NAME OR DESIGNATION OF PROGRAM, COMPUTER, DESCRIPTION OF PROGRAM OR FUNCTION, METHODS, RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM, TYPICAL RUNNING TIME, UNUSUAL FEATURES OF THE PROGRAM, RELATED AND AUXILIARY PROGRAMS, STATUS, REFERENCES, HARDWARE REQUIREMENTS, LANGUAGE, SOFTWARE REQUIREMENTS, OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS, NAME AND ESTABLISHMENT OF AUTHORS, MATERIAL, CATEGORIES

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Program name | Package id | Status | Status date |
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JN-METD-1&2 | NEA-1871/01 | Arrived | 01-FEB-1972 |

Machines used:

Package ID | Orig. computer | Test computer |
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NEA-1871/01 | IBM 370 series |

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3. DESCRIPTION OF PROGRAM OR FUNCTION

JN-METD1 solves:

A) Stationary neutron transport problems in bare spherical reactors to obtain the asymptotic time constant, the effective multiplication factor or the critical radius, and the flux distribution as a function of space and energy.

B) Stationary problems in homogeneous slabs to obtain the space, angle and energy dependent flux due to a plane isotropic, point isotropic or monodirectional boundary source. Also the first and second time moments are calculated for the time-dependent flux in the slab with a point isotropic or monodirectional delta function source on one boundary.

C) Time-dependent problems in a non-multiplying bare sphere without up-scattering of neutrons to evaluate the space, energy and time dependent flux resulting from the incidence of an external source at the centre.

D) Time-dependent problems in a non-multiplying homogeneous slab without upscattering of neutrons to evaluate the space, angle, energy and time dependent flux in the slab with a point isotropic or monodirectional source on one boundary.

JN-METD2 solves:

(a) Neutron transport problems in multilayer slab systems with isotropic scattering of neutrons to obtain the space, angle and energy dependent flux due to a stationary point isotropic boundary source. Also the first and second time moments are calculated for the time dependent flux resulting from a point isotropic delta function source on one boundary.

(b) Stationary transport problems in a multilayer slab reactor to evaluate the value of the effective multiplication factor and the flux distribution as a function of space, angle, and energy.

(c) The asymptotic decay constant is computed for the fundamental neutron distribution in a multilayer slab system.

JN-METD1 solves:

A) Stationary neutron transport problems in bare spherical reactors to obtain the asymptotic time constant, the effective multiplication factor or the critical radius, and the flux distribution as a function of space and energy.

B) Stationary problems in homogeneous slabs to obtain the space, angle and energy dependent flux due to a plane isotropic, point isotropic or monodirectional boundary source. Also the first and second time moments are calculated for the time-dependent flux in the slab with a point isotropic or monodirectional delta function source on one boundary.

C) Time-dependent problems in a non-multiplying bare sphere without up-scattering of neutrons to evaluate the space, energy and time dependent flux resulting from the incidence of an external source at the centre.

D) Time-dependent problems in a non-multiplying homogeneous slab without upscattering of neutrons to evaluate the space, angle, energy and time dependent flux in the slab with a point isotropic or monodirectional source on one boundary.

JN-METD2 solves:

(a) Neutron transport problems in multilayer slab systems with isotropic scattering of neutrons to obtain the space, angle and energy dependent flux due to a stationary point isotropic boundary source. Also the first and second time moments are calculated for the time dependent flux resulting from a point isotropic delta function source on one boundary.

(b) Stationary transport problems in a multilayer slab reactor to evaluate the value of the effective multiplication factor and the flux distribution as a function of space, angle, and energy.

(c) The asymptotic decay constant is computed for the fundamental neutron distribution in a multilayer slab system.

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4. METHODS

The JN method, an analytical approach to neutron transport in a finite system is used within the context of the multigroup and (up to) J7 approximation by assuming that the scattering of neutrons is spherically symmetric in the laboratory system. This method uses the expansion into spherical Bessel functions of the Laplace-Fourier transformed emission density of neutrons and the kernel of the integral equation (resulting from the Laplace and Fourier transformation of an integral transport equation with respect to time and space, respectively).

The JN method, an analytical approach to neutron transport in a finite system is used within the context of the multigroup and (up to) J7 approximation by assuming that the scattering of neutrons is spherically symmetric in the laboratory system. This method uses the expansion into spherical Bessel functions of the Laplace-Fourier transformed emission density of neutrons and the kernel of the integral equation (resulting from the Laplace and Fourier transformation of an integral transport equation with respect to time and space, respectively).

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6. TYPICAL RUNNING TIME

JN-METD1: Typical running time on the IBM-360/65 is nearly 4 minutes to obtain the time-dependent lowest group angular and total flux in a slab with a delta function source on one boundary (in a 7-group J7 approximation with 2 space, 3 angle and 56 time points), including the time required for obtaining the stationary flux as well as the time-dependent flux due to a Gaussian pulse source. The calculation of the stationary angular, total and leakage flux in a slab takes 1 to 2 min. in a 7-group J7 approximation with 11 space and angle points.

JN-METD2: 1.5 min to obtain for 7 energy groups and J5, the total and angular flux of lowest group neutrons at three angle and six space points in a three region slab with stationary boundary source.

JN-METD1: Typical running time on the IBM-360/65 is nearly 4 minutes to obtain the time-dependent lowest group angular and total flux in a slab with a delta function source on one boundary (in a 7-group J7 approximation with 2 space, 3 angle and 56 time points), including the time required for obtaining the stationary flux as well as the time-dependent flux due to a Gaussian pulse source. The calculation of the stationary angular, total and leakage flux in a slab takes 1 to 2 min. in a 7-group J7 approximation with 11 space and angle points.

JN-METD2: 1.5 min to obtain for 7 energy groups and J5, the total and angular flux of lowest group neutrons at three angle and six space points in a three region slab with stationary boundary source.

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7. UNUSUAL FEATURES OF THE PROGRAM

The eigenvalues (e.g. discrete neutron decay constants) of the transport equation can be computed without any knowledge of the eigenfunctions (the neutron flux) and only the parts of the eigenfunctions of interest need be calculated (e.g. the total flux in selected energy groups at selected space points).

The eigenvalues (e.g. discrete neutron decay constants) of the transport equation can be computed without any knowledge of the eigenfunctions (the neutron flux) and only the parts of the eigenfunctions of interest need be calculated (e.g. the total flux in selected energy groups at selected space points).

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NEA-1871/01, included references:

- T. Asaoka:JN-METD1, A FORTRAN-IV Programme for Solving Neutron Transport Problems with

Isotropic Scattering in Bare Spheres and Homogeneous Slabs by the JN Method,

EUR 4601e (1971)

- T. Asaoka and E. Caglioti Bonanni:

JN-METD2, A FORTRAN-IV Programme for Solving Neutron Transport Problems with

Isotropic Scattering in Multilayer Slabs by the JN Method," EUR 4839e (1972)

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14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS

The multigroup calculation of time-dependent problems in a slab requires a big computer storage for evaluating the contribution of the continuous spectrum. Since the contribution is dominant only for thin slabs, it is recommended in such cases to use the J5 approximation instead of J7. It saves also execution time of the computation by about 30%.

The multigroup calculation of time-dependent problems in a slab requires a big computer storage for evaluating the contribution of the continuous spectrum. Since the contribution is dominant only for thin slabs, it is recommended in such cases to use the J5 approximation instead of J7. It saves also execution time of the computation by about 30%.

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NEA-1871/01

source programtest-case data

test-case output

documentation

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- C. Static Design Studies
- F. Space - Time Kinetics, Coupled Neutronics - Hydrodynamics - Thermodynamics

Keywords: Bessel functions, Fourier transformation, Laplace equation, decay, flux distribution, multiplication factors, neutron flux, neutron transport theory, scattering, slabs, space dependence, spheres, time dependence, transport theory.