Transcript MANDI A Mobile Accelerator-Based Diagnostics Instrument

Commercial Neutron Generator ING-03
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
2
rear
connectors
Rad Inter Neutrons
Specs: < 3·1010 D(d,n)3He neutrons/s Total yield 2·1016 neutrons
Pulse frequency 1-100Hz Pulse width > 0.8 ms, Power 500 W
Alternative option:
T(d,n)4He, En15 MeV
W. Udo Schröder, 2003
Source: All-Russian Research Institute of
Automatics VNIIA
Nuclear Interactions of Neutrons
No electric charge  no direct atomic ionization  only
collisions and reactions with nuclei  10-6 x weaker
absorption than charged particles
Rad Inter Neutrons
3
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
Characteristic secondary nuclear radiation/products:
1. g-rays (n, g)
2. charged particles (n,p), (n, a),…
3. neutrons (n,n’), (n,2n’),…
4. fission fragments (n,f)
W. Udo Schröder, 2003
Neutron Cross Sections
Rad Inter Neutrons
4
1b=10-24cm2=100fm2
W. Udo Schröder, 2003
Neutron Mean Free Path
35
Mean Free Path of
Neutrons in Water
Neutron Mean Free Path (cm)
5
30
Rad Inter Neutrons
N  x   N 0  e x

25
1
m

1

mfp
: atomic density
: cross section
20
 = average path
length in medium
between 2 collisions
15
10
5
0

0
2
W. Udo Schröder, 2003
4
6
8
10
Neutron Energy (MeV)
12
14
 FWHM  2.35  
Neutron Resonance Capture
n-107Ag  108Ag*
Rad Inter Neutrons
6
Quantal resonance
effect at low and
thermal n energies 
wave nature of neutrons
W. Udo Schröder, 2003
Energy Transfer in Elastic Scattering
qlab
c.m. A
7
n
vn
c.m . : pn = - pA
vA
vcm|Lab
q
vn
max : vn |Lab = v
min : vn |Lab = v
W. Udo Schröder, 2003
pn + pA = 0
A
1
vA = - v
A+1
A+1
1
lab velocity of
= v
A + 1 center of gravity
vn = v
qlab
Rad Inter Neutrons
Neutron with lab velocity v , energy E,
scatters randomly off target nucleus of
mass number A at rest in lab.
vn
vcm |Lab
vn
max, min : vn |Lab = vcm |Lab ± vn
max : E n |Lab = E
2
A- 1
A+1
min : E n |Lab
(A - 1)
=E
2
(A + 1)
Neutron Energy Spectrum
8
E n |Lab µ v n |Lab
2
Rad Inter Neutrons
dE n |Lab
dq
Þ
vn
vn
r r
= v + v cm |Lab
(
µ sin q ®
dE n |Lab
dW
2
æA - 1 ö
÷
ç
÷
ç
÷ E0
èA + 1ø
2
)
µ
= ..... 2v 2
dE n |Lab
sin q d q
En
2
En =
A +1
2 E0
A
+
1
(
)
E0
A
2 cos q
(A + 1)
= const .
d s n - A (q) d s n - A (E n |Lab ) dPn - A (E n |Lab )
µ
µ
dW
dE n |Lab
dE n |Lab
W. Udo Schröder, 2003
q = 0o
vcm|Lab
vn
q = 180o
q
qlab
dP/dEn-A
Neutron with energy E0 scatters off target nucleus A at rest in lab.
Lab energy spectrum (1 coll.)
The laboratory energy
spectrum of scattered
n reflects the centerof-mass scattering
angular distribution !
Multiple n-A Scattering
N =3
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P(En-A
)
N=2
Incoming n
energy E0 = < E0>,
N successive
scattering
events
1
é A2 + 1 ù
1
ú
E 1 = êê
E
=
a
E0
0
2ú
êë(A + 1) ú
û
E2 = a E1 = a 2 E 0
.................
EN = a EN - 1 = a N E0
N=1
Þ P (E 1 ) =
Ei
Rad Inter Neutrons
<E3> <E2>
<E1>
1
(1 - a )E 0
“Logarithmic
a
æE 0 ö
1
÷
x := ln E 0 E 1 = ò dE ln çç ÷P (E ) =
dE ln E = Decrement” x
ò
aE0
1
èE ø
(1 - a )
a
2
[x ln x - x ]1
a ln a
A2 + 1 æ
A
+1ö
2
÷
ç
=
= 1+
= 1+
ln ç
¾
¾
¾®
¹ f (E 0 )
÷
A > 10
÷
çè(A + 1)2 ÷
(1 - a )
(1 - a )
2A
A
+
2
3
ø
(
W. Udo Schröder, 2003
)
E0
ln E N = ln E 0 - N x
Thermalization Through Scattering
ln E N = ln E 0 - n x
Define E%as median (< mean )
10
ln E%:= ln E N = ln E 0 - N x
E%(N ) = E 0 ×e - N x
N-therm: E0=2 MeV  0.025eV
Rad Inter Neutrons
A
W. Udo Schröder, 2003
x
N-therm
1
1.0000
18
12
0.1578
115
65
0.0305
597
238
0.0084
2172
n Angular Distribution
qlab
vn
v
vn n
11
vcm|Lab
q
v
v
vn =
A
vcm |Lab =
A+1
A+1
r2
r
r
vn |Lab = (vn + vcm |Lab )2 =
v2
2
é
=
A
+ 1 + 2A cos qù
2 ë
û
(A + 1)
2
vn2 = vn2|Lab + vcm
|Lab - 2vn |Labvcm |Lab cos qLab
2
|: v 2 (A + 1)
Rad Inter Neutrons
2
A 2 = éëA 2 + 1 + 2A cos qù
+
1
2
A
+ 1 + 2A cos q cos qLab
û
cos qLab =
cos qLab
1 + A cos q
A 2 + 1 + 2A cos q
1 +1
1 + A cos q
2
= ò d cos q
=
2
1
2
3A
A + 1 + 2A cos q
W. Udo Schröder, 2003
>0 
forward
scattering
A Dependence of Angular Distribution
Properties of n scattering depends on the sample mass number A
 Measure time-correlated flux of transmitted or reflected neutrons
Light Nucleus
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qlab
qlab :
Heavy Nucleus
qlab
Rad Inter Neutrons
cos qlab = 2 / (3A ) µ A - 1 average
p
2
2 3A
ìï - 2N ü
ïï
ï
E%(N ) » E 0 ×exp í
ý
ïï (A + 2 3) ïï
ï
îï
þ
(A fter N collisions )
Light nuclei: slowing-down and diffusion of neutron flux
Heavy nuclei: neutrons lose less energy, high reflection/transmission
W. Udo Schröder, 2003
Principle of Fast-Neutron Imaging (2)
neutrons
sample
neutrons
f0
 d 
transmitted
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incoming
f(d)
f (d) = f (0) ×T (d)
T (d) = e
- S ×d
T ransmission
Rad Inter Neutrons
S = m ×r = N A ×s A ×r
Transmission decreases
exponentially (reflectivity
increases) with thickness and
density of sample, for most
materials.
W. Udo Schröder, 2003
m = atten . coeff
r = material density
Neutron Diffusion
Multiple scattering = statistical process
Heavy materials (A>>1): random scattering
ö
1 æ
E
0
÷
N = ln çç ÷
÷
÷
x çèE 1 ø
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Number of collisions E0  E1
Probability for no collision along path length x: P(x)
1 - lx
P (x ) = ×e
l
for  = const.
Rad Inter Neutrons
Mean - square displacement
x
2
N
=N l
W. Udo Schröder, 2003
2
=
ò
¥
0
2 -x l
dx x e
ò
¥
0
dx e
-x l
= 2l
2
Neutron Mean Free Path
35
Mean Free Path of
Neutrons in Water
Neutron Mean Free Path (cm)
15
30
Rad Inter Neutrons
N  x   N 0  e x

25
1
m

1

mfp
: atomic density
: cross section
20
 = average path
length in medium
between 2 collisions
15
10
5
0

0
2
W. Udo Schröder, 2003
4
6
8
10
Neutron Energy (MeV)
12
14
 FWHM  2.35  
n-Stopping and Scintillation Process
Organic Scintillator Liquid
g
e-
Diffusion
Regime
delayed
light
g
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eg
Gd
g
e-
e-
g
10-4s
10-5s
10-6s
10-7s
Prompt
Injection of
mn neutrons
10-8s
Rad Inter Neutrons
delayed
time
time=0
W. Udo Schröder, 2003
diffusion delayed@8MeV mn
interactions
A Mobile Accelerator-Based Neutron Diagnostic Imager
Rad Inter Neutrons
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MANDI-01
W. Udo Schröder, 2003
Principle of Fast-Neutron Imaging (3)
secondary
radiation
time
Rad Inter Neutrons
18
intensity
primary
neutrons
Secondary radiation induced by
neutrons in the sample appear with
the same frequency as the neutron
pulses.
Neutron interactions with
sample nuclei may produce
characteristic secondary
radiation:
1.g-rays (n, g)
2.charged particles (n, a),…
3.neutrons (n,n’)
4.fission fragments (n,f)
depending on the sample
material
Detectors for characteristic secondary radiation improve recognition
of sample material, reduce ambiguities.
W. Udo Schröder, 2003
Stage I
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Stage II
Rad Inter Neutrons
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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 Bloaded scintillation counters)
Develop and test dedicated electronics
W. Udo Schröder, 2003