TN method for the critical thickness of one-speed neutrons in a slab with forward and backward scattering

Öztürk, Hakan; Anlı, F.; Güngör, Süleyman

doi:10.1016/j.jqsrt.2006.12.002

Cited by 18 publications

(4 citation statements)

References 14 publications

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“…As well known, in a polynomial expansion based technique, it is not waited for good results in low order approximations. Hence, higher order approximations of the present method have been successfully practiced to related problems of the transport theory in previous studies [7][8][9]. However, this study should not to be evaluated with only the numerical results but also it should be evaluated with its easily executable equations and rapid convergence.…”

Section: Discussionmentioning

confidence: 96%

“…The same procedure developed for the traditional P1 approximation is followed to obtain Eq. (8). Then, from the definition of the diffusion length, the square root of the inverse of the coefficient of the second term of Eq.…”

Section: Theorymentioning

confidence: 99%

“…In the last decade, the first kind of Chebyshev polynomials, i.e. TN method is used effectively for the solutions of the problems related with transport theory such as criticality, eigenvalue spectrum and diffusion lengths of the neutrons in bare and reflected slabs and spheres [7][8][9][10]. However, in any of those studies, T1 the lowest order approximation of the Chebyshev polynomials of first kind is not used for the calculation of the diffusion lengths calculations in the case of forward and backward scattering.…”

Section: Introductionmentioning

confidence: 99%

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The eigenvalues of one-speed neutrons in a slab with forward and backward scattering

Ege

Öztürk

2019

Teh. glas. (Online)

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The eigenvalue spectrum is studied for one-speed neutrons in a slab with forward and backward scattering. First, the transport equation describing the interaction of neutrons in a system with general geometry is given. Then, the scattering function in transport equation is chosen as the forward-backward-isotropic (FBI) scattering model. The resultant transport equation is solved using the Legendre polynomials expansion (PN method) and the Chebyshev polynomials of second kind expansion (UN method) in neutron angular flux. Then, the PN and UN moments of the equations are obtained using the properties of the Legendre and the Chebyshev polynomials of the second kind. Finally, the eigenvalues for various values of the collision and scattering parameters are calculated using different orders of the presented methods and they are given in the tables for comparison.

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Section: Discussionmentioning

confidence: 96%

Section: Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The eigenvalues of one-speed neutrons in a slab with forward and backward scattering

Ege

Öztürk

2019

Teh. glas. (Online)

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“…Another option is an expansion in terms of Chebyshev polynomials of the first or second kind, which might result in better approximate solutions (e.g. Conkie 1959;Milgram 1991;Yaşa et al 2006;Anlı et al 2006;Öztürk et al 2007;Bülbül et al 2008). Legendre and Chebyshev polynomials are special cases of the family of ultraspherical polynomials, and it is in principle also possible to expand the radiation field in ultraspherical polynomials of order 2.…”

Section: Spherical Harmonics Radiative Transfermentioning

confidence: 99%

A new analytical scattering phase function for interstellar dust

Baes

Camps

Kapoor

2022

A&A

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Context. Properly modelling scattering by interstellar dust grains requires a good characterisation of the scattering phase function. The Henyey-Greenstein phase function has become the standard for describing anisotropic scattering by dust grains, but it is a poor representation of the real scattering phase function outside the optical range. Aims. We investigate alternatives for the Henyey-Greenstein phase function that would allow the scattering properties of dust grains to be described. Our goal is to find a balance between realism and complexity: the scattering phase function should be flexible enough to provide an accurate fit to the scattering properties of dust grains over a wide wavelength range, and it should be simple enough to be easy to handle, especially in the context of radiative transfer calculations. Methods. We fit various analytical phase functions to the scattering phase function corresponding to the BARE-GR-S model, one of the most popular and commonly adopted models for interstellar dust. We weigh the accuracy of the fit against the number of free parameters in the analytical phase functions. Results. We confirm that the Henyey-Greenstein phase functions poorly describe scattering by dust grains, particularly at ultraviolet (UV) wavelengths, with relative differences of up to 50%. The Draine phase function alleviates this problem at near-infrared (NIR) wavelengths, but not in the UV. The two-term Reynolds-McCormick phase function, recently advocated in the context of light scattering in nanoscale materials and aquatic media, describes the BARE-GR-S data very well, but its five free parameters are degenerate. We propose a simpler phase function, the two-term ultraspherical-2 (TTU2) phase function, that also provides an excellent fit to the BARE-GR-S phase function over the entire UV-NIR wavelength range. This new phase function is characterised by three free parameters with a simple physical interpretation. We demonstrate that the TTU2 phase function is easily integrated in both the spherical harmonics and the Monte Carlo radiative transfer approaches, without a significant overhead or increased complexity. Conclusions. The new TTU2 phase function provides an ideal balance between being simple enough to be easily adopted and realistic enough to accurately describe scattering by dust grains. We advocate its application in astrophysical applications, in particular in dust radiative transfer calculations.

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TN approximation on the critical size of time-dependent, one-speed and one-dimensional neutron transport problem with anisotropic scattering

Öztürk

Güngör

2009

Annals of Nuclear Energy

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TN method for the critical thickness of one-speed neutrons in a slab with forward and backward scattering

Cited by 18 publications

References 14 publications

The eigenvalues of one-speed neutrons in a slab with forward and backward scattering

The eigenvalues of one-speed neutrons in a slab with forward and backward scattering

A new analytical scattering phase function for interstellar dust

TN approximation on the critical size of time-dependent, one-speed and one-dimensional neutron transport problem with anisotropic scattering

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