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PHITSBasic Lecture II:
Definition of Tally
Multi-Purpose Particle and Heavy Ion Transport code System
title 1
Jun. 2013 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
Introduction and usage of “Tally” What is Tally? Kinds of Tally How to use Tally for checking geometry How to use Tally for calculating
physical quantities
Summary
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
Contents of Lecture II
Contents 6
Introduction and usage of “Tally” What is Tally? Kinds of Tally How to use Tally for checking geometry How to use Tally for calculating
physical quantities
Summary
Kinds of Tally in PHITS 7
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…
Kinds of tally in PHITS 8
Deduce physical quantity
Visualize geometry
List of All Tallies in PHITS
[t-3dshow]
Kinds of tally in PHITS 9
• 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
[t-gshow]
Kinds of tally in PHITS 10
• 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]
Kinds of tally in PHITS 11
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)
Visualize Particle Trajectory
method of track detection 12
x-axis
z-axis
method of track detection 13
x-axis
z-axis
Visualize Particle Trajectory
method of track detection 14
x-axis
z-axis
Visualize Particle Trajectory
method of track detection 15
x-axis
z-axis
Visualize Particle Trajectory
method of track detection 16
x-axis
z-axis
Visualize Particle Trajectory
[t-cross]
Kinds of tally in PHITS 17
• 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]
Kinds of tally in PHITS 18
• 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]
Kinds of tally in PHITS 19
• 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]
Kinds of tally in PHITS 20
• 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]
Kinds of tally in PHITS 21
• 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]
Kinds of tally in PHITS 22
• 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 23
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 of Lecture II
Contents 24
Introduction and usage of “Tally” What is Tally? Kinds of Tally How to use Tally for checking geometry How to use Tally for calculating
physical quantities
Summary
Geometry Check
Tally for checking geometry 25
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!
26
[ P a r a m e t e r s ] icntl = 11・ ・ ・ ・ ・ ・
[ M a t e r i a l ]mat[1] 1H 2 16O 1
[ M a t N a m e C o l o r ] mat name color 1 Water pastelblue
[ 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
Tally for checking geometry
lec02.inp
How to use [t-3dshow]
Activate[t-3dshow]
Water cylinder with radius 10 cm and height 50cm
3dshow.eps
X
Y
Z・
Parameters used in [t-3dshow]
27
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
Tally for checking geometry
28
lec02.inp
Rotate the Picture
Tally for checking geometry
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
[ T - 3 D s h o w ] output = 3 x0 = 0 y0 = 0 z0 = 20 e-the = 135 $ 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
[ T - 3 D s h o w ] output = 3 x0 = 0 y0 = 0 z0 = 20 e-the = 135 $ eye e-phi = 45 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
Rotate azimuthal angleof eye-point by 45 deg
X
Y
Z
“Heaven” is Y direction
Rotate zenith angle of eye-point by 45 deg
29
[t-3dshow](for your FUN!)
Tally for checking geometry
You can rotate [t-3dshow] picture using Python software
See “/phits/utility/rotate3dshow” in more detail
[ P a r a m e t e r s ] icntl = 11・ ・ ・ ・ ・ ・
[ T - G s h o w ]・ ・ ・ ・ ・ ・ axis = xyoutput = 6 file = xy_gshow.out title = Check geometry ・ ・ ・ epsout = 1
[ T - G s h o w ]・ ・ ・ ・ ・ ・ axis = xzoutput = 6 file = xz_gshow.out title = Check geometry ・ ・ ・ using [T-gshow] tally epsout = 1
[ P a r a m e t e r s ] icntl = 7・ ・ ・ ・ ・ ・
[ T - G s h o w ]・ ・ ・ ・ ・ ・ axis = xyoutput = 6 file = xy_gshow.out title = Check geometry ・ ・ ・ epsout = 1
[ T - G s h o w ]・ ・ ・ ・ ・ ・ axis = xzoutput = 6 file = xz_gshow.out title = Check geometry ・ ・ ・ using [T-gshow] tally epsout = 1
30
lec02.inp
[t-gshow]
Tally for checking geometry
Activate[t-gshow]
xz_gshow.eps
xy_gshow.eps
xy plane(z = 0cm)
xz plane(y = 0cm)
Water cylinder with radius 10 cm and height 50cm
Contents of Lecture II
Contents 31
Introduction and usage of “Tally” What is Tally? Kinds of Tally How to use Tally for checking geometry How to use Tally for calculating
physical quantities
Summary
How to define Tally
Tally for calculating physical quantities
32
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 …
33
lec02.inp [ T - T R A C K ] mesh = xyz x-type = 2 nx = 100 xmin = -25. xmax = 25. y-type = 1 ny = 1 -5.0 5.0 z-type = 2 nz = 200 zmin = -20. zmax = 80. part = all e-type = 1 ne = 1 0.0 5000.0 unit = 1 axis = xz file = xz_track_all.out gshow = 1 epsout = 1
• [T-track]: Tally for calculating track-length or flux of particles in certain regions
Example of [t-track]
[T-track] can be used for visualizing particle trajectories by setting small mesh for tallying region
If you would like to visualize particle trajectory …
Tally for calculating physical quantities
Making an eps file using name specified by “file=”.(***.out → ***.eps)
Output file
In the case of 2D-plot, error files (_err.eps) are made.
34
Particle trajectory for carbon 290 MeV/u beam with radius = 2.5cm
xy_track_all.eps xz_track_all.eps
Tally for calculating physical quantities
Sample Results of [t-track]Set icntl=0 and execute PHITS …
35
xy_track_all_err.eps
xz_track_all_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.
Tally for calculating physical quantities
How to define Tally
36
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 …
Tally for calculating physical quantities
37
lec02.inp [ T - T R A C K ] mesh = xyz x-type = 2 nx = 100 xmin = -25. xmax = 25. y-type = 1 ny = 1 -5.0 5.0 z-type = 2 nz = 200 zmin = -20. zmax = 80. part = all e-type = 1 ne = 1 0.0 5000.0 unit = 1 axis = xz file = xz_track_all.out gshow = 1 epsout = 1
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)Y-axis (y-type = 1) : ny (number of mesh) : -5.0 5.0 (Boundaries, ny+1 )
Geometrical Mesh
Tally for calculating physical quantities
38
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)
Tally for calculating physical quantities
39
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
Tally for calculating physical quantities
40
[ T - T R A C K ] mesh = xyz x-type = 2 nx = 100 xmin = -25. xmax = 25. y-type = 1 ny = 1 -5.0 5.0 z-type = 2 nz = 200 zmin = -20. zmax = 80. part = all e-type = 1 ne = 1 0.0 5000.0 unit = 1 axis = xz file = xz_track_all.out gshow = 1 epsout = 1
[ T - T R A C K ] mesh = r-z r-type = 2 nr = 100 rmin = -25. rmax = 25.z-type = 2 nz = 200 zmin = -20. zmax = 80. part = all e-type = 1 ne = 1 0.0 5000.0 unit = 1 axis = rz file = rz_track_all.out gshow = 1 epsout = 1
1. Copy [t-track] tally2. Change to “mesh = r-z”3. Make “r-type” sub-section4. Delete “x-type” and “y-type”
sub-sections
lec02.inp
Change Geometrical Mesh
Tally for calculating physical quantities
41
[ T - T R A C K ] mesh = r-z r-type = 2 nr = 100 rmin = -25. rmax = 25.z-type = 2 nz = 200 zmin = -20. zmax = 80. part = all e-type = 1 ne = 1 0.0 5000.0 unit = 1 axis = rz file = rz_track_all.out gshow = 1 epsout = 1
lec02.inp
Change Geometrical Mesh
Tally for calculating physical quantities
[ T - T R A C K ] mesh = r-z r-type = 2 nr = 25 rmin = 0. rmax = 25.z-type = 2 nz = 200 zmin = -20. zmax = 80. part = all e-type = 1 ne = 1 0.0 5000.0 unit = 1 axis = rz file = rz_track_all.out gshow = 1 epsout = 1
42
lec02.inp
Change Geometrical Mesh
Tally for calculating physical quantities
How to define Tally
43
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 …
Tally for calculating physical quantities
44
Replace “part=all” by “part = 12C proton neutron”
[ T - T R A C K ] mesh = r-z r-type = 2 nr = 25 rmin = 0. rmax = 25.z-type = 2 nz = 200 zmin = -20. zmax = 80. part = all e-type = 1 ne = 1 0.0 5000.0 unit = 1 axis = rz file = rz_track_all.out gshow = 1 epsout = 1
[ T - T R A C K ] mesh = r-z r-type = 2 nr = 25 rmin = 0. rmax = 25.z-type = 2 nz = 200 zmin = -20. zmax = 80. part = 12C proton neutron e-type = 1 ne = 1 0.0 5000.0 unit = 1 axis = rz file = rz_track_12C-p-n.out gshow = 1 epsout = 1
lec02.inp
Define Particle Type
Tally for calculating physical quantities
45
[ T - T R A C K ] mesh = r-z r-type = 2 nr = 25 rmin = 0. rmax = 25.z-type = 2 nz = 200 zmin = -20. zmax = 80. part = 12C proton neutron e-type = 1 ne = 1 0.0 5000.0 unit = 1 axis = rz file = rz_track_12C-p-n.out gshow = 1 epsout = 1
12C
proton
neutron
lec02.inp
Define Particle Type
Tally for calculating physical quantities
How to define Tally
46
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 …
Tally for calculating physical quantities
47
[ T - T R A C K ] mesh = r-z r-type = 2 nr = 25 rmin = 0. rmax = 25.z-type = 2 nz = 200 zmin = -20. zmax = 80. part = 12C proton neutron e-type = 1 ne = 1 0.0 5000.0 unit = 1 axis = rz file = rz_track_12C-p-n.out gshow = 1 epsout = 1
[ T - T R A C K ] mesh = r-z r-type = 2 nr = 1 rmin = 0. rmax = 25.z-type = 2 nz = 1 zmin = -20. zmax = 80. part = 12C proton neutron e-type = 2 ne = 100 emin = 0.0 emax = 5000.0 unit = 1 axis = eng file = eng_track_12C-p-n.out gshow = 1 epsout = 1
lec02.inp
in “MeV”(not MeV/n)
Change Output Form
1. Copy [t-track] section with r-z mesh
2. Change to “axis = eng”3. Change energy-mesh
sub-section4. Change the tallied region
into one region
Tally for calculating physical quantities
48
[ T - T R A C K ] mesh = r-z r-type = 2 nr = 1 rmin = 0. rmax = 25.z-type = 2 nz = 1 zmin = -20. zmax = 80. part = 12C proton neutron e-type = 2 ne = 100 emin = 0.0 emax = 5000.0 unit = 1 axis = eng file = eng_track_12C-p-n.out gshow = 1 epsout = 1
lec02.inpChange Output Form
Tally for calculating physical quantities
49
[ T - T R A C K ] mesh = r-z r-type = 2 nr = 1 rmin = 0. rmax = 25.z-type = 2 nz = 1 zmin = -20. zmax = 80. part = 12C proton neutron e-type = 3 ne = 100 emin = 1.0 emax = 5000.0 unit = 1 axis = eng file = eng_track_12C-p-n.out gshow = 1 epsout = 1
LogarithmicScale
lec02.inpChange Energy Mesh
Tally for calculating physical quantities
Change Z-Mesh
50
[ T - T R A C K ] mesh = r-z r-type = 2 nr = 1 rmin = 0. rmax = 25.z-type = 2 nz = 2 zmin = -20. zmax = 80. part = 12C proton neutron e-type = 3 ne = 100 emin = 1.0 emax = 5000.0 unit = 1 axis = eng file = eng_track_12C-p-n.out gshow = 1 epsout = 1 angel = ymin(1e-11) ymax(1e-4)
-20≦z < 30 and30≦z < 80
lec02.inp
Tally for calculating physical quantities
ANGEL parameter:To change layouts of eps figures.(See the ANGEL Manual)
Few carbon ions can reach over 30 cm depth (behind Bragg peak)
51
[ T - T R A C K ] mesh = r-z r-type = 2 nr = 1 rmin = 0. rmax = 25.z-type = 1 nz = 3 -20. 0. 30. 80.part = 12C proton neutron e-type = 3 ne = 100 emin = 1.0 emax = 5000.0 unit = 1 axis = eng file = eng_track_12C-p-n.out gshow = 1 epsout = 1 angel = ymin(1e-11) ymax(1e-4)
lec02.inp
-20≦z < 0 and0≦z < 30 and30≦z < 80
Shape peak is observed in the void region (before the entrance)
Change Z-Mesh
Tally for calculating physical quantities
-20≦z < 0
0≦z < 30 30≦z < 80
Carbon energy gradually decreases
How to define Tally
52
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 …
Tally for calculating physical quantities
Change Unit
53
[ T - T R A C K ] mesh = r-z r-type = 2 nr = 1 rmin = 0. rmax = 25.z-type = 1 nz = 3 -20. 0. 30. 80.part = 12C proton neutron e-type = 3 ne = 100 emin = 1.0 emax = 5000.0 unit = 1 axis = eng file = eng_track_12C-p-n.out gshow = 1 epsout = 1 angel = ymin(1e-11) ymax(1e-4)
[ T - T R A C K ] mesh = r-z r-type = 2 nr = 1 rmin = 0. rmax = 25.z-type = 1 nz = 3 -20. 0. 30. 80. part = 12C proton neutron e-type = 3 ne = 100 emin = 1.0 emax = 5000.0 unit = 2 axis = eng file = eng_track_12C-p-n.out gshow = 1 epsout = 1 angel = ymin(1e-11) ymax(1e-4)
lec02.inp
Tally for calculating physical quantities
Change fromunit=1(1/cm2/source) tounit=2(1/cm2/MeV/source)
Change Unit
54
lec02.inp
[ T - T R A C K ] mesh = r-z r-type = 2 nr = 1 rmin = 0. rmax = 25.z-type = 1 nz = 3 -20. 0. 30. 80. part = 12C proton neutron e-type = 3 ne = 100 emin = 1.0 emax = 5000.0 unit = 2 axis = eng file = eng_track_12C-p-n.out gshow = 1 epsout = 1 angel = ymin(1e-11) ymax(1e-4)
Tally for calculating physical quantities
per energy bin width(/MeV)
Contents of Lecture II
Contents 55
Introduction and usage of “Tally” What is Tally? Kinds of Tally How to use Tally for checking geometry How to use Tally for calculating
physical quantities
Summary
Summary 56
• 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 57
• 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)
Homework
Example Answer
Homework 58
Proton (up) and neutron (down) fluences
Depth-dose distribution inside (up)and outside (down) beam radius