1. Lecture 8: Response functions
F1-F4 review
Specifying dose response functions
Cross-section based
Dose response functions
Getting energy spectra
Mesh-based spatial tallies

2. Particle crossing tally: F1
Syntax:
Description: Tally of current integrated over a surface. Prefixing with ‘*’ changes the units—particles to MeV. Like other tallies, the time dependence is inherited from the source—the code doesn’t care.
MCNP5 Manual Page: 3-78

3. Surface flux tally: F2 Syntax:
Description: Tally of flux averaged over a surface. Prefixing with ‘*’ changes the units—particles/cm2 to MeV/cm2.
MCNP5 Manual Page: 3-78

4. Cell flux tally: F4 Syntax:
Description: Tally of flux averaged over a cell. Prefixing with ‘*’ changes the units—particles/cm2 to MeV/cm2.
MCNP5 Manual Page: 3-78

5. Response function: DE, DF
Syntax:
Description: Used to specify a fixed (non-reaction-based) response function of interpolated (DEi,DFi) pairs.
Either axis can be linear- or log-based.
(A=LIN or LOG…B=LIN or LOG)
MCNP5 Manual Page: 3-97
Example:
F4:n 31
DE4 LIN 0 1 2
DF4 LIN

6. ANSI/ANS Dose Response Functions

7. Multiplier/cross section response: FM
Syntax:
Description: Provides a constant multiplier to be applied to the tally. Since Monte Carlo is normally done on a per-particle basis, this allows you to include a source strength (or units change). Other use is to put in cross-section dependent response functions to make a tally keep up with particular reaction rates.
MCNP5 Manual Page: 3-93

8. Using MCNP-Provided Response Functions
The alternate use of the FM card is to use energy dependent values that MCNP knows to get the reaction rates that you want;
Cross sections for any reaction in any material covered by the libraries (using ENDF MT numbers)
Special “dosimetry” cross sections for special purposes
Syntax:
FM14:x C mat# reaction#
x=particle type
C=multiplier (negative means times atom-density of mat#--in which case C is generally the negative cell volume)
reaction#=any standard ENDF MT # + any of the special reaction values from Table 3.5 of MCNP manual

9. Energy bins: En Syntax: En
Description: Upper bounds of energy bins (MeV) for tally n
MCNP5 Manual Page: 3-90

10. Set up a Tally Mesh (MCNP5)
The first modification that we are going to put in is to set up a MESH TALLY
This is a mesh of rectangles (you can also do a cylindrical mesh) that the answer will be collected on.
This uses the FMESH card, with the following syntax:
FMESHx4:n ORIGIN x0 y0 z0 IMESH x1 IINTS nx
JMESH y1 JINTS ny KMESH z1 KINTS nz
FACTOR source_strength OUT IJ
where:
(x0,y0,z0) is the lower left corner of the mesh
(x1,y1,z1) is the upper right corner of the mesh
nx,ny,nz tell how many divisions there are in the mesh in the 3 dimensions

11. Description of Problem
A hollow (thick) aluminum ball:

12. Tutorial 3 Base Code Tutorial 3, base case
c Cells *
imp:n=1
imp:n=1
imp:n=0
c Surfaces *
1 sph
2 sph
c Data cards *
mode n
sdef pos = erg=10 m
f1:n 1 2
ctme .25
PRINT

13. Variations
Outer surface current in 0.1 MeV energy increments, 0.05 cosine increments
Outer surface flux in 0.1 MeV energy increments
Cell flux (in Al)
Cell flux with ANSI dose response
Dose map

14. Description of Problem
Just using an empty sphere with a source at origin:

15. Tutorial 2 Code Tutorial 2, base case
c Cells *
imp:n=1
imp:n=0
c Surfaces *
1 sph
c Data cards *
mode n
sdef pos = erg=10
f1:n 1
ctme .25
PRINT

16. Variations ERG: U235 fission neutron spectrum
8 cm cube source centered on (0,0,0)
4 cm spherical source around origin
18 cm (r=1 cm) x-axis cylinder source centered on origin