Issues with the use of neutron transport codes
Nigel Hawkes
Introduction
Neutron transport codes are very powerful but very complex.
I’ll give a couple of examples where their behaviour has been
found to differ from what you might expect.
Disclaimer:
• I’m not saying that these are the most important issues.
• I’m not warning about or recommending any particular code.
MCNPX Example
1. Pulse Height tally in MCNPX
• Pulse Height tally with neutrons (F8:n) is allowed in MCNPX.
• We know you must keep everything analogue:
– Turn off variance reduction
– Force fully analogue neutron capture
• Yet things can still go wrong
MCNPX: F8 Pulse Height tally
Simple problem:
H2
n
g
•Neutrons at a single energy Ei
produced at the centre of a huge
volume of hydrogen.
•All neutrons are eventually
captured to give a 2.2 MeV
gamma.
•All the gammas are also
absorbed in the hydrogen.
MCNPX: F8 Pulse Height tally
Pulse Height Spectrum (F8:n)
Normalised Counts
1
0.8
0.6
Expected
0.4
0.2
0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
E - E i (multiples of 2.2 MeV)
4.0
4.5
5.0
MCNPX: F8 Pulse Height tally
Pulse Height Spectrum (F8:n)
Normalised Counts
1
0.8
0.6
Expected
MCNPX
0.4
0.2
0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
E - E i (multiples of 2.2 MeV)
4.0
4.5
5.0
MCNPX: F8 Pulse Height tally
What went wrong?
• Gamma production not correlated with fate of neutron.
• A fundamental property of the libraries – can’t easily be
changed.
• Also happens with some other reactions ((n, n'), (n, 2n), (p,
n), …).
• Some reactions OK ((gamma, n), (gamma, p), …).
Moral: be careful with F8.
MCNP Example
2. MCNP near critical
• Neutron detector near a sub-critical assembly + external
source.
• Want to know how the count rate varies with k-eff (ratio of
neutrons produced in one generation to those used up in the
previous generation).
• Repeatedly increase the k-eff a bit (by changing a control
rod) and calculate the final equilibrium count rate each time.
• On the real system, measure the count rate and read off the
k-eff.
MCNP: Near critical
Equilibrium Count Rate vs k-eff
0.25
count rate
0.20
0.15
MCNP
0.10
0.05
0.00
0.700
0.750
0.800
0.850
0.900
k-eff
0.950
1.000
1.050
MCNP: Near critical
Equilibrium Count Rate vs k-eff
0.25
count rate
0.20
0.15
Diff'l Equations
MCNP
0.10
0.05
0.00
0.700
0.750
0.800
0.850
0.900
k-eff
0.950
1.000
1.050
MCNP: Near critical
Equilibrium Count Rate vs k-eff
count rate
2
1.5
Diff'l Equations
MCNP
1
0.5
0
0.700
0.750
0.800
0.850
0.900
k-eff
0.950
1.000
1.050
MCNP: Near critical
Count rate vs. Time
1000
Settles
slowly
Count rate
800
600
Settles
quickly
400
200
0
0
50
100
150
Time
200
250
MCNP: Near critical
What went wrong?
• Near critical, the system can take several minutes to settle.
• This is 1010 MCNP time steps.
• Histories were cut off before the true population was built up.
Moral:
• Start some of the neutrons from the fuel, not just from the
external source.
• Watch for warnings.
MCBEND Example
3. Point Estimators in MCBEND
•Neutron sources have internal structure and do not emit
equally in all directions.
•We sometimes want to calculate this anisotropy for a particular
source type.
•We have used MCNP in the past, but recently started using
MCBEND as well.
MCBEND: Point estimators
Geometry:
Axis
•Source is cylindrical with an axis of
symmetry.
θ
Source
•For scoring, set up a thin spherical
shell in the vacuum around the
source.
•Divide the shell into regions and
score the fluence in each region.
•Also set up ‘point estimators’, which
give the fluence at a point directly,
without averaging over a volume.
MCBEND: Point estimators
Source Anisotropy - MCBEND Results
1.2000
Anisotropy
1.0000
0.8000
Volume averages
Point estimators
0.6000
0.4000
0.2000
0.0000
0
30
60
90
120
150
Polar angle (deg.) from non-weld end
180
MCBEND: Point estimators
What went wrong?
• Anisotropies are only a few percent, so we need a large
number of histories (50 million).
• The Point Estimator module is single precision.
• The later histories stopped making any difference to the
accumulating total.
Moral:
• Do a sanity check on the results.
• Calculate more than one way if possible.
• Hope that the double precision version appears soon!
Conclusions
“Trust no-one, Mr. Mulder”
– Well-Manicured Man, The XFiles