rad inter neutrons w. udo schröder, 2003 2 commercial neutron generator ing-03 vniia source:...
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Rad
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Commercial Neutron Generator ING-03
Source: All-Russian Research Institute of Automatics VNIIAVNIIA
1300 mm
rear connectors
source
window
Specs: < 3·1010 D(d,n)3He neutrons/s Total yield 2·1016 neutrons
Pulse frequency 1-100Hz Pulse width > 0.8 s, Power 500 W
Alternative option: T(d,n)4He, En15 MeV
Neutrons can be produced in a variety of reactions, e.g., in nuclear fission reactors or by the D(d,n)3He or T(d,n)4He reactions
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Nuclear Interactions of Neutrons
Characteristic secondary nuclear radiation/products:
1. -rays (n, )2.charged particles (n,p), (n),…3.neutrons (n,n’), (n,2n’),…4.fission fragments (n,f)
No electric charge no direct atomic ionization only collisions and reactions with nuclei 10-6 x weaker absorption than charged particles
Processes depend on available n energy En:
En ~ 1/40 eV (= kBT) Slow diffusion, capture by nuclei
En < 10 MeV Elastic scattering, capture, nucl. excitation
En > 10 MeV Elastic+inel. scattering, various nuclear reactions, secondary charged
reaction products
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Neutron Cross Sections
1b=10-
24cm2=100fm2
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Neutron Mean Free Path
FWHM 2.35
xN x N 0 e
1 1mfp
35
30
25
20
15
10
5
0
2 4 6 8 10 12 14 Neutron Energy (MeV)
0
Neutr
on M
ean F
ree P
ath
(cm
)
Mean Free Path of Neutrons in Water
: atomic density : cross section = average path length in medium between 2 collisions
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Neutron Resonance Capture
n-107Ag 108Ag*
Quantal resonance effect at low and thermal n energies wave nature of neutrons
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Energy Transfer in Elastic Scattering
|
. . : 0
11 11
1
n A n A
n A
cmLab
cm p p p p
Av v v v
A A
v vA
= - + =
= = -+ +
=+
|
|
max :
1min :
1
n Lab
n Lab
v v
Av v
A
=
-=
+
Neutron with lab velocity , energy E, scatters randomly off target nucleus of mass number A at rest in lab.
lab
labvcm|Lab
vnvn|Lab
vn
vn
( )( )
| |
|
2
| 2
max,min :
max :
1min :
1
n Lab cmLab n
n Lab
n Lab
v v v
E E
AE E
A
= ±
=
-=
+
n A
c.mc.m..
vn vA
lab velocity of center of gravity
v
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Neutron Energy Spectrum
( )( )
( ) ( ) ( )
| |
22 2
| 2
| | |
| |
| |
..... 2 cos1
sin .sin
n Lab cmLabn Lab
n Lab n Lab n Lab
n A n Lab n A n Labn A
n Lab n Lab
AE v v v v
A
dE dE dEconst
d d d
d E dP Edd dE dE
q
qq q q
ss q - --
µ = + =+
µ ® µ =W
Þ µ µW
r r
2
0 0
11
AE E
A
æ ö- ÷ç ÷ç ÷çè ø+
Neutron with energy E0 scatters off target nucleus A at rest in lab.
labvcm|Lab
vnvn|Lab
vn
vn
( )
2
02
11n
AE E
A+
=+
En
dP/d
En-A
Lab energy spectrum (1 coll.)
The laboratory energy spectrum of scattered n reflects the center-of-mass scattering
angular distribution !
=
0
o
=
180
o
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Multiple n-A Scattering
( )
( )
1
11 0 0
22 1 0
0
2
1 0
2
1
.................
1(
1
1
)
1
NN N
E E E
E E E
E E E
P EE
A
A
a
a
a
a
a
a -
é ùê ú= =ê úê úë û
= =
= =
=-
+
Þ
+
( ) ( )( )
[ ]( ) ( )
0
00 1
1
2 21
0102
0 1: ln ln
1
ln ln 1 11
ln
1 ln ( )1
221 2 ( 1 3)
E
E
A
E E dE P E dE E
x x x
EE
AA A
f EA A
a
a
a
a
a aa
x
a >
= = = =-
æ ö- +
æ
+
ö÷ç ÷ç ÷è
÷ç= = + = + ¾¾¾® ¹÷ç ÷ç ÷ç- - +è
ø
ø +
ò ò
Incoming n energy E0 = < E0>, N successive scattering events
“Logarithmic Decrement”
0ln lnNE E Nx= -
N = 1
Ei
P(E
n-A) N =
2
N =3
<E1><E2><E3>
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Thermalization Through Scattering
0ln lnNE E nx= -
0
0
( )
ln : ln ln
( )
N
N
Define E as median mean
E E E N
E N E e x
x
-
<
= = -
= ×
%
%
%
A N-therm
1 1.0000 18
12 0.1578 115
65 0.0305 597
238 0.0084 2172
N-therm: E0=2 MeV 0.025eV
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n Angular Distribution
( )
|
2 2| |
22
2
( )
1 2 cos1
1 1n cmLab
n Lab n cmLab
v vv A v
v v v
vA
A
A A
A
q
= =
= + =
é ù= + +ë û
+ +
+
r r r
1
21
1 coscos
1 2 cos
1 2cos
2 3Lab dA A A
A q
qqq
+
-
+
+=
+= ò
( )22 2 2 2| | | |
2 2 2
2 cos |: 1
1 2 cos 1 2 1 2 cos cos
n n Lab cmLab n Lab cmLab Lab
Lab
v v v v v v A
A A A A A
q
q q q
= + - +
é ù= + + + - + +ë û
labvcm|Lab
vnvn|Lab
vn
2
1 coscos
1 2 cosLab
A
A A
q
+=
+ + > 0
forward scattering
vn
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A Dependence of Angular Distribution
1
0
cos 2/ (3 )
22 3
2( ) exp
( 2 3)
( )
lab
lab
A A average
A
NE N E
A
After N collisions
q
pq
-= µ
-
ì üï ï-ï ïï ï» × í ýï ï+ï ïï ïî þ
:
%
Properties of n scattering depends on the sample mass number A
Measure time-correlated flux of transmitted or reflected neutrons
lab
lab
Light Nucleus
Heavy Nucleus
Light nuclei: slowing-down and diffusion of neutron flux
Heavy nuclei: neutrons lose less energy, high reflection/transmission
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Principle of Fast-Neutron Imaging (2)
( ) (0) ( )
( )
.A A
T
T e Transmission
N
atten coeff
material density
d
f d f d
d
m r s r
m
r
- S×
= ×
=
S = × = × ×
=
=
()
incoming transmitted
neutrons neutrons
Transmission decreases Transmission decreases exponentially (reflectivity exponentially (reflectivity increases) with thickness increases) with thickness and density of sample, and density of sample, for most materialsfor most materials.
sam
pl
e
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Neutron Diffusion
Multiple scattering = statistical processHeavy materials (A>>1): random scattering
0
1
1ln
EN
Ex
æ ö÷ç= ÷ç ÷ç ÷çè ø
1( )
x
P x e l
l
-= ×
2 2 2 2
0 02
x x
N
Mean square displacement
x N dxx e dxel l
l l¥ ¥- -
-
= = =ò ò
Probability for no collision along path length x: P(x)
Number of collisions E0 E1
for = const.
Rad
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W. Udo Schröder, 2003
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Neutron Mean Free Path
FWHM 2.35
xN x N 0 e
1 1mfp
35
30
25
20
15
10
5
0
2 4 6 8 10 12 14 Neutron Energy (MeV)
0
Neutr
on M
ean F
ree P
ath
(cm
)
Mean Free Path of Neutrons in Water
: atomic density : cross section = average path length in medium between 2 collisions
Rad
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n-Stopping and Scintillation Process
e- e-
10-7s
10-6s
10-5s
10-4s
10-8s
Prompt Injection of mn neutrons
diffusion delayed@8MeV mn interactions
GdGd
e-
e-
delayed
delayed light
Organic Scintillator Liquid Diffusion Regime
time
time=0
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MANDI-01
A Mobile Accelerator-Based Neutron Diagnostic Imager
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Neutron interactions with sample nuclei may produce characteristic secondary radiation: 1.-rays (n, )2.charged particles (n, ),…3.neutrons (n,n’)4.fission fragments (n,f)depending on the sample material
Principle of Fast-Neutron Imaging (3)
time
inte
nsi
ty
primary neutrons
secondary radiation
Secondary radiation induced by neutrons in the sample appear with the same frequency as the neutron pulses.
Detectors for characteristic secondary radiation improve recognition of sample material, reduce ambiguities.
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Required R&D• Design and construct MANDI test mounts & hardware• Measure n energy spectra and angular distributions
with and without different types of collimators.• Design and test B-loaded plastic shielding/moderator.• Perform extensive pulsed-beam coincidence
measurements of 2.5-MeV n transport through a range of materials varying in density and spatial dimensions.
• Measure n amplification in thick fissile targets• Assess sensitivity and quality of transmission and
backscattering imaging • Develop computer model simulations
• Develop large-area detectors (e.g., BF3 or BC454 B-loaded scintillation counters)
• Develop and test dedicated electronics
Sta
ge I
Sta
ge II