Sensitivity calculations

Serpent relies on the collision history based first order GPT equivalent implementation to calculate sensitivities of various responses to various perturbations. As a simple example, the sensitivity of the effective multiplication factor to the different nuclear cross sections can be calculated.

Input

Adding a response

Basic responses

Basic responses can be set up with the syntax

sens resp NAME FLAG

Where the different response names and flags are as follows

NAME	explanation of NAME	FLAG	explanation of FLAG
keff	sensitivity of effective multiplication factor to perturbation	0/1	OFF/ON
beff	sensitivity of effective delayed neutron fraction to perturbation	0/1	OFF/ON
leff	sensitivity of effective prompt generation time to perturbation	0/1	OFF/ON

Omitting (or forgetting) the flag from the definition, will turn the response on by default.

Reaction rate ratios

Sensitivities of reaction rate ratios to perturbations can be set up to be calculated with

set sensresp detratio NAME DET1 DET2

Where the paramters are:

NAME	: the name of the response. Will be used in output.
DET1	: Name of the numerator detector, i.e. the one whose reaction rate is being divided.
DET2	: Name of the denominator detector, i.e. the one whose reaction rate is the dividing value.

The two detectors have to be set up separately in normal Serpent fashion.

Notes:

• Currently, each detector can have only one bin.
• Currently, only the indirect effect of the perturbation is calculated and the direct effect must be calculated separately and added to the result.

Adding a perturbation

set senspert NAME FLAG

Where the different perturbation names and flags are as follows

NAME	explanation of NAME	FLAG	explanation of FLAG
xs	perturbation of basic cross sections	0/1	OFF/ON
chi	perturbation of fission spectrum	0/1	OFF/ON
nubar	perturbation of fission nubar	0/1	OFF/ON
eleg	perturbation of Legendre moments of elastic scattering angular distribution	0/1/2/3/4/5/6/7	Number of Legendre moments to perturb.

Omitting (or forgetting) the flag from the definition will turn the perturbation on by default. The default number of Legendre moments to include is 3.

Choosing nuclides to perturb

The perturbed nuclides can be specified by giving a list of the ZAI-numbers to include

set senspert zailist ZAI1 ZAI2 ... 

for example

set senspert zailist 922350 922380

for perturbations affecting ²³⁵U and ²³⁸U. By giving the control words total and/or sum in the list of ZAI-numbers, the total sensitivity over all ZAIs present in the calculation and the sum sensitivity of the listed ZAIs will be calculated, respectively.

All nuclides present in the calculation can be included with

set senspert zailist all

this will automatically include the calculation of the total sensitivity.

Choosing materials to perturb

The materials, where the perturbations are applied can similarly be specified by giving a list of the material names

set senspert matlist MAT1 MAT2 ...

for example

set senspert matlist fuel coolant

for perturbations affecting interactions in materials fuel and coolant. By giving the control words total and/or sum in the list of material names, the total sensitivity over all materials present in the calculation and the sum sensitivity of the listed materials will be calculated, respectively.

All materials present in the calculation can be included with

set senspert matlist all

this will automatically include the calculation of the total sensitivity.

Additional options

The options for sensitivity calculations can be set using the

set sensopt ...

syntax.

Energy grid for scoring

The energy grid used for scoring the sensitivities can be set using

set sensopt egrid ENAME

where ENAME is a name of an energy grid definition.

Number of latent generations

The number of latent generations used for k-effective sensitivity calculations can be set with

set sensopt latgen NGEN

where NGEN is the number of generations to use. The number of summation generations for reaction rate ratios and bilinear-ratios will be NGEN+1

Event bank size

The default size of the allocated event bank can be too small for some sensitivity calculations resulting in the following error:

Fatal error in function EventFromBank:

Event bank is empty

Simulation aborted.

The event bank size can be set using

set nbuf NBUF EBANK

where NBUF is the neutron buffer size (default is 5) and EBANK is the event bank size (default is 100).