P HI T S Basic Lecture II: Definition of Tally Multi-Purpose Particle and Heavy Ion Transport code...

PHITSBasic Lecture II:

Definition of Tally

Multi-Purpose Particle and Heavy Ion Transport code System

title 1

Oct. 2014 revised

Purpose 2

Learn how to deduce various physics quantities from the PHITS simulation

Purpose of This Lecture

You can obtain this kind of results at the end of this lectureParticle fluence (left) and depth-dose distribution (right)

for the simulation condition for homework

Contents of Lecture II

Contents 3

What is Tally?

Introduction and usage of “Tally” How to use Tally for checking geometry How to use Tally for calculating physical

quantities

Kinds of TallySummary

What is Tally?

What is tally? 4

Tally: a record of the number or amount of something, especially one that you can keep adding to;[Oxford Advanced Learner’s Dictionary (7th edition), OXFORD.]

In PHITS, the word of “Tally” used for functions toDeduce physical quantities such as flux and heat,

orDepict the 2D or 3D geometry in certain area

What is tally? 5

PHITS simulates the motion of each particle using the Monte Carlo method. You can estimate their average behavior by calculating various physical quantities as flux and deposition energy in a certain region, using “Tally”

Result of [t-track] (Track-length tally)

How many particles were passed through this region? → Use “track-length” tally

Concept of Tally

Kinds of Tally in PHITS 6

Calculating physical quantity– Particle flux 　→ [t-track], [t-cross]– Heat and deposition energy → [t-heat], [t-deposit]– Secondary particles → [t-yield], [t-product]– LET or microdosimetric distribution → [t-let], [t-sed]

Checking geometry– 2-dimensional visualization → [t-gshow], [t-rshow]– 3-dimensional visualization → [t-3dshow]

Tally Types• Various tally functions are implemented in PHITS• Many physical quantities can be deduced from the

PHITS simulation by selecting appropriate tally

For example…

Visualize Particle Trajectory

method of track detection 7

x-axis

z-axis


x-axis

z-axis



x-axis

z-axis



x-axis

z-axis



x-axis

z-axis



Contents 12

What is Tally?


quantities


Geometry Check

Tally for checking geometry 13

Every time you construct new geometry, it is better to check the geometry using [t-3dshow] or [t-gshow]

Otherwise you would obtain wrong results without noticing miss-definition of the geometry, especially when you make an overlapping region!

Exercise 1

14

Confirm the geometry of lec02.inp in 2 dimensions using [t-gshow] tally.

Tally for checking geometry

[ M a t e r i a l ]mat[1] 1H 2 16O 1

・・・・・・

[ S u r f a c e ] 10 so 500. 11 cz 10. 12 pz 0. 13 pz 50.

[ C e l l ] 100 -1 10 101 1 -1. -11 12 -13 110 0 -10 #101

A water cylinder with a radius of 10 cm and a height of 50 cm.

lec02.inp

50 cm

10 c

m

• Copy & paste 2 [t-gshow] sections from t-gshow.inp.• Set icntl=7 in [parameters] section and execute PHITS.

Answer 1

15Tally for checking geometry

lec02.inp

gshow_xz.eps

gshow_xy.eps

The height is 50cm.

The radius is 10cm.

[ P a r a m e t e r s ] icntl = 7・・・・・・

[ T - G s h o w ]・・・・・・ axis = xyfile = gshow_xy.outoutput = 6epsout = 1

[ T - G s h o w ]・・・・・・ axis = xzoutput = 6 file = gshow_xz.outepsout = 1

Confirm the geometry of lec02.inp in 2 dimensions using [t-gshow] tally.

xy-plane

xz-plane

How is this geometry shown in 3 dimensions?

Exercise 2


gshow_xy.eps gshow_xz.eps

Confirm the geometry of lec02.inp in 3 dimensions using [t-3dshow] tally.

• Copy & paste [t-3dshow] section from t-3dshow.inp.• Set “icntl=11” in [parameters] section and execute

PHITS.


lec02.inp


[ T - 3 D s h o w ] output = 3 x0 = 0 y0 = 0 z0 = 20 e-the = 90 $ eye e-phi = 0 e-dst = 120 l-the = 90 $ light l-phi = 0 l-dst = 100 w-wdt = 50 $ window w-hgt = 50 w-dst = 30・・・・・・

3dshow.eps

X

Y

Z・

Answer 2Confirm the geometry of lec02.inp in 3 dimensions using [t-3dshow] tally.

Parameters used in [t-3dshow]

18

Origin (x0,y0,z0)

(e-the,e-phi,e-dst)

w-hgt(w-mnh)

w-dst

w-wdt(w-mnw)

e-dst

Picture FlameEye Point

Light source(l-the,l-phi,l-dst)

w-mnw × w-mnh ＝ #Pixel 100 × 100 (default)

PolarCoordinates

Polar coordinates

XYZ-coordinates


19

lec02.inp

Exercise 3


3dshow.eps

[ T - 3 D s h o w ] output = 3 x0 = 0 y0 = 0 z0 = 20 e-the = 90 $ eye e-phi = 0 e-dst = 120 l-the = 90 $ light l-phi = 0 l-dst = 100 w-wdt = 50 $ window w-hgt = 50 w-dst = 30 heaven = y mirror = 0 line = 1 shadow = 2 resol = 1file = 3dshow.out title = Check geometry using [T-3dshow] tally epsout = 1


X

Y

Z・X

Y

Z


Rotate azimuthal angleof eye-point by 45 deg

X

Y

Z

“Heaven” is Y direction

Rotate zenith angle of eye-point by 45 deg

Let’s rotate the picture.


Contents 20

What is Tally?


quantities


How to define Tally

Tally for calculating physical quantities

21

What kind of physical quantity

Select type of tally: [t-track], [t-deposit] etc. in where

Select geometrical mesh: mesh= reg, xyz, r-zof what particle

Select particle type: part = neutron, proton etc. in which unit e.g. (cm/source), (1/cm2/source) etc.

Select unit: unit = 1, 2, 3 … in what output form

Select output axis: axis = eng, reg, xy, etc.

You have to determine …

22

[ T - T R A C K ] title = Track Detection in xyz mesh mesh = xyz x-type = 2 nx = 25 xmin = -25. xmax = 25.y-type = 2 ny = 25 ymin = -25. ymax = 25. z-type = 1 nz = 1 -5.0 5.0e-type = 1 ne = 1 0.0 5000.0 unit = 1 axis = xy file = track_xy.out part = all gshow = 1 epsout = 1


Example of [t-track] tally (in t-track.inp).

Geometrical mesh

Particle type

Unit of output

Output form

• [T-track]: Tally for calculating track-length or flux of particles in certain regions

[T-track] can be used for visualizing particle trajectories by setting small mesh for tallying region

Exercise 4

23

Confirm particle fluence using [t-track] tally.

How is the behavior of the particles?

[ S o u r c e ] s-type = 1 proj = 12C dir = 1.0 r0 = 2.5 z0 = -10. z1 = -10. e0 = 250.

lec02.inp

A carbon beam of 250MeV/u


• Copy & paste 2 [t-track] sections from t-track.inp.• Set “icntl=0” in [parameters] section and execute

PHITS.

24

lec02.inp


Answer 4


[ T - T r a c k ]・・・・・・ axis = xy file = track_xy.out part = all gshow = 1 epsout = 1

[ T - T r a c k ]・・・・・・ axis = xz file = track_xz.out part = all gshow = 1 epsout = 1

Output file

Making an eps file using name specified by “file=”.

(***.out → ***.eps)

•In the case of 2D-plot, error files (_err.eps) are made.

Confirm particle fluence using [t-track] tally.

25

lec02.inp



[ T - T r a c k ]・・・・・・ axis = xy file = track_xy.out part = all gshow = 1 epsout = 1

[ T - T r a c k ]・・・・・・ axis = xz file = track_xz.out part = all gshow = 1 epsout = 1

track_xz.eps

track_xy.eps

A carbon beam of 250MeV/u with a radius of 2.5cm

Answer 4Confirm particle fluence using [t-track] tally.

26

track_xy_err.eps track_xz_err.eps


Error file (*_err.eps)• In the case of 2D-plot such as tallies with “axis=xy,

rz”, errors are output in another file named *_err.eps.• Warm colors indicate that relative standard errors are

large (close to 1), while cold colors mean small erros.

How to define Tally

27









[ T - T R A C K ] ・・・・・・ mesh = xyz x-type = 2 nx = 25 xmin = -25. xmax = 25.y-type = 2 ny = 25 ymin = -25. ymax = 25. z-type = 1 nz = 1 -5.0 5.0e-type = 1 ne = 1 0.0 5000.0 unit = 1 axis = xy file = track_xy.out part = all gshow = 1 epsout = 1

28

lec02.inp


Geometrical Mesh

mesh = xyz :Define tally region according to xyz coordinates ⇒ You need to specify x-type, y-type, z-typeX-axis (x-type = 2) : xmin (minimum value) : xmax (maximum value) : nx (number of mesh)Z-axis (z-type = 1) : nz (number of mesh) : -5.0 5.0 (Boundaries, nz+1 ）

29

e-type = 1 ne = 10 0 1 2 3 5 10 15 20 30 50 100

Replace “e” to “x” if you want to define x-mesh

e-type = 2 ne = 100 emin = 0 emax = 1000

1: Define #mesh and their boundaries

2,3: Define #mesh and their minimum & maximum values(2: linear, 3: logarithmic interval)

e-type = 3 ne = 100 emin = 0.1 emax = 5000

e-type = 4 edel = 100 emin = 0 emax = 5000

e-type = 5 edel = 1.301 emin = 0.1 emax = 5000

=log10(20)

How to Define Mesh• Mesh is a common concept used in many tallies• x-type, y-type, z-type, r-type, e-type, t-type, a-type etc.

x-axis y-axis z-axis radius energy time angle

• You can define each mesh using the following 5 types

4,5: Define interval of mesh and their minimum & maximum values(4: linear, 5: logarithmic interval)


30

xyz mesh:Divide the regionsin XYZ coordinates

X

Y

Z

Z

R

Geometrical Mesh TypesThere are 3 types of geometrical mesh in PHITS

r-z mesh:Divide the regions

in Cylindrical coordinates

reg mesh:Divide the regionsin cells defined in

PHITS virtual space


Exercise 5

31

In order to look the figures more clearly, increase the number of mesh in the [t-track] tally.• Multiply nx and ny in the [t-track]

section with “axis=xy” by four.• Multiply nx and nz in the [t-track]

section with “axis=xz” by four.


track_xz.epstrack_xy.eps

A higher resolution is needed.

32Tally for calculating physical quantities

[ T - T R A C K ] ・・・・・・ mesh = xyz x-type = 2 nx = 100 xmin = -25. xmax = 25.y-type = 2 ny = 100 ymin = -25. ymax = 25. z-type = 1 nz = 1 -5.0 5.0・・・・・・ axis = xy file = track_xy.out part = all gshow = 1 epsout = 1

lec02.inp track_xy.eps

We can look the figure with good resolution by increase nx and ny.

Answer 5In order to look the figures more clearly, increase the number of mesh in the [t-track] tally.


[ T - T R A C K ] ・・・・・・ mesh = xyz x-type = 2 nx = 100 xmin = -25. xmax = 25. y-type = 1 ny = 1 -5.0 5.0z-type = 2 nz = 200 zmin = -20. zmax = 80.・・・・・・ axis = xz file = track_xz.out part = all gshow = 1 epsout = 1

lec02.inp track_xz.eps

Answer 5In order to look the figures more clearly, increase the number of mesh in the [t-track] tally.

How to define Tally

34









Exercise 6

35

Show the fluence of each particle separately.• Replace “part=all” in the [t-track] tally with

“axis=xz” by “part=12C proton neutron”.


[ T - T R A C K ] ・・・・・・ axis = xz file = track_xz.out part = all gshow = 1 epsout = 1

lec02.inp track_xz.eps

How are the behaviors of 12C, proton, and neutron?


[ T - T R A C K ] ・・・・・・ axis = xz file = track_xz.out part = 12C proton neutron gshow = 1 epsout = 1

lec02.inp

12C

proton

neutron

track_xz.eps

Answer 6Show the fluence of each particle separately.

How to define Tally

37









[ T - T R A C K ] ・・・・・・ x-type = 2 nx = 100 xmin = -25. xmax = 25. y-type = 1 ny = 1 -5.0 5.0z-type = 2 nz = 200 zmin = -20. zmax = 80. e-type = 1 ne = 1 0.0 5000.0 unit = 1 axis = xz file = track_xz.out・・・・・・

lec02.inp

Exercise 7

38

Show the particle fluence as a function of its energy.

• Replace “axis=xz” by “axis=eng”.

• Set “e-type=2” and set ne, emin, and emax to be 100, 0, and 5000, respectively. (See “ How to Define Mesh” in 29 page.)

• Set “nx=1” and “nz=1” to reduce the number of pages of output.

• Change the output file name to “track_eng.out”.


[ T - T R A C K ] ・・・・・・ x-type = 2 nx = 1 xmin = -25. xmax = 25. y-type = 1 ny = 1 -5.0 5.0z-type = 2 nz = 1 zmin = -20. zmax = 80. e-type = 2 ne = 100$ 0.0 5000.0 emin = 0.0 emax = 5000.0 unit = 1 axis = eng file = track_eng.out・・・・・


lec02.inp track_eng.eps

Energy distribution of each particle

The beam energy is 250×12=3000MeV

Answer 7Show the particle fluence as a function of its energy.

in “MeV”(not MeV/n)

lec02.inp

Exercise 8

40

Change the horizontal axis to Logarithmic scale.

• Set “e-type=3” and “emin=1.0”.


[ T - T R A C K ] ・・・・・・ e-type = 2 ne = 100$ 0.0 5000.0 emin = 0.0 emax = 5000.0 unit = 1 axis = eng file = track_eng.out・・・・・

track_eng.eps

This figure is shown in linear scale.

lec02.inp


[ T - T R A C K ] ・・・・・・ e-type = 3 ne = 100$ 0.0 5000.0 emin = 1.0 emax = 5000.0 unit = 1 axis = eng file = track_eng.out・・・・・

track_eng.eps

We can confirm the low energy region in detail.

Answer 8Change the horizontal axis to Logarithmic scale.

[ T - T R A C K ] mesh = xyzAdd “reg parameter”x-type = 2 nx = 1 xmin = -25. xmax = 25. y-type = 1 ny = 1 -5.0 5.0z-type = 2 nz = 1 zmin = -20. zmax = 80. delete・・・・・・

lec02.inp

Exercise ９

42

Show the energy distributions on the inside and outside of the cylinder.

• Change to region mesh （ mesh = reg ）

• Specify the two regions to tally; 101(inside) and 110(outside)

• Delete or comment out parameters for mesh = xyz


[ T - T R A C K ] mesh = regreg = 101 110$ x-type = 2$ nx = 1$ xmin = -25.$ xmax = 25.$ y-type = 1$ ny = 1$ -5.0 5.0$ z-type = 2$ nz = 1$ zmin = -20.$ zmax = 80. ・・・・・・

lec02.inp

Answer ９


In water

outside

Show the energy distributions on the inside and outside of the cylinder.

Exercise 10

44

[ T - Deposit ] title = Energy deposition in xyz mesh mesh = xyz・・・・・・ unit = 1material = alloutput = doseaxis = xzfile = deposit.outpart = allgshow = 1epsout = 1

t-deposit.inp


Confirm energy deposition using [t-deposit] tally.

• Copy & paste [t-deposit] section from t-deposit.inp.

• [T-deposit]: Tally for calculating deposit energy in materials


deposit.eps

Energy deposition by the carbon beam.

Energy deposition by the secondary particles.

Answer 10Confirm energy deposition using [t-deposit] tally.

How to define Tally

46










Exercise 11

47

Change the unit of the output of the [t-deposit] tally, [MeV/cm3/source], to [Gy/source].

• Replace “unit=1” by “unit=0”.


lec02.inp

It should be noted that when a region includes more than two materials, dose in the region does not equal to average value of the region. Example; E1/M1+E2/M2 [PHITS] ≠ (E1+ E2)/(M1+ M2) [average dose]

Calculating deposit energy in the unit of Gy=J/kg.


deposit.eps

The unit and its scale have changed.


lec02.inp

Answer 11Change the unit of the output of the [t-deposit] tally, [MeV/cm3/source], to [Gy/source].

[ T - Deposit ] title = Energy deposition in xyz mesh mesh = xyz x-type = 2 xmin = -25.00000 xmax = 25.00000 nx = 100 y-type = 1 ny = 1 -5.0 5.0 z-type = 2 zmin = -20.00000 zmax = 80.00000 nz = 200・・・・・・ axis = xz file = deposit.out・・・・・・

Exercise 12

49

Show z-distribution of the energy deposition in the water cylinder using r-z mesh.

• Replace “mesh=xyz” by “mesh=r-z” and set r-type and z-type sub-sections.

• Set radial range from 0 to 10 cm• Replace “axis=xz” by “axis=z”.


lec02.inp

Answer 12


lec02.inp deposit.eps

A Bragg peak of the carbon beam is shown at z=12cm.

Show z-distribution of the energy deposition in the water cylinder using r-z mesh.

[ T - Deposit ] title = Energy deposition in xyz mesh mesh = r-z$ x-type = 2 $ xmin = -25.00000$ xmax = 25.00000$ nx = 100 r-type = 1 nr = 1 0.0 10.0 z-type = 2 zmin = -20.00000 zmax = 80.00000 nz = 200・・・・・・ axis = zfile = deposit.out・・・・・・

Exercise 13

51

Using ANGEL, change the region of y-axis in deposit.eps.

• Add “p: ymin(1e-11) ymax(1e-9)” to the 77th line of deposit.out.

• Execute ANGEL.


Answer 13


The region between 10-

11and 10-9 for the vertical axis is shown.

Using ANGEL, change the region of y-axis in deposit.eps.

・・・・・・#newpage:# no. = 1 ir = 1# r = ( 0.0000E+00 - 1.0000E+01 )p: ymin(1e-11) ymax(1e-9)x: z [cm]y: Dose [Gy/source] p: xlin ylog afac(0.8) form(0.9)h: n x y(all ),hh0l n # z-lower z-upper dose r.err -2.0000E+01 -1.9500E+01 0.0000E+00 0.0000・・・・・・

deposit.out deposit.eps

Setting Angel parameters, you can adjust some conditions of graphs.


Contents 53

What is Tally?


quantities


Kinds of tally in PHITS 54

Deduce physical quantity

List of All Tallies in PHITS[t-track] Track length tally definition

[t-cross] Surface crossing tally definition

[t-heat] Heat developing tally definition

[t-deposit] Deposit tally definition

[t-deposit2] Deposit2 tally definition

[t-yield] Residual nuclei yield tally definition

[t-product] Produced particle tally definition

[t-dpa] DPA tally definition

[t-let] LET tally definition

[t-sed] SED tally definition

[t-time] Time tally definition

[t-star] Star density tally definition

[t-dchain] Dchain tally definition

[t-userdefined] User defined tally definition

[t-gshow] Region surface display definition for graphical plot

[t-rshow] Physical quantity region display definition for graphical plot

[t-3dshow] 3D graphical geometry plot definition

Visualize geometry

[t-3dshow]


• Tally for visualizing the geometry in 3-dimension from a viewpoint of a certain location in PHITS virtual space

• Activated only when icntl=11 in the [parameters] section

56

[t-3dshow](for your FUN!)


You can rotate [t-3dshow] picture using Python softwareSee “/phits/utility/rotate3dshow” in more detail

[t-gshow]


• Tally for visualizing the geometry in 2-dimension cut by certain slices

• Show region boundary, cell number, material ID etc.• Other tallies can be used for this purpose by setting

icntl=8 in the [parameters] section (see Lecture I)

[t-track]


You can visualize the trajectory of particle using [t-track] by setting small mesh for tallying regions

• Tally for calculating track-length (cm) of particles in certain regions

• Average flux (/cm2) in the region can be also deduced from this tally, dividing the track length (cm) by the volume of the region (cm3)

[t-cross]


• Tally for calculating flux or current (/cm2) of particles crossing certain surfaces

• Current is simply added by 1 when a particle cross the surface, while flux is added by 1/cos()

[t-heat], [t-deposit]


• Tally for calculating deposition energy (MeV) in certain regions

• Only ionization energy losses by charged particles are scored by [t-deposit] tally → Event-by-event data can be also deduced!

• Neutron and photon doses are calculated by the Kerma approximation in [t-heat] tally

Bragg peak calculated by [t-heat] tally

[t-yield], [t-product]


• Tally for calculating the number of secondary particles generated by nuclear reactions in certain regions

• Energy or time distribution of secondary particles can be obtained from [t-product] tally

• Yield of each nuclide can be depicted on nuclear chart using [t-yield] tally

Example of [t-yield] tally

[t-dpa]


• Tally for calculating the radiation damage index DPA in certain regions

• DPA is the average number of displaced atoms per atom of a material, and is calculated from the flux multiplied with the damage cross section

Depth-DPA distribution calculated using [t-dpa]

[t-let], [t-sed]


• Tally for calculating the probability densities of deposition energy or flux in terms of LET, lineal energy (y), or specific energy (z) in microscopic sites distributed in certain regions

• Useful for radiobiological calculations

Example of [t-let] tally*SED representsSpecific Energy Distribution

[t-deposit2]


• Tally for calculating event-by-event deposition energies in two regions

• Output the contour map of their correlation• Useful for simulating experimental data obtained by

using two detectors

Example of [t-deposit2] tally

[t-dchain]

Kinds of tallies in PHITS 65

Irradiation Cooling

Time dependence of radioactivities inside water phantom irradiated by 150 MeV proton for 6 min

• Tally for generating the input files for DCHAIN-SP, which can calculate the time evolution of the radioactive nuclides during and after irradiation

• DCHAIN-SP is also included in the PHITS package


Contents 66

What is Tally?


quantities


Summary 67

• A variety of information can be deduced from the PHITS simulation using functions called “Tally”

• 2 types of tallies are implemented in PHITS, one is for visualizing PHITS geometry, and the other is for calculating physical quantities

• Properness of the geometry can be checked by the tallies for its visualization: [t-3dshow] and [t-gshow]

• For defining tally, you have to determine …

Summary

what kind of physical quantity in where of what particle in which unit in what output form

Homework 68

• Depict the neutron and proton fluences, respectively, in your homework study

• Adjust [t-deposit] to see the Bragg peak of proton

• Change the minimum & maximum values of y axis in the graph for the depth-dose distribution (use “angel” parameters)

• Investigate the difference of the depth-dose distributions between the inside and outside of beam center (within the radius of 2.5cm or not) by set r-z mesh

Homework

Example Answer

Homework 69

Proton (up) and neutron (down) fluences

Depth-dose distribution inside (up)and outside (down) beam radius

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P HI T S Basic Lecture II: Definition of Tally Multi-Purpose Particle and Heavy Ion Transport code...

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