# Flattop k-eff sensitivity example

This example demonstrates some basic sensitivity calculation capabilities for the Popsy (Flattop) critical experiment (PU-MET-FAST-006 in the ICSBEP handbook).

## Description

The experimental configuration consists of a plutonium alloy sphere (radius 4.5332 cm) reflected by a natural uranium blanket (outer radius 24.1420 cm). The multiplication factor of the system is close to unity (being a critical experiment). This input calculates the sensitivity of the multiplication factor to perturbations applied to the cross sections of ^{235}U, ^{238}U, ^{239}Pu and ^{240}Pu. A processing script for MATLAB/OCTAVE is provided for printing and plotting out the sensitivities.

## Input

**Input for Popsy (Flattop) sensitivity calculation example:**

% --- Core outer surface and blanket outer surface surf s1 sph 0.0 0.0 0.0 4.5332 surf s2 sph 0.0 0.0 0.0 24.1420 % --- Divide space to core, blanket and outside cell c1 0 core -s1 cell c3 0 blanket s1 -s2 cell c4 0 outside s2 % --- Core is made from plutonium alloy mat core sum 94239.03c 3.6697e-2 94240.03c 1.8700e-3 94241.03c 1.1639e-4 31000.03c 1.4755e-3 % --- Blanket is made from natural uranium mat blanket sum 92234.03c 2.6438e-6 92235.03c 3.4610e-4 92238.03c 4.7721e-2 % --- Cross section libraries %set acelib "<path-to-acelib>" % --- Neutron population set pop 10000 100000 50 1 100 100 % --- Write output each 100 cycles set outp 100 % --- Modify event buffer size to 3 events per neutron set nbuf 3 3 % --- Use unresolved resonance sampling for the fast system set ures 1 2 % --- Define Vitamin-J energy grid (one of the defaults) ene myvit-j 4 nj23 % %%% % %%% --- Sensitivity options % %%% % --- Run sensitivity calculation using Vitamin-J energy grid sens opt egrid myvit-j % --- Use 15 latent generations for the sensitivity calculations sens opt latgen 15 % --- Use 10 generations for Iterated Fission Probability set ifp 10 % %%% % %%% --- Sensitivity responses % %%% % --- Calculate sensitivity of k-effective to perturbations sens resp keff % %%% % %%% --- Sensitivity perturbations % %%% % --- Separate perturbations for the different nuclides and total sens pert zailist 922350 922380 942390 942400 total % --- Do not calculate material-wise perturbations (only total) sens pert matlist total % --- Perturb cross sections separately for each MT number sens pert xs all % --- Score sensitivity results directly to a matrix for each particle % Assume 0.2 matrices needed per generation per particle sens opt direct 0.2

## Output

The contents of some long arrays have been replaced with "...".

**Output for Popsy (Flattop) sensitivity calculation example:**

% Number of different bins in sensitivity calculation: SENS_N_MAT = 1; SENS_N_ZAI = 5; SENS_N_PERT = 7; SENS_N_ENE = 175; % Materials included in sensitivity calculation: SENS_MAT_LIST = [ 'total ' ]; % Indices for different materials: iSENS_MAT_TOT = 1; % Nuclides included in sensitivity calculation: SENS_ZAI_LIST = [ 0 % total 922350 922380 942390 942400 ]; % Indices for different ZAIs: iSENS_ZAI_TOT = 1; iSENS_ZAI_922350 = 2; iSENS_ZAI_922380 = 3; iSENS_ZAI_942390 = 4; iSENS_ZAI_942400 = 5; % Reactions included in sensitivity calculation: SENS_PERT_LIST = [ 'total xs ' 'ela scatt xs ' 'sab scatt xs ' 'inl scatt xs ' 'capture xs ' 'fission xs ' 'nxn xs ' ]; % Indices for different perturbations: iSENS_PERT_TOT_XS = 1; iSENS_PERT_ELA_XS = 2; iSENS_PERT_SAB_XS = 3; iSENS_PERT_INL_XS = 4; iSENS_PERT_CAPT_XS = 5; iSENS_PERT_FISS_XS = 6; iSENS_PERT_NXN_XS = 7; % Sensitivity calculation energy group boundaries: SENS_E = [ ... ]; % Sensitivity calculation energy group lethargy widths: SENS_LETHARGY_WIDTHS = [ ... ]; % Sensitivities with 15 latent generations: % Effective multiplication factor: ADJ_PERT_KEFF_SENS = [ ... ]; ADJ_PERT_KEFF_SENS = reshape(ADJ_PERT_KEFF_SENS, [2, SENS_N_ENE, SENS_N_PERT, SENS_N_ZAI, SENS_N_MAT]); ADJ_PERT_KEFF_SENS = permute(ADJ_PERT_KEFF_SENS, [5, 4, 3, 2, 1]); ADJ_PERT_KEFF_SENS_E_INT = [ ... ]; ADJ_PERT_KEFF_SENS_E_INT = reshape(ADJ_PERT_KEFF_SENS_E_INT, [2, SENS_N_PERT, SENS_N_ZAI, SENS_N_MAT]); ADJ_PERT_KEFF_SENS_E_INT = permute(ADJ_PERT_KEFF_SENS_E_INT, [4, 3, 2, 1]);