1Lecture 8: Response functionsLecture 8: Response functions

F1-F4 review Specifying dose response functions

• Cross-section based• Dose response functions

Getting energy spectra Mesh-based spatial tallies

2Particle crossing tally: F1Particle 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

1 2 3xx : ( )pl S S SF 1

3Surface flux tally: F2Surface 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

1 2 3xx : ( )pl S S SF 2

4Cell flux tally: F4Cell 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

1 2 3xx : ( )pl C C CF 4

5

Response function: DE, DFResponse 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 31DE4 LIN 0 1 2DF4 LIN 10 20 0

0

5

10

15

20

25

0 0.5 1 1.5 2 2.5

k

k

ppn B p

xxn A x

21

21

DF

DE

6

ANSI/ANS Dose Response FunctionsANSI/ANS Dose Response Functions

7Multiplier/cross section response: FMMultiplier/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

value

# ( # )

n

n C mat reaction s

FM

FM

8

Using MCNP-Provided Response FunctionsUsing 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: EnEnergy 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)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 IJwhere:

(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 ProblemDescription of Problem A hollow (thick) aluminum ball:

12

Tutorial 3 Base CodeTutorial 3 Base CodeTutorial 3, base casec *********************************************************************c *c *c *c *********************************************************************c *c Cells *c *c *********************************************************************1 0 -1 imp:n=12 1 -2.702 1 -2 imp:n=199 0 2 imp:n=0

c *********************************************************************c *c Surfaces *c *c *********************************************************************1 sph 0 0 0 102 sph 0 0 0 15

c *********************************************************************c *c Data cards *c *c *********************************************************************mode nsdef pos = 0. 0 0 erg=10m1 13027 1f1:n 1 2ctme .25PRINT

13

VariationsVariationsA. Outer surface current in 0.1 MeV energy

increments, 0.05 cosine incrementsB. Outer surface flux in 0.1 MeV energy incrementsC. Cell flux (in Al)D. Cell flux with ANSI dose responseE. Dose map

14

Description of ProblemDescription of Problem Just using an empty sphere with a source at

origin:

15

Tutorial 2 CodeTutorial 2 CodeTutorial 2, base casec *********************************************************************c *c Cells *c *c *********************************************************************1 0 -1 imp:n=199 0 1 imp:n=0

c *********************************************************************c *c Surfaces *c *c *********************************************************************1 sph 0 0 0 10

c *********************************************************************c *c Data cards *c *c *********************************************************************mode nsdef pos = 0. 0 0 erg=10 f1:n 1 ctme .25PRINT

16

VariationsVariationsA. ERG: U235 fission neutron spectrum

B. 8 cm cube source centered on (0,0,0)

C. 4 cm spherical source around origin

D. 18 cm (r=1 cm) x-axis cylinder source centered on origin