1. Tally Specification in MCNP
Presented by:
A. O. Ezzati
Department of Energy Engineering,
Sharif University of Technology
By:
Dr. M. Shahriari

2. Tallies in MCNP:
The user can instruct MCNP to make various tallies related to :
particle current
particle flux
energy deposition.

3. Tallies in MCNP:
MCNP tallies are normalized to be per starting particle except for a few special cases with
criticality sources.
Currents can be tallied as a function of direction
across any set of surfaces, surface segments, or
sum of surfaces in the problem.
Charge can be tallied for electrons and positrons

4. Standard Tallies : MCNP provides : six standard photon tallies
seven standard neutron tallies,
six standard photon tallies
four standard electron tallies
These basic tallies can be modified by the user
in many ways

5. Standard Tallies : Tally Mnemonic Description .
F1:N or F1:P or F1:E Surface current
F2:N or F2:P or F2:E Surface flux
F4:N or F4:P or F4:E Track length estimate
of cell flux
F5a:N or F5a:P Flux at a point or ring
detector
F6:N or F6:P or F6:N,P Track length estimate of
energy deposition
F7:N Track length estimate of
fission energy deposition
F8:N or F8:P or F8:E Pulse height tally
or F8:P,E

6. Standard tallies : Tally Fn Quantity Fn Units *Fn Multiplier *Fn Units
particle E
MeV F2
1/(|m| * A)
1/ cm2
MeV/cm2 F4
Tl / V F5
p(m ) * exp(-l)/(2pR2 )

7. Standard tallies : Tally Fn Quantity Fn Units *Fn Multiplier *Fn Units
Tl * st(E) * H(E) * ra/m
MeV/g
1.6E-22
Jerk/g F7
Tl * sf(E)* Q *ra/m F8
pulses E
MeV
1 jerk=109 J

8. Surface Current Tally :
This tally is the number of particles
(quantity of energy for *F1) crossing a surface.
The scalar current is related to the flux as :
J(r, E, t, m) =|m| F(r, E, t , m)

9. Surface Flux Tally :
This tally is average particle flux (energy flux for *F2) crossing a surface.

10. Cell Flux Tally :
This tally is average particle flux (energy flux for *F4) in a volume.

11. Detector Flux Tally :
A point detector is a deterministic estimate of the particle flux (energy flux for *F5) at a point in a space.

12. Surface and Cell Tallies(tally types 1, 2, 4, 6, and 7)
Simple Form: Fn:pl S1 ... Sk
General Form: Fn:pl S1 (S2 ... S3) (S4 ... S5) S6 S7 ...
n = tally number
pl = N or P or N,P or E
Si = problem number of surface or cell for tallying, or T
Example 1: F2:N T
Example 2: F1:P (1 2) (3 4 5) 6
Example 3: F371:N (1 2 3) (1 4) T

13. Detector Tallies (tally type 5)
Form for point detectors: Fn:pl X Y Z ±Ro n = tally number. pl = N for neutrons or P for photons, X Y Z = location of the detector point. R= radius of the sphere of exclusion: in centimeters, if Ro is entered as positive, in mean free paths, if entered as negative. (Negative entry illegal in a void.)

14. Detector Tallies (tally type 5)
Form for ring detectors: Fn:pl ao r ±Ro
n = tally number
a = the letter X, Y, or Z.
pl = N for neutrons or P for photons
ao = distance along axis “a” where the ring
plane intersects the axis.
r = radius of the ring in centimeters.
± Ro = same meaning as for point detectors, but
describes a sphere about the point selected
on the ring.

15. Pulse Height (tally type 8)
Simple Form: Fn:pl S1 ... Sk General Form: Fn:pl S1 (S2 ... S3) (S4 ... S5) S6 S7 ... n = tally number pl = P,E or P,E Si = problem number of cell for tallying, or T. 1) F8:P, F8:E, and F8:P,E are all equivalent tallies. 2) *F8 is an energy deposition tally 3)+F8 is a charge deposition tally in units of electron charge 4) The pulse height tally is not allowed with neutrons

16. En Tally Energy Card
Form: En E1 ... Ek n = tally number. Ei = upper bound (in MeV) of the ith energy bin for tally n. Default: If the En card is absent, there will be one bin over all energies unless this default has been changed by an E0 card. Use: Required if EMn card is used. Example 1: E Example 2: E0 2 4i 7 or E Example 3: E8 0 1E-5 1E-3 1E-1 …

17. Tn Tally Time Card
Form: Tn T1 ... Tk n = tally number. Ti = upper bound (in shakes) of the ith time bin for tally n. Default: If the Tn card is absent, there will be one bin over all times unless this default has been changed by a T0 card. Use: Required if TMn card is used. Example: T NT

18. Cn Cosine Card (tally type 1 only)
Form: Cn C1 ... Ck n = tally number. Ci = upper cosine limit of the ith angular bin for surface current tally n. C1 > -1. Ck = 1. Default: If the Cn card is absent, there will be one bin over all angles unless this default has been changed by a C0 card. Use: Tally type 1. Required if CMn card is used. Example: C This will tally currents within the angular limits (1) 180o to 150o, (2) 150o to 120o, (3) 120o to 90o, (4) 90o to 60o, (5) 60o to 30o, and (6) 30o to 0o with respect to the positive normal.

19. EMn Energy Multiplier Card
Form: EMn M1 ... Mk n = tally number. Mi = multiplier to be applied to the ith energy bin. Default: None. Use: Requires En card. Tally comment recommended. Tallies can also be changed to be per unit energy if the entries are 1/D E for each bin. * TMn and CMn cards are same as EMn with respect to Tn and Cn Cards

20. FSn Tally Segment Card (tally types 1, 2, 4, 6, 7)
Form: FSn S1 ... Sk n = tally number. Si = signed problem number of a segmenting surface. Default: No segmenting. Use: Not with detectors. May require SDn card. Advantage: it is not necessary to specify the problem geometry with extra cells just for tallying. Example 1: F2:N 1 FS , 3 -4, 3 4 Example 2: F1:N 1 2 T FS1 -3 T -3, 3, T over cells 1, 2, T

21. FQn Print Hierarchy Card
Form: FQn a1 a2 ... a8 n = tally number ai = F—cell, surface, or detector S—segment M—multiplier C—cosine E—energy T—time Example: F2:N 2 3 E FQ2 F E

22. IMP Cell Importance Cards
Form: IMP:n x1 x2 xi xI n = N for neutrons, P for photons, E for electrons. N,P or P,E or N,P,E is allowed if importances are the same for different particle types. xi = importance for cell i I = number of cells in the problem Default: If an IMP:P card is omitted in a MODE N P problem, all photon cell importances are set to unity unless the neutron importance is 0. Then the photon importance is 0 also. Example1: IMP:N 1 1 0, IMP:P Example2: IMP:N,P Example3: IMP:N,P 1 4r 0

23. Precision of Monte Carlo Calculations
From CLT :
mx-Sx<E(x)< mx +Sx % confidence interval
mx -2Sx<E(x)< mx +2Sx % confidence interval
mx -3Sx<E(x)< mx +3Sx % confidence interval
Estimated Relative Error is defined as:
R=Sx / mx ,
therefore :
mx(1-R)<E(x)< mx(1+R) % confidence interval

24. Guidelines for Interpreting the Relative Error
Range of R Quality of the Tally
0.5 to Not meaningful
0.2 to Factor of a few
0.1 to Questionable
< Generally reliable except for point detector
< Generally reliable for point detector
* R2 is proportional to N
* FOM=1/(R2T)

25. Estimation of Precision
For a variable x with PDF f(x) the true answer (or mean) is:
The true mean is estimated by sample mean :
The Variance of population is defined as:

26. Estimation of Precision
And the Standard deviation is defined as square root of variance, s.
s is seldom known, but can be steamated by Monte Carlo as S
and
The estimated variance of is given by:

27. Estimation of Precision
The Estimated Relative Error is defined as:
Statistical error Sx can be reduced by :
Making smaller S (variance reduction techniques)
Making large N ( more history run)

28. Accuracy and Precision
The results of Monte Carlo calculations refers only to statistical error and precision and not to accuracy.

29. Error Estimation for a bin:

30. Relative error for a bin with estimated mean value and N history
0.1
0.9487
0.6708
0.0949
0.0424
0.2
0.6325
0.4472
0.0632
0.0283
0.3
0.4830
0.3416
0.0483
0.0216
0.4
0.3873
0.2739
0.0387
0.0173
0.5
0.3162
0.2236
0.0316
0.0141
0.6
0.2582
0.1826
0.0258
0.0115
0.7
0.2070
0.1464
0.0207
0.0093
0.8
0.1581
0.1118
0.0158
0.0071
0.9
0.1054
0.0745
0.0105
0.0047

31. CONTINUE - RUN
Countinue run is used to continue running histories in a problem that was terminated earlier, for example with nps 1000 and then to run up to nps
Command line :
mcnp c i=inp r=runtpe
and in the inp file :
CONTINUE
nps 10000
print 160

32. Problem Cutoffs NPS n CTME T (in minute) CUT:pl T E WC1 WC2 SWTM
pl : N, P or E
T : time in shake, (1 shake=1E-8 sec)
E : lower energy cutoff in MeV
WC1 and WC2 : weight cutoffs.
SWTM : minimum source weight
Default values: very large(1E+37),0,-0.5,0.25

33. Problem Cutoffs ELPT:pl x1 x2 x3 … xI pl : N, P or E
xi : lower energy cutoff of ‘cell i’ in MeV
I : number of cells in problem

34. Special characters nR : repeat the immediately preceding entry n times
nI : insert n linear interpolates between preceding
and following entries.
nJ : jump n entry in input card
Examples:
IMP:N IMP:N 1 4r 0
E E2 1 6i 4.5
CUT:N 1E CUT:N j 0.1

35. Print Output Tables PRINT x x = no entry gives the full output file
x = x1 x2 … basic output plus tables x1, x2 ,…
x = -x1 –x2 … prints full output except the tables x1,x2,…
Example: print
print -160
BASIC tables can not be turned off
DEFAULT tables are automatically printed but can be turned off by print card.

36. Print Output Tables

37. Print Output Tables

38. Print Output Tables

39. Tally Plotting in MCNP

40. MCPLOT Tally Plotting Commands
mcnp inp= filename ixrz
MCNP runs the problem specified in filename and then the prompt mcplot > appears for MCPLOT commands. Both cross-section data and tallies can be plotted.
mcnp inp= filename ixz
is the most common way to plot cross-section data. The problem cross sections are read in but no transport occurs.

41. Parameter–setting Commands
TALLY n Define tally n as the current tally.
n is the n on the Fn card in the INP file
RESET aa Reset the parameters of command aa to
their default values.
aa can be a parameter setting command, COPLOT, or ALL. If aa is ALL, the parameters of all parameter–setting commands are reset to their default values.

42. Titling commands.
TITLE n “aa” Use aa as line n of the main title at the top of the plot.
The allowed values of n are 1 and 2.
The maximum length of aa is 40 characters.
XTITLE “aa” Use aa as the title for the x axis.
YTITLE “aa” Use aa as the title for the y axis.
LABEL “aa” Use aa as the label for the current curve..

43. Commands that specify the form of 2D plots.
LINLIN Use linear x axis and linear y axis.
LINLOG Use linear x axis and logarithmic y axis.
LOGLIN Use logarithmic x axis and linear y axis.
LOGLOG Use logarithmic x axis and log. y axis
XLIMS min max
YLIMS min max
HIST Make histogram plots.
PLINEAR Make piecewise–linear plots.
BAR Make bar plots.
NOERRBAR Suppress error bars.

44. Tally plotting through MCNP run
MPLOT mcplot commands
Example: mplot tally 4 free e linlin xlims 1 10 noerr

45. Commands for cross section plotting.
XS m
Plot a cross section according to the value of m:
Mn a material card in the INP file.
Example: XS M15
z a nuclide ZAID.
Example: XS C.
MT n Plot reaction n of material XS m.
PAR p Plot the data for particle type p, where:
p can be n, p, or e of material Mn.
COPLOT
Example: mt=-5 XS p coplot XS p

46. ENDF/B REACTION TYPES MT Microscopic Cross-Section Description 1 total
elastic
(n,2n)
(n,3n)
fission
(n,g)
(n,p)
(n,a)

47. Total cross section (MT=1)

48. Absorption cross section (MT=-2)

49. (n,n’) cross section (MT=51)

50. Pb photon cross sections (MT=-5,-1,-3,-4)

51. Total photon cross sections for Pb and Cu

52. Tally Multiplier Card FMn (C m reaction list 1) …
C = multiplicative constant
n = tally number
m = material number
reaction list i = sums and products of ENDF
or special reaction numbers
FM is used to calculate any quantity of the form :

53. ENDF and Special FM Reaction Numbers for Neutrons
ENDF MT
Special FM
Cross section 1 -1
Total 2 -3
Elastic -2
Total absorption -4
Average heating number -6
Total fission -7
Fission n -8
Fission Q(MeV/fission) 16
(n,2n) 17
(n,3n)
102
(n,g)
103
(n,p)
107
(n,a)

54. Special FM Reaction Numbers for Photons and Electrons
Cross section -5
Total -1
Incoherent -2
Coherent -3
Photoelectric with fluorescence -4
Pair production -6
heating number
Electrons 1
dE/dx electron collision stopping power 2
dE/dx electron radiative stopping power 3
dE/dx total electron stopping power 4
Electron range 5
Electron radiation yield

55. Duplication of F6 and F7 tallies using FM4 :
Standard F6 and F7 tallies can be duplicated by F4 tallies with appropriate
FM4 cards. The FM4 card to duplicate F6 is
F4:N n
FM4 C M 1 -4
For F7 it is
FM4 C M -6 -8
C = x number of atoms per gram
R1 =1 ENDF reaction number for total cross section (barns)
R2 =-4 reaction number for average heating number (MeV/collision)
R1 =-6 reaction number for total fission cross section (barns)
R2 =-8 reaction number for Fission Q (MeV/fission)

56. Tally Multiplier Card – Attenuator Set
FMn (C -1 m px)
C = multiplicative constant
n = tally number
m = material number
px=density times thickness of attenuating material,
atom density if positive, mass density if negative
The attenuator set can include more than one layer:
C -1 m1 px1 m2 px2
In which case the factor is :

57. Tally Multiplier Card – Attenuator Set
The attenuator set can also be part of a bin set, for example:
F4:N 1
FM4 ((C1 m1 R1)(C2 m2 R2)(C3 -1 m3 px3))
In this case attenuator factor is applied to every bin created by the
multiplier set.

58. Tally Multiplier examples :
F25:N FM M
C= atoms per barn.cm (atomic density) of material 1001
M = material number for material being heated
R1 = reaction number for total fission cross section (barn)
R2 = reaction number for fission Q (MeV/fission)

59. Tally Multiplier examples :
F4:n 1
SD4 1
FM4 ( : 17) $ bin 1 =(n,2n)+(n,3n) reaction rates
( ) $ bin 2 =capture (n,0n) reaction rate
( ) $ bin 3 =fission reaction rate M
C=-1 means atom density (atoms/barn.cm) in that cell for tally
type 4

60. Tally Multiplier examples :
F4:n 10
FM4 (-1 1 (1 -4)(-2))(-1 1 1) M
In this example there are threedifferent tallies, namely
a) $ neutron heating in MeV/cm3 from 12C in cell 10
b) $ neutron absorption (#/ cm3 ) in 12C in cell 10
c) $ total neutron reaction (#/ cm3 ) in 12C in cell 10

61. Dose Energy & Dose Function

63. Macrobodies:

66. Perturbation

67. Perturbation

68. Perturbation

69. Perturbation