Alpha eigenvalue calculations with Tripoli-4®

Computing adjoint-weighted kinetics parameters in Tripoli-4® by the Iterated Fission Probability method

“…where L is the net disappearance operator and k eff is the effective multiplication factor, can be similarly estimated by computing the neutron flight time from birth to disappearance by absorption or spatial leakage (Spriggs et al, 1997;Zoia et al, 2014a). Extending the capabilities of Monte Carlo codes to adjoint-weighted kinetics parameters demands the adjoint flux u y , which in principle requires the simulation of particles flowing backward from death to birth: in continuous-energy transport codes, this turns out to be a daunting task that is still a subject of active research (Hoogenboom, 2003).…”

Computation of fundamental time-eigenvalue of the neutron transport equation

“…The basic strategy is to seek then the value a for which k ¼ 1 (Zoia et al, 2014). So, the a-eigenvalue can be found by the iterative scheme as follows (Du and Zhang, 1988):…”

“…(7) is known to be numerically unstable and leads to anomalous termination. To overcome this limitation, in Ye et al (2007) and Zoia et al (2014) an improved algorithm which has been shown to be numerically stable, has been provided. It has been suggested to rewrite Eq.…”

“…In particular, it has been shown that under mild assumptions a dominant discrete eigenvalue a exists, which is real, larger than the real parts of all the other a, and whose associated eigenfunction is non-negative (Larsen and Zweifel, 1974;Zoia et al, 2014). Usually, the dominant discrete eigenvalue is called the fundamental eigenvalue.…”

“…The standard power iteration method cannot be used to compute the a-eigenvalue because the magnitude of fundamental a-eigenvalue is not the largest (Modak and Gupta, 2007). To find the fundamental a-eigenvalue, a a À k power iteration method has been developed in some recent papers, and adopted by many neutron transport codes (Briesmeiser, 2000;Ye et al, 2007;Zoia et al, 2014;Zoia et al, 2015). Although the power iteration method dominates the field of eigenvalue computation, other methods have emerged, for instance, implicitly restarted Arnoldi method (IRAM) (Lathouwers, 2003;K oph azi and Lathouwers, 2012) and nonlinear solution method (Fichtl and Warsa, 2013).…”