1. Monte Carlo methods in ADS experiments Study for state exam 2008 Mitja Majerle “Phasotron” and “Energy Plus Transmutation” setups (schematic drawings)

2. What are Accelerator Driven Systems ?

3. Accelerator Driven Systems Subcritical reactor Subcritical reactor Wider choice for reactor fuel ( 238 U, 232 Th) Wider choice for reactor fuel ( 238 U, 232 Th) Transmutation of nuclear waste Transmutation of nuclear waste Increased safety Increased safety Accelerator Accelerator Protons or light ions of energy around 1 GeV Protons or light ions of energy around 1 GeV Very high powers (hundreds of MW) Very high powers (hundreds of MW) Stable beam Stable beam Spallation reaction Spallation reaction

4. Spallation (process in which hadrons or light ions are ejected from the nucleus due to impact of relativistic particle) In textbooks divided to two phases: In textbooks divided to two phases: Intra Nuclear Cascade Intra Nuclear Cascade De-excitation (evaporation, fission) De-excitation (evaporation, fission) INC phase has to be corrected at lower energies to fit the experiments – preequilibrium phase INC phase has to be corrected at lower energies to fit the experiments – preequilibrium phase

5. Calculations Monte Carlo method: Monte Carlo method: Event by event simulation on nuclear scale Event by event simulation on nuclear scale Accuracy  sqrt(N)  sqrt(calculation time), Accuracy  sqrt(N)  sqrt(calculation time), Parallelization is possible (MPI, PBS) Parallelization is possible (MPI, PBS) Used codes: MCNPX, FLUKA Used codes: MCNPX, FLUKA Resources: Resources: CESNET Meta Centrum CESNET Meta Centrum 56 processors on OJS (MPI and PBS) 56 processors on OJS (MPI and PBS)

6. How MC code works Pseudorandom numbers -  Pseudorandom numbers -  Example - photon source in matter: Example - photon source in matter: Determine track (  for direction) Determine track (  for direction) Determine where the reaction will happen - l=1/  ln(  Determine where the reaction will happen - l=1/  ln(  Determine which interaction will happen (photoeffect, Compton, pair production …) -  Determine which interaction will happen (photoeffect, Compton, pair production …) -  Determine angles – , energies of generated particles (physics) Determine angles – , energies of generated particles (physics) Loop until particles escape from the phase space of interest Loop until particles escape from the phase space of interest Tallying: Tallying: Count the particles that passed through selected phase space (surfaces, volumes, deposited energy …) Count the particles that passed through selected phase space (surfaces, volumes, deposited energy …) Precision and accuracy: Precision and accuracy: Wrong physics => wrong results Wrong physics => wrong results Central limit theorem – for large N, Central limit theorem – for large N, results distribution approach normal distribution

7. Phasotron experiment Simple, lead target (diameter 10 cm, length 0.5 m) Simple, lead target (diameter 10 cm, length 0.5 m) Intensive protons 660 MeV, 10 min Intensive protons 660 MeV, 10 min Activation detectors, iodine samples ( 129 I) Activation detectors, iodine samples ( 129 I)

8. Simulated neutron spectrum

9. NAA experimental data

10. Exp/sim comparisons MCNPX - INCL4/ABLA MCNPX – CEM03 FLUKA

11. Proton influence Proton fluence in the target central plane – around 30 th cm protons are scattered out of the target Contribution of proton reactions to total reaction rate

12. Iodine samples Sample 1 – 9 th cmSample 2 – 21 st cm

13. Systematic uncertainties Simulations with changed parameters are compared Simulations with changed parameters are compared Beam parameters (3 mm ~ 15% uncertainty) Beam parameters (3 mm ~ 15% uncertainty) Detector displacement (1 mm ~ <5%) Detector displacement (1 mm ~ <5%) Worse situation: Worse situation: Around 30 th cm, protons exit the target, beam parameters have bigger influence Around 30 th cm, protons exit the target, beam parameters have bigger influence Iodine samples – not precise placement Iodine samples – not precise placement

14. Energy Plus Transmutation

15. SABRINA plot from MCNPX input file, provided by J. Šolc.

16. MC analysis Influence of setup parts Influence of setup parts polyethylene box polyethylene box iron and detectors have negligible influence iron and detectors have negligible influence Systematic uncertainties – displacements: Systematic uncertainties – displacements: incident beam : 3mm = 15-20% uncertainty incident beam : 3mm = 15-20% uncertainty detectors displacement: 5mm = 20% detectors displacement: 5mm = 20% The calculations apply only to threshold activation detectors. The calculations apply only to threshold activation detectors.

17. Polyethylene box – biological shielding Neutron spectra inside box Neutron spectra emitted to environment

18. Neutron production, k eff At 1.5 GeV experiment, 50 neutrons were produced per proton At 1.5 GeV experiment, 50 neutrons were produced per proton Maximum production (proton -1 GeV -1 ) in 1- 1.5 GeV range Maximum production (proton -1 GeV -1 ) in 1- 1.5 GeV range k eff =0.202 k eff =0.202 flooded with water k eff rises to 0.41 (and heavy water 0.26) flooded with water k eff rises to 0.41 (and heavy water 0.26) Total neutron production with the EPT setup.

19. MC vs. experiment Good agreement below 1.25 AGeV Good agreement below 1.25 AGeV Wrong predictions at 1.5 and 2 GeV Wrong predictions at 1.5 and 2 GeV Similar behavior reported for thin target experiments – could there be any connection ? Similar behavior reported for thin target experiments – could there be any connection ? FLUKA calculations of reaction rates in Au detectors placed in the first gap

20. Conclusion Phasotron experiment Phasotron experiment Completely analyzed Completely analyzed Good agreement with MC codes Good agreement with MC codes Uncertainties ca. 15% Uncertainties ca. 15% EPT EPT All performed experiments (4x protons, 2x deuterons) were simulated All performed experiments (4x protons, 2x deuterons) were simulated Significant disagreement with MC codes at higher energies Significant disagreement with MC codes at higher energies Uncertainties 30% Uncertainties 30% Outlooks Outlooks MC in spectrometry – revision of spectrometry methods used at our work (precision of different corrections: geometrical, COI …) MC in spectrometry – revision of spectrometry methods used at our work (precision of different corrections: geometrical, COI …) Is EPT disagreement connected with thin target experiments ? Is EPT disagreement connected with thin target experiments ? Acknowledgments to META Centrum, where most of presented calculations were performed.