Application of ADVANTG Variance Reduction Parameters for MCNP6 at ESS

1. Application of ADVANTG Variance Reduction Parameters for MCNP6 at ESS ICANS XXIII, Chattanooga, Tennessee, USA Thomas M. Miller, Douglas Di Julio, & Valentina Santoro Spallation Physics Group, Target Division www.europeanspallationsource.se October 17, 2019

2. Outline • Brief introduction to ADVANTG • CADIS • FW-CADIS • How we deal with the some of the limitations of ADVANTG • Example applications • Accelerator • Target • Neutron beamline

3. ADVANTG [1] • What does ADVANTG do? • It generates variance reduction parameters for you, in an automated fashion • This includes weight windows and consistent biased source distributions • How does it work, in words… • ADVANTG will discretize your MCNP5 input creating a Denovo input • Denovo will run an adjoint transport simulation of your problem calculating energy and spatial dependent adjoint fluxes and estimate the MCNP tally response(s) • ADVANTG will use the Denovo adjoint fluxes and estimates of the tally response(s) to generate weight windows and a consistent biased source

4. CADIS • CADIS - Consistent Adjoint Driven Importance Sampling, creates an importance map and source biasing that work together • Intended for a source / detector problem. Multiple sources is fine, but not ideal for multiple detectors • Depends on the problem geometry, materials, and tally definition • Does NOT depend on the Monte Carlo (forward) source • Key idea when using ADVANTG • One only needs an approximate (coarse) adjoint solution to provide significantly improved tally convergence • If one has an exact adjoint solution, the Monte Carlo simulation is not needed • How does CADIS work, a little math…

5. CADIS [2,3] • Define the adjoint source • Solve for the adjoint flux • Estimate the response • Construct weight windows and biased source

6. FW-CADIS • Forward Weighted CADIS provides a method to generate variance reduction parameters for multiple tallies • Like CADIS, depends on the problem geometry, materials, and tally definition, but also depends on the Monte Carlo (forward) source • CADIS with multiple tallies (detectors) will usually produce uneven statistical uncertainties for the different tallies • FW-CADIS intends to produce tallies with similar statistical uncertainties. • How does FW-CADIS work • Words… Runs a forward Denovo to estimate the tally responses and weights the adjoint sources by these estimates of the responses. Then the same as CADIS • Still simple math…

7. FW-CADIS [4] • CADIS quantifies importance as expected contribution to • Multiple tallies without FW (regular CADIS) • This optimizes the total response • Contributions to the largest magnitude response(s) have high importance • Low-magnitude responses will tend to be neglected • Multiple tallies with FW • This optimizes all responses simultaneously • Contributions to high and low-magnitude responses have equal importance

8. Dealing with ADVANTG Limitations • ADVANTG version 3 was developed for MCNP5 • Limited to table based cross section, usually 20 MeV or less • Limited to a single neutron or photon source • Does not understand input parameters new to MCNP6/X • New MCNP6/X Input Parameters • ADVANTG reads the MCNP5 runtpe file to pass all necessary information from MCNP to Denovo • Simplest solution guaranteed to work • Make a copy of your MCNP6/X input and comment out / delete any non-MCNP5 input data • Copy new input data generated by ADVANTG from output/inp_edits.txt to your original MCNP6/X input file • Elegant solution, but not guaranteed to work • Use the ADVANTG input mcnp_input_template, however, this sometimes fails to work

9. Dealing with ADVANTG Limitations • Table based cross sections, usually ≤ 20 MeV • This applies to MCNP5, but also Denovo • MCNP6/X alleviate this restriction for MCNP • For Denovo the HILO2k library [5] is now included with ADVANTG 3.0.3 (but not documented) • Pros • Neutron cross sections up to 2 GeV • Legendre coefficients up to P9 • Cons • Cross sections for only 32 elements / isotopes • Data below 20 MeV based on ENDF/B-V • Photon cross sections up to 20 MeV • Short term need – collapse HILO2k from 105 groups to 20 – 30 groups • Long term need – Develop a new cross section library

10. Dealing with ADVANTG Limitations • Neutron OR photon source • 6/X can have sources with more than one particle species • Run ADVANTG for neutron and photon source separately • What about particles other than neutrons or photons, like protons • Run an MCNP6/X simulation with your source and a mesh tally of neutrons and/or photons • Convert the mesh tally to an SDEF (collapse each cell in mesh tally to a point source) • For some applications at ESS, we ignore the photons created by protons and focus on the neutrons and their secondary photons • Shielding or activation outside the monolith and along neutron beamlines • This simplification usually cannot be applied along the ESS proton beamline

11. Dealing with ADVANTG Limitations • Normalization of WW • ADVANTG will normalize the WW based on the neutron or photon source and the estimated response • This normalization likely not appropriate for other particle species • Not a problem when other particles are nearly monoenergetic and have most particle producing reactions in a “small” volume (protons in ESS target) • Normalize WW such that average mid-point of WW in “small” volume and group for monoenergetic source is 1.0 • Have not attempted this along ESS proton beamline, e.g., 1 W/m beam loss source

12. Dealing with ADVANTG Limitations • Narrow steaming paths • Monte Carlo codes have difficulty sampling narrow steaming gaps • Deterministic codes have difficulty resolving narrow streaming gaps (in spatial and angular dimensions) • To resolve forward peaked scattering of high energy particles, need high order Legendre polynomial representation of scattering cross sections • To resolve narrow streaming gaps spatially, very small mesh cells are needed • To resolve small scattering angles down a gap, a large number of quadrature angles are needed • These needs to resolve spatial and angular dimensions run counter to the philosophy of an approximate adjoint solution – a delicate balance is need • Consider ADVANTG input mcnp_ww_collapse_factor to include finer resolution in the Denovo simulation, but reduce the size of the WW input file

13. Dealing with ADVANTG Limitations • Narrow steaming paths cont… • Little can be done regarding the resolution of the scattering cross sections and spatial mesh in Denovo • However, specialized quadrature sets can be used to help with the angular resolution in Denovo • The user must provide these themselves via ADVANTG inputs denovo_quadratureuserdefined and denovo_quad_file • A useful type of quadrature is the Gauss-Lobatto quadrature [6] set that has angles along the axis of the unit sphere

14. Application to Proton Accelerator

15. Proton Beamline Example • Analyze dose rate behind a temporary shielding wall in the accelerator tunnel during commissioning (”Occupancy area”) • The proton beam stop is a Faraday cup surrounded by shielding • Proton energies of 40 and 74 MeV were considered

16. Proton Beamline Example • CADIS was used for this analysis because… • This avoided the need to generate a neutron and photon source for Denovo • The required tally was total dose on the back of the temporary shield wall (a mesh tally) • The response function was the same for all tallies (each cell of the mesh tally) • The spatial variation of the total dose on the back of the shield wall was not very large (not orders of magnitude)

17. Proton Beamline Example • Mesh dose for 74 MeV protons (µSv/hr/µA) • Relative error

18. Application to Target Monolith

19. Target Monolith Example • Calculate the neutron dose rate everywhere in the connection cell • Dose in a number of materials, including Si, and biological dose • Use a proton source in the MCNP6 simulations, so generate a neutron source for ADVANTG / Denovo • Energy and spatial dependent flux mesh tally, convert to a series of energy dependent point sources

20. Target Monolith Example • FW-CADIS was used for this analysis because… • It was not difficult to generate a neutron source for Denovo • Dose rates in several different materials were needed over a large mesh tally • These materials were not actually in the model, rather the KERMA approximation was used (F4 tally with FM card, similar to an F6 tally) • Regarding the neutron source generated for Denovo • See section 9.1 of the ADVANTG 3.0.3 manual, there are some limitations when building a source whose energy and spatial dependence is not completely separable

21. Target Monolith Example • Mesh dose (µSv/hr) • Relative error

22. Target Monolith Example • Default FW-CADIS behavior is to converge the total response, so only energy ranges that contribute the most the response will be well converged • To converge all energy ranges use input fwcadis_response_weighting false

23. Application to Neutron Beamline

24. Neutron Beamline Example • Calculate neutron dose rate along the NMX neutron beamline inside the bunker and just outside the bunker • This beamline is curving in the bunker and the outer bunker shielding • The source is the energy and angular dependent current of neutrons entering the beamline

25. Neutron Beamline Example • FW-CADIS was used for this analysis because… • A neutron source readily available • Dose rate over a large mesh tally was needed, and there are significant amounts of shielding along portions of this tally • A Gauss-Lobatto quadrature was used with an angle on the polar axis, which was pointed down / parallel to the axis of the beamline • Without this specialized quadrature, the ADVANTG WWs induced a large amount of over splitting, causing the MCNP simulation to be inefficient

26. Neutron Beamline Example • Adjoint solution / importance with Gauss-Lobatto quadrature

27. Neutron Beamline Example • 150 MeV WWs

28. Neutron Beamline Example • Mesh dose (µSv/hr) • Relative error

29. Neutron Beamline Example • Results without ADVANTG WWs • 1e9 histories, 93.7 min, 192 cores • Dose entering bunker wall • 887 µSv/hr ± 14% • Figure-of-merit: 0.545 • Dose exiting bunker wall • No non-zero results • Results with ADVANTG WWs • 1e9 hist., 171.1 min (includes ADVANTG), 192 cores • Dose entering bunker wall • 958 µSv/hr ± 0.7% • Figure-of-merit: 119 • Speed Up: 218 • Dose exiting bunker wall • 2.8 µSv/hr ± 8.3% • Figure-of-merit: 0.848 • Speed Up: ? (infinite)

30. References • ADVANTG 3.0.3 • [1] ORNL/TM-2013/416 Rev. 1, 2015 • CADIS • [2] Nuclear Science & Engineering, 128, 186-208, 1998 • [3] Progress of Nuclear Energy, 42(1), 2003 • FW-CADIS • [4] Nuclear Science and Engineering, 176, 37-57, 2014 • HILO2k cross sections • [5] Lillie & Gallmeier, “HILO2k: A New HILO Library to 2 GeV,” informal paper, available from RSICC as DLC-220, 2003 • Gauss-Lobatto quadrature • [6] Abramowitz & Stegun, Handbook of Mathematical Functions, Chapter 25.4.32