Transcript MANDI A Mobile Accelerator-Based Diagnostics Instrument

Backscatter neutron spectrometer
Nuclear Interactions of Neutrons
Rad Inter Neutrons
2
No electric charge  no direct atomic ionization
Magnetic moment  interaction with magnetized materials
Collisions and reactions with nuclei 
10-6 x weaker absorption than for charged particles
Processes depend on available n energy En:
En ~ 1/40 eV
(= kBT) Slow diffusion, capture by nuclei
En <
10 MeV
En >
10 MeV
Elastic scattering, capture, nucl. excitation
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, 2011
Neutron Cross Sections
3
n-hydrogen
n-carbon
Rad Inter Neutrons
1b=
10-24cm2
=100fm2
W. Udo Schröder, 2011
Neutron Mean Free Path
Mean Free Path of Neutrons in Water
Pass x without collision :
Ps ( x )  N  x  N 0   e  x

Gaussian Prob.Distribution
(Range Straggling)
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 x x
dN( x )
 
 exp  
2
dx
2


x

2




Rad Inter Neutrons
W. Udo Schröder, 2011
x  ;  x2  2   2
FWHM  2.35   x

Los Alamos nuclear data files
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

1

(mfp)
 = average path length in medium
between 2 collisions
: number density (atoms/ volume),
: cross section
Neutron Diffusion
In very thick absorbers, e.g., water tanks, concrete walls:
Multiple scattering = statistical process
Heavy materials (A>>1): random scattering
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Probability for no collision along path length x: Ps(x)
Probability for collisions at [x, x+dx]: dPcoll=-dN/N(x)=-1/
x
Rad Inter Neutrons
(
)
dPcoll (x ) d N coll N (x )
dPs (x ) = e dx ®
=
= 1l
dx
dx
Mean - square displacement along trajectory
-
2
N
x
l
=N l
2
=
ò
¥
2 - x l
dx x e
0
ò
¥
dx e
- x l
= 2l
for  = const.
2
0
But E ¹ const . ® l ¹ const ., N collisions :
E 0 ® .... ® E N » E 0e
W. Udo Schröder, 2011
- Nx
ö
E
1 æ
÷
; logarithmic decrem . x =
ln ççç 0 ÷
÷
N çèE N ÷
ø
Energy Transfer in Elastic Scattering
qlab
c.m. A
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n
vn
c.m . : pn = - pA
A
vn = v
A+1
vA
q
qlab
vcm|Lab
Rad Inter Neutrons
Neutron with lab velocity v , energy E,
scatters randomly off target nucleus of
mass number A at rest in lab.
vn
W. Udo Schröder, 2011
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vA = - v
A+1
1
A+1
lab velocity of
center of gravity
vn
vcm |Lab = v
vn
max, min : vn |Lab = vcm |Lab ± vn
max : E n |Lab = E
max : vn |Lab = v
min : vn |Lab = v
pn + pA = 0
2
A- 1
A+1
min : E n |Lab
A - 1)
(
=E
(A + 1)
2
Scattered-Neutron Energy Spectrum
Neutron with energy E0 scatters off
target nucleus A at rest in lab.
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vn
q = 0o
vn
q = 180o
vcm|Lab
vn
dP/dEn
q
qlab
Lab energy spectrum (1 coll.)
En
2
2
æA - 1 ö
÷
ç
÷
ç
÷ E0
èA + 1ø
E n |Lab µ v
2
2
r r
= v+v
(
n |Lab
cm |Lab
) = vr
r
r
= v2 + v2
+ 2v 2
Rad Inter Neutrons
dq
Þ
µ sin q ®
d s n - A (q)
dW
W. Udo Schröder, 2011
µ
dE n |Lab
dW
(
µ
d s n - A E n |Lab
dE n |Lab
r
+ v2
cm |Lab
A
2
dE n |Lab
sin q d q
E0
cm |Lab
cos q
= const .
) µ dP (E
n- A
A +1
2 E0
(A + 1)
r r
+ 2v ×v
(A + 1)
cm |Lab
dE n |Lab
2
En =
n |Lab
dE n |Lab
)
The laboratory energy
spectrum of scattered
n reflects the centerof-mass scattering
angular distribution !
Multiple n-A Scattering
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Incoming neutron
energy E0
N successive
elastic scatterings
E2
EN = a EN - 1 = a N E0
N=1
Ei
<E3> <E2>
E1
é 2
ù
êA + 1 ú
1
ú
= ê
E
=
a
E0
0
êA + 1 2 ú
) úû
êë(
= a E 1 = a 2E 0
.................
N=2
P(En-A)
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N =3
<E1>
Þ P (E 1 ) =
1
(1 - a )E
0
ln E N » ln E 0 - N x ® E N » E 0 ×e - N x
Evaluate “Logarithmic Decrement” x
Rad Inter Neutrons
a
éx ln x - x ù
æE ö÷
E0
a
1
êë
úû1
x := ln E 0 E 1 = ò dE ln ççç 0 ÷
P
E
=
dE
ln
E
=
(
)
aE0
÷
çè E ø÷
(1 - a ) ò1
(1 - a )
2
ö
a ln a
A2 + 1 æ
A
+1÷
2
ç
÷
= 1+
= 1+
ln ç
¾
¾
¾®
¹ f (E 0 )
A > 10
2÷
ç
çè(A + 1) ÷
2A
A+ 23
ø
(1 - a )
(
W. Udo Schröder, 2011
)
Thermalization Through Scattering
ln E N = ln E 0 - N x
Define E%as median (< mean )
ln E%:= ln E N = ln E 0 - N x
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E%(N ) = E 0 ×e - N x
N-therm: E0=2 MeV  0.025eV
Rad Inter Neutrons
A
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x
N-therm
1
1.0000
18
12
0.1578
115
65
0.0305
597
238
0.0084
2172
Slow-Neutron Resonance Capture
n-107Ag  108Ag*
Rad Inter Neutrons
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Quantal resonance effect at low
and thermal n energies  wave
nature of neutrons
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Excited
Ag* nucleus
deexcites
and/or bdecays
n-Stopping and Scintillation Process in Thick Detector
Prompt Injection of m neutrons
n1
Fast Moderation Process
Organic Scintillator
g
e-
Diffusion
Regime
delayed
light
g
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e-
n2
g
n3
Rad Inter Neutrons
10-4s
10-5s
10-6s
i
g
e-
e10-7s
 LOPi
10-8s
LOP 
delayed
Gd
Gd
g
time
time=0
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diffusion delayed@8MeV mn
interactions
SuperBall Neutron Calorimeter
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Rad Inter Neutrons
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2 signals of
equal total
light output
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I
Q1-Q2
Pulse Shape Analysis
Q1 
t1
t1
 I(t )dt
t0
Q2 
t2
t2
 I(t )dt
fast
component
slow
t1
Q1  Q2  Q  L(Energy )
W. Udo Schröder, 2011
Q1-Q2
Rad Inter Neutrons
t0
Total n-H Cross Section Parameterization
Approximate parameterization for
applications (detector efficiency estimates)
Cross section in barns (b)
1b = 10-24cm2
 n (E) 
3 b
1.206 E   1.86  0.0941E  0.0001306 E 2 

b
1.206 E   0.4223  0.13E 
2
2
Rad Inter Neutrons
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Non-Linear Light Output Response
For a given energy,
electrons & photons have
the highest light output
W. Udo Schröder, 2011
NE 213 liquid scintillator:
e-equivalent energies Ee  Ep


 0.18MeV 1 2 E p3 2 E p  5.25MeV
Ee (E p )  
0.63E p  1.10MeV E p  5.25MeV
Thin-Detector Light Output Response
1 Light Output Response 5”x2” NE-213
1.5
2.0
Neutron Energy
2.1
Rad Inter Neutrons
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2.5
3.0 MeV
Thin detector:
1 n-p interaction within
detector (n leaves)
Equivalent to g-e Compton
Each fixed neutron energy
produces recoil proton
energy (Ep) distribution 
produces distribution in LO
(light output).
LO response is calibrated
with g-rays  electronequivalent energy Eee (eVee).
Equivalent to full-energy peak?
 Thick detector (many  thick)
W. Udo Schröder, 2011
Convert measured Eee  Ep
Unfold Ep distribution
Efficiency of p-Recoil NeutronDetectors
F1
F2
q = 0o
5”x2” NE-213
En
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dP/dEp
angle dependent n-p energy transfer  continuous recoil energy spectrum
ET
Rad Inter Neutrons
Electronic
detector threshold
 (En , ET ) 
Ep=En
F2
F1  F2

ET 
  (En ) 1 

E
n 

 (En )    X (n,y )(En ) all n  induced
X ,y
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ET
Detector Efficiency Estimates
Rad Inter Neutrons
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 ETh
  E , ETh , d   1 
E

Eth=1 MeV
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
  1  exp    n ( E )  nH  d 

Detector thickness
d =10cm
Hydrogen density
(atoms/cm3) NE-213
nH=4.86·1022/cm3
Approximate intrinsic
detection efficiency
(E)
Probability for
detection if incident
neutron trajectory is
perpendicular to
detector face.
Total efficiency
contains (E) and
solid-angle factor DW.
Associated-Particle/Neutron TOF
Reference time-zero t0: true TOF = tmeas-t0
a) from accelerator signal,
b) associated particle* of known E
c) g-ray* (v=c)
*measured with same or different detector
d
Rad Inter Neutrons
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d= target-detector flight distance
tg
Non  relativistically :
m
m d 
E  2  

2
2  t  t0 
Spectrum
2
dN ( E ) dN  t ( E )  dt


dE
dt
dE
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Rad Inter Neutrons
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n Angular Distribution
qlab
vn
v
vn n
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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
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>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
A verage scattering R
cos qlab = 2 / (3A ) µ A - 1
qlab :
Heavy Nucleus
Rad Inter Neutrons
qlab
p
2
2 3A
ìï
ü
ïï
2
N
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, 2011
Principle of Fast-Neutron Radiography(Imaging)
neutrons
neutrons
sample
Comparison of different radiations
f0
Rad Inter Neutrons
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incoming
 d 
f(d)
transmitted
f (d) = f (0) ×T (d)
T (d) = e - S ×d T ransmission
S = m ×r = N A ×s A ×r
m = atten . coeff
r = material density
Transmission decreases exponentially (reflectivity increases) with
thickness and density of sample.
Neutrons more penetrating  use for thick samples
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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
Rad Inter Neutrons
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rear
connectors
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, En14.5 MeV
W. Udo Schröder, 2011
Source: All-Russian Research Institute of
Automatics VNIIA
A Mobile Accelerator-Based Neutron Diagnostic Imager
Rad Inter Neutrons
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MANDI-01
W. Udo Schröder, 2011
Principle of Fast-Neutron Imaging (3)
secondary
radiation
time
Rad Inter Neutrons
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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, 2011
Stage I
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, 2011