Cristian Bungau ThorEA Meeting - Oxford - April 2010

Physics - the GEANT4 style Usually, Monte Carlo codes (like FLUKA and MCNPX) come with their own physics models and the user is given default selections, so he/she does not have to bother too much with the physics issue. for example in MCNP(X) the Bertini model is used by default for nucleons and pions and the ISABEL model for other particle types; There are many different (data based, parametrized and theory-driven) models using different approximations and each has its own applicable energy range. Therefore each model will describe better some processes and not that good other processes. for example: the pion production is well described by the Bertini model while the neutron spallation by the Binary/Liege models, etc. Due to the vast range of applications, GEANT4 will NOT give the user any default physics models, the user alone has to work out what models to use for what processes. Even the simple transportation process has to be implemented by the user. It is not coming in by default even if obviously without it nothing is simulated, and so it always has to be added in.

Geometry details Y stabilized Zirconia (ZrO 2 +Y 2 O 3 (3 mole pc)) caps Fuel Steel 232 ThO UO 2

And in more detail... vertical view In G4 one must NOT have overlapping volumes...

Code development While MCNPX is able to do reactor criticality calculations, GEANT4 is not. Also, in GEANT4 each particle interacts with pre-defined materials, independently to the other particles created in any given event. to convert existing 232 Th into 233 U “allow” neutrons produced by each proton to “act” on isotopes produced by previous proton events; Useful advice on GEANT4 code development has been received from developers at the GEANT4 collaboration workshop in Italy (INFN);

GEANT4 provides an abstract base class which the user can use to create his/her own filter class: class G4VSDFilter { public: G4VSDFilter(G4Stringname); virtual G4VSDFilter(); public: virtual G4bool Accept(const G4Step*) const = 0; } and it is the Accept() function which will act as the corresponding filter. Code development (2) Using this the user can create his/her own messenger class to define a /score/filter/ command. I have written and added three new classes to GEANT4: G4SDTimeFilter used for implementing for the first time the notion of time evolution of the number of particles; G4SDParticleWithTimeFilter used for simulating the time evolution of the number of neutrons in different neutron generations, and of the number of different isotopes inside the core; G4SDParticleWithVolumeFilter used for simulating the number of neutrons and of different isotopes inside different geometry volumes;

For the homogeneous core it was found that the reactor becomes critical for more than 6% 233 UO 2. The value of 5% 233 UO 2 was selected for the simulations. Submitted paper for publication in the PRST-AB journal; Referee’s comment: the value of 5% 233 UO 2 selected by the authors is a fairly underestimated value for a Th based ADSR; Criticality in GEANT4 Next - Estimate the criticality for more realistic (hexagonal) fuel rods geometries: there are 215 fuel bundles; ~14 tons fuel;

it was found that, in the case of fuel rods geometries, the reactor is sub-critical even for 10% 233 UO 2. Criticality in GEANT4 (2) In the same time, preliminary MCNPX tests showed that the criticality should be for 1% 233 UO 2, for 1.7% 233 UO 2 and 1.02 for 1.8% 233 UO 2. It was not possible to reproduce these results with GEANT4, as all the simulations clearly showed that the reactor was sub-critical even for 10% 233 UO 2.

10% 233 UO 2

The MCNPX predicts the criticality by generating neutrons with energies characteristic to conventional reactors, directly into the simulated fuel geometry; In GEANT4, we are dealing with spallation neutrons produced by the 1 GeV protons. The neutrons energy spectrum is not the one present in conventional reactors, this explaining the sudden drop in the number of neutrons during the first (tens) nanoseconds. Once the “wrong energy” neutrons have escaped the criticality (in its “classical” definition) starts to approach the value of 1. However no matter how one defines the criticality, it can be clearly seen that the number of neutrons is continuously decreasing with time and hence the reactor is (by any standards) sub-critical. Explanation for the differences

GEANT4, the MCNPX style the way MCNPX works out the criticality is by generating directly into the core the neutrons with energies characteristic to neutrons present in conventional reactors; so instead of using spallation neutrons to run the reactor, I implemented the neutrons energy spectrum used by MCNPX into GEANT4, so the same neutrons are now generated by GEANT4 into the reactor core; the criticality can now be simulated by the two codes for the same input parameters;

Criticality results

Concentration of 233 UO 2 Criticality 0.2% % % % % % % %> 1. For a concentration of 233 UO 2 greater than 1.9%, the criticality exceeds the value of 1, and the reactor becomes super-critical. This brings the GEANT4 and MCNPX results into agreement. Criticality results (2)

So why using spallation neutrons will not result in having a critical reactor even for 10% 233 UO 2 ? conventional reactor neutrons spallation neutrons conventional reactor neutrons All histograms are normalized (to 1000) for direct comparison

And the low energy neutrons... All histograms are normalized (to 1000) for direct comparison conventional reactor neutrons spallation neutrons conventional reactor neutrons

Conclusion GEANT4 and MCNPX predict the same reactor criticality values when considering the fuel being inside “conventional” nuclear reactors, i.e. that do not rely upon spallation neutrons to run. Due to the different energy spectra of the spallation neutrons produced by the 1 GeV proton beam, the accelerator driven reactor remains subcritical even at high concentrations of 233 UO 2.