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Neutron and photon transport

Publié le 29 novembre 2018

When simulating a particle history, Tripoli-4® begins by sampling a source particle form the corresponding distribution. Then, the particle is tracked as customary by performing a series of free flights followed by collisions with the surrounding nuclei. Non-analog transport is adopted, which means the particle weight is progressively updated during the simulation according to standard variance-reduction techniques, such as implicit capture, Russian roulette, or particle splitting. The particle history terminates when some stopping condition is met:

  1. the particle energy is lower than the user-defined energy cut-off ;
  2. the particle position lies outside the geometry (i.e., a geometrical leakage is met) ;
  3. the particle weight is lower than the default (or user-defined) Russian roulette threshold.

Assuming that free flights are performed in analog simulation, i.e., without applying any biasing technique, the displacement operator kernel used to sample the track-length from the last collision is exponential, with parameter Σt(r,E) being the macroscopic total cross-section at position r and energy E.

If the flight ends within the geometry, the collided nuclide is sampled according to its microscopic cross-section at the incident energy E, times its concentration in the current medium. Then, implicit capture is applied which means that an interaction type is sampled according to its microscopic cross-section, among all possible scattering interactions available at energy E for the collided nuclide. As absorptions are not sampled, the particle weight is multiplied by the probability that the particle has survived the collision.

Finally, energy and direction of the particle emerging from the collision are computed, from kinematics laws and/or nuclear data available for the chosen interaction and nuclide.

Some research works [1] have pointed out some relevant shortcomings of the so called 'Sampling of the Velocity of the Target nucleus' (SVT) algorithm, which is currently used in most Monte Carlo codes for the Doppler broadening of the elastic scattering kernel [2]. A correct treatment of elastic scattering kernels in heavy nuclei close to cross-section resonances (typically in the epithermal region) may have a substantial impact on the calculation of reactor physics parameters. To overcome the limitations of SVT, the Doppler Broadening Rejection Correction (DBRC [3]) and the Weight Correction Method (WCM [4]) have been implemented in Tripoli-4® [5].

For reactions with multiple outgoing neutrons, only one neutron is simulated, the multiplicity of the reaction being taken into account in the outgoing-neutron weight.

When running in criticality or fixed-source sub-critical mode, fission is also sampled at each collision. When the collided nuclide is fissile, both prompt neutrons and delayed neutrons are sampled by using the average energy-dependent prompt and delayed yields and spectra read in the nuclear data evaluation. The user can specify whether both prompt and delayed neutrons are to be simulated, or just prompt neutrons.

In coupled neutron-photon transport simulations, photonuclear reactions can be taken into account: in this case, photonuclear reactions are also forced at each photon collision (similarly as done for neutron fission) and the associated weight is changed accordingly [6].

Tripoli-4® allows full simulation results to be recorded in ROOT track files, by closely following a methodology initially proposed for high-energy particle physics [7]. These track files store all events undergone by the particles during the simulation (boundary crossing, collisions, and so on). At each event, the track structure associates information such as the weight of the particle, its position, the identifier of the collided nucleus, and so on. Such track files can be then analyzed by the user by resorting to the T4RootTools. These tools allow particle histories to be visualized, standard tallies to be computed based on tracks, and user-defined tallies to be also calculated. Moreover, a plug-in for the ROOT TTree structure is provided as well, which is well suited for massive data mining.


[1] W. Rothenstein, R. Dagan, Ann. Nucl. Energy 22, 723-730 (1995).

[2] R.R. Coveyou, R.R. Bate, R.K. Osborn, J. Nucl. Eng. 2, 153-167 (1956).

[3] B. Becker, R., Dagan, G. Lohnert, Ann. Nucl. Eng. 36, 470-474 (2009).

[4] T. Mori, Y. Nagaya, J. Nucl. Sci. Tech. 46, 793-798 (2009).

[5] A. Zoia, E. Brun, C. Jouanne, F. Malvagi, Ann. Nucl. Energy 54, 218-226 (2012).

[6] O. Petit, N. Huot, C. Jouanne, Nucl. Sci. Technol. 2, 798-802 (2011).

[7] R. Brun, F. Rademakers, Nucl. Instrum. Methods A 389, 81-86 (1997).