PHITS
Multi-Purpose Particle and Heavy Ion Transport code System
Basic Lecture II:
Definition of Tally
Oct. 2014 revised
title
1
Purpose of This Lecture
Learn how to deduce various physics
quantities from the PHITS simulation
You can obtain this kind of results at the end of this lecture
Particle fluence (left) and depth-dose distribution (right)
for the simulation condition for homework
Purpose
2
Contents of Lecture II
 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 Tally
 Summary
Contents
3
What is Tally?
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 to
 Deduce physical quantities such as flux and heat,
or
 Depict the 2D or 3D geometry in certain area
What is tally?
4
Concept of Tally
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”
How many particles were
passed through this region?
→ Use “track-length” tally
Result of [t-track] (Track-length tally)
What is tally?
5
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…
 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]
Kinds of Tally in PHITS
6
Visualize Particle Trajectory
z-axis
x-axis
method of track detection
7
Visualize Particle Trajectory
z-axis
x-axis
method of track detection
8
Visualize Particle Trajectory
z-axis
x-axis
method of track detection
9
Visualize Particle Trajectory
z-axis
x-axis
method of track detection
10
Visualize Particle Trajectory
z-axis
x-axis
method of track detection
11
Contents of Lecture II
 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 Tally
 Summary
Contents
12
Geometry Check
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!
Tally for checking geometry
13
Exercise 1
Confirm the geometry of lec02.inp in 2 dimensions
using [t-gshow] tally.
• Copy & paste 2 [t-gshow] sections from t-gshow.inp.
• Set icntl=7 in [parameters] section and execute PHITS.
lec02.inp
[Material]
mat[1] 1H 2 16O 1
・・・・・・
[Surface]
10 so
500.
11 cz
10.
12 pz
0.
13 pz
50.
[Cell]
100 -1
10
101
1 -1. -11 12 -13
110
0
-10 #101
10 cm
A water cylinder with a radius of 10 cm and
a height of 50 cm.
50 cm
Tally for checking geometry
14
Answer 1
Confirm the geometry of lec02.inp in 2 dimensions
using [t-gshow] tally.
lec02.inp
[Parameters]
icntl = 7
・・・・・・
[T-Gshow]
・・・・・・
axis = xy
file = gshow_xy.out
output = 6
epsout = 1
[T-Gshow]
・・・・・・
axis = xz
output = 6
file = gshow_xz.out
epsout = 1
gshow_xy.eps
xy-plane
The radius is
10cm.
gshow_xz.eps
xz-plane
The height is
50cm.
Tally for checking geometry
15
Exercise 2
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.
gshow_xy.eps
gshow_xz.eps
How is this geometry shown in 3 dimensions?
Tally for checking geometry
16
Answer 2
Confirm the geometry of lec02.inp in 3 dimensions
using [t-3dshow] tally.
lec02.inp
[Parameters]
icntl = 11
・・・・・・
Y
・
Z
[T-3Dshow]
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
・・・・・・
X
3dshow.eps
Tally for checking geometry
17
Parameters used in [t-3dshow]
Polar
coordinates
Eye Point
(e-the,e-phi,e-dst)
Picture Flame
Polar
Coordinates
Light source
(l-the,l-phi,l-dst)
e-dst
w-dst
w-hgt
(w-mnh)
w-wdt
(w-mnw)
w-mnw × w-mnh ＝ #Pixel
100 × 100 (default)
Origin (x0,y0,z0) XYZ-coordinates
Tally for checking geometry
18
Exercise 3
lec02.inp
Let’s rotate the picture.
[T-3Dshow]
output = 3
x0 = 0
y0 = 0
Rotate zenith angle of
z0 = 20
eye-point by 45 deg
e-the = 135
90 $$ eye
eye
e-phi = 0
45
Rotate azimuthal angle
e-dst = 120
of eye-point by 45 deg
l-the = 90 $ light
l-phi = 0
l-dst = 100
w-wdt = 50 $ window
w-hgt = 50
w-dst = 30
heaven = y
“Heaven” is Y direction
mirror = 0
line = 1
shadow = 2
resol = 1
file = 3dshow.out
title = Check geometry using [T-3dshow] tally
epsout = 1
Y
YY
Z
ZZ
・
X
X
X
3dshow.eps
Tally for checking geometry
19
Contents of Lecture II
 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 Tally
 Summary
Contents
20
How to define Tally
You have to determine …
 What kind of physical quantity
Select type of tally: [t-track], [t-deposit] etc.
 in where
Select geometrical mesh: mesh= reg, xyz, r-z
 of 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.
Tally for calculating physical quantities
21
Example of [t-track] tally (in t-track.inp).
[T-TRACK]
title = Track Detection in xyz mesh
mesh = xyz
x-type = 2
nx = 25
xmin = -25.
xmax = 25.
Geometrical
y-type = 2
ny = 25
mesh
ymin = -25.
ymax = 25.
z-type = 1
Unit of
nz = 1
output
-5.0 5.0
e-type = 1
ne = 1
0.0 5000.0
Output form
unit = 1
axis = xy
file = track_xy.out
part = all
gshow = 1
Particle type
epsout = 1
• [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
Tally for calculating physical quantities
22
Exercise 4
Confirm particle fluence using [t-track] tally.
• Copy & paste 2 [t-track] sections from t-track.inp.
• Set “icntl=0” in [parameters] section and execute PHITS.
lec02.inp
[Source]
s-type = 1
proj = 12C
dir = 1.0
r0 = 2.5
z0 = -10.
z1 = -10.
e0 = 250.
A carbon beam
of 250MeV/u
How is the behavior of the particles?
Tally for calculating physical quantities
23
Answer 4
Confirm particle fluence using [t-track] tally.
lec02.inp
[Parameters]
icntl = 0
・・・・・・
[T-Track]
・・・・・・
axis = xy
file = track_xy.out
part = all
gshow = 1
epsout = 1
[T-Track]
・・・・・・
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.
Tally for calculating physical quantities
24
Answer 4
Confirm particle fluence using [t-track] tally.
lec02.inp
track_xy.eps
[Parameters]
icntl = 0
・・・・・・
[T-Track]
・・・・・・
axis = xy
file = track_xy.out
part = all
gshow = 1
epsout = 1
[T-Track]
・・・・・・
axis = xz
file = track_xz.out
part = all
gshow = 1
epsout = 1
track_xz.eps
A carbon beam of 250MeV/u with a radius of 2.5cm
Tally for calculating physical quantities
25
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.
track_xy_err.eps
track_xz_err.eps
Tally for calculating physical quantities
26
How to define Tally
You have to determine …
 What kind of physical quantity
Select type of tally: [t-track], [t-deposit] etc.
 in where
Select geometrical mesh: mesh= reg, xyz, r-z
 of 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.
Tally for calculating physical quantities
27
Geometrical Mesh
lec02.inp
[T-TRACK]
・・・・・・
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 5.0
e-type = 1
ne = 1
0.0 5000.0
unit = 1
axis = xy
file = track_xy.out
part = all
gshow = 1
epsout = 1
mesh = xyz
:Define tally region according
to xyz coordinates
⇒ You need to specify
x-type, y-type, z-type
X-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）
Tally for calculating physical quantities
28
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
1: Define #mesh and
their boundaries
e-type = 1
ne = 10
0 1 2 3 5 10
15 20 30 50 100
2,3: Define #mesh and their minimum & maximum values
(2: linear, 3: logarithmic interval)
e-type = 2
ne = 100
emin = 0
emax = 1000
e-type = 3
ne = 100
emin = 0.1
emax = 5000
4,5: Define interval of mesh and their minimum & maximum values
(4: linear, 5: logarithmic interval)
e-type = 4
edel = 100
emin = 0
emax = 5000
e-type = 5
edel = 1.301 =log10(20)
emin = 0.1
emax = 5000
Replace “e” to “x” if you
want to define x-mesh
Tally for calculating physical quantities
29
Geometrical Mesh Types
There are 3 types of geometrical mesh in PHITS
xyz mesh:
r-z mesh:
reg mesh:
Divide the regions
in XYZ coordinates
Divide the regions
in Cylindrical coordinates
Divide the regions
in cells defined in
PHITS virtual space
Z
R
Z
Y
X
Tally for calculating physical quantities
30
Exercise 5
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_xy.eps
track_xz.eps
A higher resolution is needed.
Tally for calculating physical quantities
31
Answer 5
In order to look the figures more clearly, increase
the number of mesh in the [t-track] tally.
lec02.inp
[T-TRACK]
・・・・・・
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
track_xy.eps
We can look the figure
with good resolution
by increase nx and ny.
Tally for calculating physical quantities
32
Answer 5
In order to look the figures more clearly, increase
the number of mesh in the [t-track] tally.
lec02.inp
[T-TRACK]
・・・・・・
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.
・・・・・・
axis = xz
file = track_xz.out
part = all
gshow = 1
epsout = 1
track_xz.eps
Tally for calculating physical quantities
33
How to define Tally
You have to determine …
 What kind of physical quantity
Select type of tally: [t-track], [t-deposit] etc.
 in where
Select geometrical mesh: mesh= reg, xyz, r-z
 of 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.
Tally for calculating physical quantities
34
Exercise 6
Show the fluence of each particle separately.
• Replace “part=all” in the [t-track] tally with
“axis=xz” by “part=12C proton neutron”.
lec02.inp
track_xz.eps
[T-TRACK]
・・・・・・
axis = xz
file = track_xz.out
part = all
gshow = 1
epsout = 1
How are the behaviors of 12C, proton,
and neutron?
Tally for calculating physical quantities
35
Answer 6
Show the fluence of each particle separately.
track_xz.eps
lec02.inp
[T-TRACK]
・・・・・・
axis = xz
file = track_xz.out
part = 12C proton neutron
gshow = 1
epsout = 1
12C
proton
neutron
Tally for calculating physical quantities
36
How to define Tally
You have to determine …
 What kind of physical quantity
Select type of tally: [t-track], [t-deposit] etc.
 in where
Select geometrical mesh: mesh= reg, xyz, r-z
 of 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.
Tally for calculating physical quantities
37
Exercise 7
Show the particle fluence as a function of
its energy.
lec02.inp
[T-TRACK]
・・・・・・
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.
e-type = 1
ne = 1
0.0 5000.0
unit = 1
axis = xz
file = track_xz.out
・・・・・・
• 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”.
Tally for calculating physical quantities
38
Answer 7
Show the particle fluence as a function of
its energy.
lec02.inp
[T-TRACK]
・・・・・・
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.
e-type = 2
ne = 100
$
0.0 5000.0
emin = 0.0
in “MeV”
emax = 5000.0
(not MeV/n)
unit = 1
axis = eng
file = track_eng.out
・・・・・
track_eng.eps
The beam energy is
250×12=3000MeV
Energy distribution of each particle
Tally for calculating physical quantities
39
Exercise 8
Change the horizontal axis to Logarithmic scale.
• Set “e-type=3” and “emin=1.0”.
lec02.inp
track_eng.eps
[T-TRACK]
・・・・・・
e-type = 2
ne = 100
$
0.0 5000.0
emin = 0.0
emax = 5000.0
unit = 1
axis = eng
file = track_eng.out
・・・・・
This figure is shown in linear scale.
Tally for calculating physical quantities
40
Answer 8
Change the horizontal axis to Logarithmic scale.
lec02.inp
track_eng.eps
[T-TRACK]
・・・・・・
e-type = 3
ne = 100
$
0.0 5000.0
emin = 1.0
emax = 5000.0
unit = 1
axis = eng
file = track_eng.out
・・・・・
We can confirm the low energy region in detail.
Tally for calculating physical quantities
41
Exercise ９
Show the energy distributions on the inside
and outside of the cylinder.
lec02.inp
[T-TRACK]
mesh = xyz
Add “reg parameter”
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.
delete
・・・・・・
• 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
Tally for calculating physical quantities
42
Answer ９
Show the energy distributions on the inside
and outside of the cylinder.
lec02.inp
[T-TRACK]
mesh = reg
reg = 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.
・・・・・・
Tally for calculating physical quantities
In water
outside
43
Exercise 10
Confirm energy deposition using [t-deposit] tally.
• Copy & paste [t-deposit] section from t-deposit.inp.
t-deposit.inp
[ T - Deposit ]
title = Energy deposition in xyz mesh
mesh = xyz
・・・・・・
unit = 1
material = all
output = dose
axis = xz
file = deposit.out
part = all
gshow = 1
epsout = 1
• [T-deposit]: Tally for calculating
deposit energy in materials
Tally for calculating physical quantities
44
Answer 10
Confirm energy deposition using [t-deposit] tally.
deposit.eps
Energy deposition by
the carbon beam.
Energy deposition by the
secondary particles.
Tally for calculating physical quantities
45
How to define Tally
You have to determine …
 What kind of physical quantity
Select type of tally: [t-track], [t-deposit] etc.
 in where
Select geometrical mesh: mesh= reg, xyz, r-z
 of 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.
Tally for calculating physical quantities
46
Exercise 11
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
[ T - Deposit ]
title = Energy deposition in xyz mesh
mesh = xyz
・・・・・・
unit = 1
material = all
output = dose
axis = xz
file = deposit.out
part = all
gshow = 1
epsout = 1
Calculating deposit energy in
the unit of Gy=J/kg.
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]
Tally for calculating physical quantities
47
Answer 11
Change the unit of the output of the [t-deposit]
tally, [MeV/cm3/source], to [Gy/source].
lec02.inp
[ T - Deposit ]
title = Energy deposition in xyz mesh
mesh = xyz
・・・・・・
unit = 0
material = all
output = dose
axis = xz
file = deposit.out
part = all
gshow = 1
epsout = 1
deposit.eps
The unit and its scale
have changed.
Tally for calculating physical quantities
48
Exercise 12
Show z-distribution of the energy deposition in
the water cylinder using r-z mesh.
lec02.inp
[ 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
・・・・・・
• 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”.
Tally for calculating physical quantities
49
Answer 12
Show z-distribution of the energy deposition in
the water cylinder using r-z mesh.
lec02.inp
deposit.eps
[ 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 = z
file = deposit.out
・・・・・・
A Bragg peak of the carbon
beam is shown at z=12cm.
Tally for calculating physical quantities
50
Exercise 13
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.
Tally for calculating physical quantities
51
Answer 13
Using ANGEL, change the region of y-axis in
deposit.eps.
deposit.eps
deposit.out
・・・・・・
#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
・・・・・・
Setting Angel parameters, you
can adjust some conditions of
graphs.
The region between 10-11and 10-9
for the vertical axis is shown.
Tally for calculating physical quantities
52
Contents of Lecture II
 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 Tally
 Summary
Contents
53
List of All Tallies in PHITS
Deduce physical
quantity
Visualize geometry
[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
Kinds of tally in PHITS
54
[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
Kinds of tally in PHITS
55
[t-3dshow](for your FUN!)
You can rotate [t-3dshow] picture using Python software
See “/phits/utility/rotate3dshow” in more detail
Tally for checking geometry
56
[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)
Kinds of tally in PHITS
57
[t-track]
• 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)
You can visualize the
trajectory of particle
using [t-track] by setting
small mesh for tallying
regions
Kinds of tally in PHITS
58
[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(q)
Kinds of tally in PHITS
59
[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
Kinds of tally in PHITS
60
[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
Kinds of tally in PHITS
61
[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]
Kinds of tally in PHITS
62
[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
*SED represents
Specific Energy Distribution
Example of [t-let] tally
Kinds of tally in PHITS
63
[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
Kinds of tally in PHITS
64
[t-dchain]
• 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
Irradiation
Cooling
Time dependence of radioactivities inside water phantom irradiated by 150 MeV proton for 6 min
Kinds of tallies in PHITS
65
Contents of Lecture II
 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 Tally
 Summary
Contents
66
Summary
• 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 …
 what kind of physical quantity
 in where
 of what particle
 in which unit
 in what output form
Summary
67
Homework
• 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
68
Example Answer
Proton (up) and neutron (down) fluences
Depth-dose distribution inside (up)
and outside (down) beam radius
Homework
69