Stability and bifurcation analysis of Generation IV reactors via point reactor models with temperature reactivity feedback

Doron Sivan, Ehud Meron, Shai Kinast

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


While the stability of present-day reactors is well studied, stability analysis of Generation IV reactors is in its very beginning. In this paper, the stability of point nuclear reactor models with temperature reactivity feedbacks is analyzed. The examined models are referred to as G-L reactor models, which are point reactor models with G delayed neutron-emission groups, L temperature lumps (regions) and a linear reactivity feedback for each temperature. G-L reactor models are applicable for modeling four out of the six Generation IV reactor types (Gas Fast Reactor, Lead Fast Reactor, Sodium Fast Reactor and Very High Temperature Reactor). New analytical stability and bifurcation results of general G-L reactor models and of the G1-L2 reactor model are derived. These analytical results add a different perspective to the previous studies of Generation IV reactors, most of which are based only on numerical analysis. In particular, the codimension-1 bifurcations of general G-L reactor models are characterized, and a classification of the linear stability region in the G1-L2 model is derived. Then, stability and bifurcation analysis of a G1-L2 model of a Generation IV HTR-type microreactor is performed, using both analytical methods and the numerical continuation method. The nominal design point of this microreactor is shown to be globally asymptotically stable, while in other regions of the parameter space, a bistability of the operating steady state and a limit cycle, or of two limit cycles, is demonstrated.

Original languageEnglish
Article number104674
JournalProgress in Nuclear Energy
StatePublished - 1 Jun 2023


  • Bifurcation analysis
  • Generation IV reactors
  • Microreactor
  • Nuclear reactor stability analysis
  • Point reactor model
  • Temperature reactivity feedback

ASJC Scopus subject areas

  • Nuclear Energy and Engineering
  • Safety, Risk, Reliability and Quality
  • Energy Engineering and Power Technology
  • Waste Management and Disposal


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