Basic Output Analysis in Serpent

After running a Serpent simulation, several output files are generated. Each file contains different types of information:

The main results file (*_res.m) contains the most important simulation results. Let's examine its key sections:

Criticality Results

For k-eigenvalue (criticality) calculations, the most important results are:

% Output from pin_cell_res.m
% -- Criticality eigenvalue (k-eff) --
IMP_KEFF = [ 1.34721 0.00095 ];
ANA_KEFF = [ 1.34728 0.00091 ];

These values represent:

• IMP_KEFF: Implicit k-effective (collision estimate)
• ANA_KEFF: Analog k-effective (absorption estimate)
• Format: [ value statistical_uncertainty ]

Neutron Balance

The neutron balance table shows production and loss rates:

% -- Neutron balance --
LOSS_CAPT = 3.25933E-01;  % Capture
LOSS_FISS = 6.74215E-01;  % Fission
LOSS_LEAK = 0.00000E+00;  % Leakage
TOT_LOSS  = 1.00015E+00;  % Total loss

PROD_FISS = 1.00000E+00;  % Fission source
PROD_NXN  = 1.47723E-04;  % (n,xn) reactions
TOT_PROD  = 1.00015E+00;  % Total production

Energy-Integrated Reaction Rates

The results file also contains various reaction rates:

% -- Reaction rates by material --
TOT_FISSRATE = [ 6.74215E-01 0.00083 ];  % Total fission rate
NUBAR = [ 2.43943E+00 0.00000 ];  % Average neutrons per fission

% Material-wise data
MAT_fuel_FISSRATE = [ 6.74215E-01 0.00083 ];  % Fission rate in fuel
MAT_fuel_ABSRATE = [ 1.00015E+00 0.00000 ];   % Absorption rate in fuel
MAT_water_ABSRATE = [ 0.00000E+00 0.00000 ];  % Absorption rate in water

Detector outputs (*_det*.m) contain user-defined tallies specified in the input file. These are powerful tools for detailed analysis.

Energy-Dependent Flux Spectrum

A common detector is the energy-dependent flux spectrum:

% -- Flux spectrum detector --
DET_ENERGY = [ 1.00000E-11 1.00000E-10 ... 1.00000E+2 ];  % Energy bin boundaries
DET_FLUX = [ 
  4.53211E-3 0.012;  % First energy bin (flux + rel. error)
  7.82145E-3 0.009;  % Second energy bin
  ... 
];

Spatial Distribution Detectors

Mesh detectors provide spatial distributions:

% -- Mesh detector (2D) --
DET_MESH_X = [ -0.63 -0.42 -0.21 0.0 0.21 0.42 0.63 ];  % X-mesh boundaries
DET_MESH_Y = [ -0.63 -0.42 -0.21 0.0 0.21 0.42 0.63 ];  % Y-mesh boundaries
DET_MESH_VAL = [  % Values for each mesh element (flux, reaction rate, etc.)
  1.23456E-3 0.012, 2.34567E-3 0.010, ... ;  % First row
  3.45678E-3 0.009, 4.56789E-3 0.008, ... ;  % Second row
  ... 
];

Monte Carlo results always have statistical uncertainties. Understanding and evaluating these errors is crucial:

Relative Statistical Errors

In Serpent output, most results include a relative statistical error:

• Format: [ value rel_error ]
• For example: [ 1.34721 0.00095 ] means k-eff = 1.34721 ± 0.00095 (relative)
• The absolute error would be 1.34721 × 0.00095 = 0.00128

Interpreting Error Magnitude

Visualizing Serpent results helps with interpretation and analysis. Serpent generates some visualizations automatically, and you can create additional ones using MATLAB, Python, or other tools.

Geometry Plots

If you used set gcu in your input, Serpent creates geometry plots:

• *_geom1.png: XY cross-section
• *_geom2.png: XZ cross-section
• *_geom3.png: YZ cross-section

MATLAB/Octave Visualization

Since output files are already in MATLAB format, it's straightforward to create plots:

% MATLAB/Octave script to plot flux spectrum
% Run this after loading the _det0.m file
figure;
semilogx(DET_ENERGY(1:end-1), DET_FLUX(:,1), 'b-', 'LineWidth', 2);
xlabel('Energy (MeV)');
ylabel('Flux per unit lethargy');
title('Neutron Flux Spectrum');
grid on;

Python Visualization

For Python users, you'll need to parse the output files first:

# Python script to plot flux spectrum
import numpy as np
import matplotlib.pyplot as plt
import re

# Function to extract values from Serpent output
def extract_serpent_array(filename, array_name):
    with open(filename, 'r') as f:
        text = f.read()
    pattern = array_name + r's*=s*[(.*?)];'
    match = re.search(pattern, text, re.DOTALL)
    if match:
        data_str = match.group(1)
        # Convert to numpy array
        data = np.array([float(x) for x in data_str.split() if x.strip()])
        return data
    return None

# Extract energy bins and flux
energy = extract_serpent_array('pin_cell_det0.m', 'DET_ENERGY')
flux_data = extract_serpent_array('pin_cell_det0.m', 'DET_FLUX')
flux = flux_data[::2]  # Values are at even indices
error = flux_data[1::2]  # Errors are at odd indices

# Plot
plt.figure(figsize=(10, 6))
plt.semilogx(energy[:-1], flux, 'b-', linewidth=2)
plt.xlabel('Energy (MeV)')
plt.ylabel('Flux per unit lethargy')
plt.title('Neutron Flux Spectrum')
plt.grid(True)
plt.show()

Evaluating whether your simulation has properly converged is critical for reliable results.

Shannon Entropy

Serpent tracks the Shannon entropy of the fission source distribution, which is a measure of source convergence:

% Shannon entropy data from _res.m file
SRC_ENT = [
  4.59813E+00;  % First inactive cycle
  4.61247E+00;  % Second inactive cycle
  ...
  4.63576E+00;  % Final active cycle
];

A properly converged simulation should show a stable plateau in the Shannon entropy.

k-effective Convergence

You can examine k-effective values over cycles:

% k-effective by cycle
ANA_KEFF_CYCLE = [
  1.32145 0;  % First inactive cycle (zero error)
  1.34023 0;  % Second inactive cycle
  ...
  1.34683 0.00435;  % First active cycle (with error)
  1.34795 0.00312;  % Second active cycle
  ...
];

Example 1: Criticality Assessment

For a reactor physics calculation, you might analyze:

• k-effective: Is the system critical (k ≈ 1.0)?
• Neutron spectrum: What's the thermal/fast neutron ratio?
• Fission distribution: Is power evenly distributed?
• Material temperatures: Are there any significant feedback effects?

Example 2: Parameter Study

For studying the effect of a parameter (e.g., fuel enrichment):

1. Run multiple simulations with different enrichment values
2. Extract k-effective from each run
3. Plot k-effective vs. enrichment
4. Determine the enrichment needed for criticality

% MATLAB example for parameter study
enrichment = [2.0, 3.0, 4.0, 5.0];  % Enrichment values
keff = [0.942, 1.023, 1.099, 1.168];  % k-effective results
errors = [0.0009, 0.0008, 0.0008, 0.0007];  % Statistical errors

figure;
errorbar(enrichment, keff, errors, 'o-', 'LineWidth', 2);
xlabel('Enrichment (%)');
ylabel('k-effective');
title('Effect of Fuel Enrichment on Criticality');
grid on;

% Find enrichment for k=1.0 using linear interpolation
crit_enrich = interp1(keff, enrichment, 1.0);
fprintf('Estimated critical enrichment: %.2f%%
', crit_enrich);

Handling Large Output Files

For complex models with many detectors or mesh tallies, output files can become very large. Tips for handling these:

• Use specific detectors rather than excessively fine meshes
• Consider processing output files in chunks
• For large mesh data, save visualizations rather than raw data

Dealing with Poor Statistics

If your results have high statistical errors:

• Run more particles (increase set pop first parameter)
• Run more active cycles (increase set pop second parameter)
• Consider variance reduction techniques for difficult problems
• Use spatial averaging if appropriate

Comparing with Experiments or Other Codes

When validating against experiments or benchmarking against other codes:

• Always include statistical uncertainties in comparisons
• Consider systematic uncertainties (nuclear data, modeling approximations)
• Look for consistent biases that might indicate modeling issues
• Document all assumptions and differences in models