑(Ang-Yu Chen)

指導教授 ： 薛燕婉 ； 許榮鈞

國立清華大學/原子科學院/工程與系統科學系/博士(2008年)

摘要

本研究所建立之TORT-coupled MCNP計算法，乃是以CADIS演算法為基礎，自行將TORT伴隨計算所得的伴隨函數，轉換為蒙地卡羅程式MCNP使用變異數降低技巧所需之「重要性加權射源」與「重量視窗」，以提高MCNP追蹤粒子之計算效率。此法可有效的降低MCNP計算所得結果之變異數，特別是對大體積分佈射源或是深穿透的問題。首先透過小型PWR壓力槽問題，驗證所建立計算法之正確性。然後將其應用在兩個困難的屏蔽問題：清華大學水池式反應器THOR之硼中子捕獲治療(BNCT)照射室門外劑量之評估，與用過核燃料貯存護箱表面劑量率計算。
在BNCT照射室門外劑量計算問題中，粒子通率自射源至照射室活動門外處衰減達七個次冪。因此蒙地卡羅法計算中使用有效的變異數降低技巧是非常必需的。研究結果發現，相對於未使用變異數降低技巧之MCNP計算，TORT-coupled MCNP計算法對BNCT照射室門外劑量率之計算效率可改善100至1000倍。由於二次光子是該處劑量之主要貢獻者，進一步對光子權重視窗進行調整做最佳化處理，可額外改善50~75%之計算效率。
本研究第二個實際案例：台電貯存護箱表面劑量率評估計算，是一個深穿透、輻射源分佈範圍廣大、牽涉到輻射潺流效應的高難度屏蔽計算問題。對這樣一個困難的輻射安全評估問題，蒙地卡羅計算必須搭配有效的變異數降低技巧，才能在合理計算時間內獲得統計誤差可接受的計算結果。除了TORT-coupled MCNP計算法外，本研究亦使用了其他兩種計算法，分別是傳統的MCNP搭配幾何分裂變異數降低技巧，與業界常用之SAS4分析程式。本研究完整比對了三種計算方法計算護箱表面各處之劑量率所得結果之準確性及計算效率。研究結果發現，本研究所建立之TORT-coupled MCNP計算法基於其有效且具一致性的射源加權與遷移加權變異數降低技巧，使其計算結果準確可靠，且其整體計算效率在這三種不同的計算方法當中是最高的。

關鍵字

BNCT照射室 ； 輻射屏蔽 ； 蒙地卡羅計算 ； 變異降低 ； 伴隨函數應用 ； 貯存護箱

並列摘要

The TORT-coupled MCNP method established in this study is an implementation of the consistent adjoint driven importance sampling (CADIS) methodology for Monte Carlo variance reduction. It utilizes the deterministic TORT adjoint function to perform source biasing and consistent transport biasing with weight window technique in the MCNP Monte Carlo simulation. It has been proved to be very effective in accelerating the MCNP calculations especially for those cases involving distributed sources and/or deep-penetration problem. The method is first verified by a benchmark calculation for a small PWR pressure vessel problem. After that, we have successfully applied this method in two real world difficult shielding problems: one is the shielding evaluation of the BNCT treatment room at Tsing Hua Open-pool reactor (THOR), and the other is the surface dose rate calculation for a spent fuel storage cask.
In the first case for the shielding evaluation of the BNCT treatment room at THOR, the radiation attenuation from beam exit to detector outside the treatment room is more than seven orders of magnitudes. This is why an effective variance reduction technique is very important for solving this problem by Monte Carlo simulation. We have demonstrated that, with this method, the computational efficiency can be improved significantly by two to three orders of magnitude compared to an analog MCNP calculation. Since the neutron-induced secondary gamma rays are the main contribution to the total dose outside the treatment room, we have found that further optimization of the photon weight windows can lead to additional 50-75% improvement in the overall computational efficiency.
In the second case for the surface dose rate calculations of the NAC-UMS spent fuel storage cask, it involves difficult problems of deep penetration and radiation streaming resulting from a large volumetric source. Effective variance reduction techniques are indispensable for a Monte Carlo simulation to obtain results of small statistic errors within reasonable computing time. In addition to the TORT-coupled MCNP method, we also adopted two conventional techniques in this problem, i.e. the traditional cell importance method in MCNP and the popular SAS4 analysis sequence in the SCALE5.1 package. This study thoroughly compares the accuracy and computation efficiencies of MCNP and SAS4 in the surface dose rate calculation of the NAC-UMS storage cask. Due to the effective source biasing and consistent transport biasing, the TORT-coupled MCNP calculation shows overall a superior computation efficiency in this case study.

並列關鍵字

BNCT treatment room ； radiation shielding ； Monte Carlo simulation ； variance reduction ； adjoint function-derived weight window ； spent fuel storage cask

參考文獻

ANS, 1977. Neutron and gamma-ray fluence-to-dose factors, ANSI/ANS-6.1.1-1977. American Nuclear Society, La Grange Park, IL.

Broadhead, B.L., Tang, J.S., Childs, R.L., Parks, C.V., Taniuchi, H., 1997. Evaluation of shielding analysis methods in spent-fuel cask environments. Nucl. Tech. 117, 206-222.

Broadhead, B.L., Wagner, J.C., 2005. Effective biasing schemes for duct streaming problems. Radiat. Prot. Dosim. 116, 504-507.

George I.B., Glasstone, S., 1970. Nuclear Reactor Theory. Van Nostrand Reinhold Company.

Haghighat, A et al., 1995. Evaluation of the Uncertainties in the Source Distribution for Pressure Vessel Neutron Fluence Calculations. Nucl. Technol., 109, 54.