One-Speed Neutron Transport Eigenvalues for Reflected Slabs and Spheres

Garis, N.S.

doi:10.13182/nse91-a23796

Cited by 27 publications

(4 citation statements)

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“…Many workers [1,5,[15][16][17][18][19][20][21][22][23][24]30] have reported fundamental time constants and lowest criticality eigenvalues for various system shapes and sizes. Numerical results for the fundamental decay constant have been given with linearly anisotropic scattering as a function of the size of the system [2,5,[29][30][31][32][33][34][35][36][37]. These results have also been extended to higher eigenvalues as reported by Dahl and Sjöstrand [30,34].…”

Section: Introductionmentioning

confidence: 80%

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Influence of anisotropic scattering on the size of time-dependent systems in monoenergetic neutron transport

Yildiz¹

1999

J. Phys. D: Appl. Phys.

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Criticality type eigenvalues of the one-speed transport equation in a homogeneous slab with anisotropic scattering and Marshak boundary conditions are considered. The connection between the transport equations for a critical and for a time-decaying system is established, and thus the time-dependent equation is reduced to the stationary one. Variation of the size of the time-dependent system with anisotropic scattering is studied numerically. Calculations for different combinations of the scattering parameters and the selected values of the time decay constant using the method are reported. Results are discussed and compared with those already obtained using various methods available in the literature.

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Section: Introductionmentioning

confidence: 80%

“…There is a relation between the decay constant and critical parameters. This equivalence can be used to transfer results from critical to time-dependent systems [2,5,6,[15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Influence of anisotropic scattering on the size of time-dependent systems in monoenergetic neutron transport

Yildiz¹

1999

J. Phys. D: Appl. Phys.

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“…Kritiklik probleminde amaç, ikincil nötron sayısı ile reaktörün kalınlığı arasında matematiksel bir bağıntı elde etmektir. Problem birçok araştırmacının üzerinde çalıştığı sayısal çözümleme açısından zor bir problemdir [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38].…”

Section: Kritiklik Problemiunclassified

Lineer-Kuadratik Anizotropik Saçılma için Kritiklik Probleminde Yansıtıcı Özdeğerleri

Türeci

2019

Süleyman Demirel Üniversitesi Fen Edebiyat Fakültesi Fen Dergisi

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Özet:Tek-hızlı nötron transport teoride son zamanlarda çalışılan lineer-kuadratik anizotropik saçılma fonksiyonu belirli kritik levha kalınlıkları için yansıtıcı öz değerlerini çözmek amacıyla kullanılır. Lineer-kuadratik anizotropik saçılma özelliği gösteren nükleer materyale sahip bir düzlem reaktör göz önüne alınmıştır ve problem yansıtıcı sınır koşullarını içermektedir. Amaç belirli ikincil nötron sayılarına ve belirli reaktör kalınlıklarına göre yansıtıcı katsayılarını bulmaktır. Sayısal sonuçlar Modified FN yöntemi kullanılarak bulunmuştur. Abstract:The recently studied Linear-Quadratic anisotropic scattering function in one-speed neutron transport theory is used to solve the reflection eigenvalues for the certain critical slab thicknesses. A slab reactor including the nuclear material is taken into account for the linearquadratic anisotropic scattering with the reflection boundary condition. The aim is to find the reflection coefficients according to the secondary neutron numbers and the reactor thickness. The numerical results are obtained by using the Modified FN method.

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“…The critical slab problem was investigated by Mitsis [2] with the Case method [3,4], Carlvik [5], Sahni and Sjöstrand [6][7][8], Sahni [9], Dahl and Sjöstrand [10]. It was investigated for the reflecting boundary conditions by Garis [11], Garis and Sjöstrand [12], Atalay [13], Türeci et al [14]. The problem was investigated with different methods such as the Case method, CN Method [15], FN method [16] and HN method [17].…”

Section: Introductionmentioning

confidence: 99%

The Slab Critical Thickness Problem with Reflecting Boundary Condition for the Anlı-Güngör Scattering Function

Gülderen,

Türeci

2023

Cumhuriyet Science Journal

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The criticality equation, which defines the relation between the secondary neutron number and the thickness of the slab, and the numerical solutions of this equation are investigated with reflecting boundary condition for the recently studied the Anlı-Güngör (AG) scattering function. The analytical calculations are performed by HN method. The numerical results are calculated with Wolfram Mathematica software for the varying secondary neutron number, the varying scattering parameter, and the varying reflection coefficient. The critical slab thickness values decrease for increasing reflection coefficient as expected.

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One-Speed Neutron Transport Eigenvalues for Reflected Slabs and Spheres

Cited by 27 publications

References 0 publications

Influence of anisotropic scattering on the size of time-dependent systems in monoenergetic neutron transport

Influence of anisotropic scattering on the size of time-dependent systems in monoenergetic neutron transport

Lineer-Kuadratik Anizotropik Saçılma için Kritiklik Probleminde Yansıtıcı Özdeğerleri

The Slab Critical Thickness Problem with Reflecting Boundary Condition for the Anlı-Güngör Scattering Function

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