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

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

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

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

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

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 )

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

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)

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

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

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

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 1 3 6 T Example 2: F1:P (1 2) (3 4 5) 6 Example 3: F371:N (1 2 3) (1 4) T

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.)

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.

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

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: E2 .1 .5 10 20 Example 2: E0 2 4i 7 or E0 2 3 4 5 6 7 Example 3: E8 0 1E-5 1E-3 1E-1 …

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: T2 -1 1 1.0+37 NT

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: C1 -.866 -.5 0 .5 .866 1 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.

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

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 FS2 -3 -4 -3, 3 -4, 3 4 Example 2: F1:N 1 2 T FS1 -3 T -3, 3, T over cells 1, 2, T

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 E2 0.1 2 20 FQ2 F E

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 1 0 0 Example2: IMP:N,P 1 1 1 1 1 0 Example3: IMP:N,P 1 4r 0

Precision of Monte Carlo Calculations From CLT : mx-Sx<E(x)< mx +Sx 68% confidence interval mx -2Sx<E(x)< mx +2Sx 95% confidence interval mx -3Sx<E(x)< mx +3Sx 99.7% confidence interval Estimated Relative Error is defined as: R=Sx / mx , therefore : mx(1-R)<E(x)< mx(1+R) 68% confidence interval

Guidelines for Interpreting the Relative Error Range of R Quality of the Tally . 0.5 to 1 Not meaningful 0.2 to 0.5 Factor of a few 0.1 to 0.2 Questionable < 0.10 Generally reliable except for point detector < 0.05 Generally reliable for point detector ---------------------------------------- * R2 is proportional to N * FOM=1/(R2T)

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:

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:

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)

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

Error Estimation for a bin:

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

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 10000. Command line : mcnp c i=inp r=runtpe and in the inp file : CONTINUE nps 10000 print 160

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

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

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 1 1 1 1 1 0 IMP:N 1 4r 0 E2 1 1.5 2 2.5 3 3.5 4 4.5 E2 1 6i 4.5 CUT:N 1E+37 0.1 CUT:N j 0.1

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 110 120 print -160 BASIC tables can not be turned off DEFAULT tables are automatically printed but can be turned off by print card.

Print Output Tables

Print Output Tables

Print Output Tables

Tally Plotting in MCNP

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.

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.

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..

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.

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

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 92235.50C. 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 82000.02p coplot XS 29000.02p

ENDF/B REACTION TYPES MT Microscopic Cross-Section Description 1 total 2 elastic 16 (n,2n) 17 (n,3n) 18 fission 102 (n,g) 103 (n,p) 107 (n,a)

Total cross section (MT=1)

Absorption cross section (MT=-2)

(n,n’) cross section (MT=51)

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

Total photon cross sections for Pb and Cu

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 :

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)

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

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 =10-24 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)

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 :

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.

Tally Multiplier examples : F25:N 0 0 0 0 FM25 0.00253 1001 -6 -8 M1001 92238.60 0.9 92235.60 0.1 C=0.00253 atoms per barn.cm (atomic density) of material 1001 M =1001 material number for material being heated R1 =-6 reaction number for total fission cross section (barn) R2 =-8 reaction number for fission Q (MeV/fission)

Tally Multiplier examples : F4:n 1 SD4 1 FM4 (-1 1 16: 17) $ bin 1 =(n,2n)+(n,3n) reaction rates (-1 1 -2) $ bin 2 =capture (n,0n) reaction rate (-1 1 -6) $ bin 3 =fission reaction rate M1 92235 -94.73 92238 -5.27 C=-1 means atom density (atoms/barn.cm) in that cell for tally type 4

Tally Multiplier examples : F4:n 10 FM4 (-1 1 (1 -4)(-2))(-1 1 1) M1 6012 1 In this example there are threedifferent tallies, namely a) -1 1 1 -4 $ neutron heating in MeV/cm3 from 12C in cell 10 b) -1 1 -2 $ neutron absorption (#/ cm3 ) in 12C in cell 10 c) -1 1 1 $ total neutron reaction (#/ cm3 ) in 12C in cell 10

Dose Energy & Dose Function

Macrobodies:

Perturbation

Perturbation

Perturbation

Perturbation