Rad

In

ter

Neu

tron

s

W. Udo Schröder, 2003

2

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

Rad

In

ter

Neu

tron

s

W. Udo Schröder, 2003

3

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

Rad

In

ter

Neu

tron

s

W. Udo Schröder, 2003

4

Neutron Cross Sections

1b=10-

24cm2=100fm2

Rad

In

ter

Neu

tron

s

W. Udo Schröder, 2003

5

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

In

ter

Neu

tron

s

W. Udo Schröder, 2003

6

Neutron Resonance Capture

n-107Ag 108Ag*

Quantal resonance effect at low and thermal n energies wave nature of neutrons

Rad

In

ter

Neu

tron

s

W. Udo Schröder, 2003

7

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

Rad

In

ter

Neu

tron

s

W. Udo Schröder, 2003

8

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

Rad

In

ter

Neu

tron

s

W. Udo Schröder, 2003

9

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>

Rad

In

ter

Neu

tron

s

W. Udo Schröder, 2003

10

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

Rad

In

ter

Neu

tron

s

W. Udo Schröder, 2003

11

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

qq

q

+=

+ + > 0

forward scattering

vn

Rad

In

ter

Neu

tron

s

W. Udo Schröder, 2003

12

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

Rad

In

ter

Neu

tron

s

W. Udo Schröder, 2003

13

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

Rad

In

ter

Neu

tron

s

W. Udo Schröder, 2003

14

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

In

ter

Neu

tron

s

W. Udo Schröder, 2003

15

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

In

ter

Neu

tron

s

W. Udo Schröder, 2003

16

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

Rad

In

ter

Neu

tron

s

W. Udo Schröder, 2003

17

MANDI-01

A Mobile Accelerator-Based Neutron Diagnostic Imager

Rad

In

ter

Neu

tron

s

W. Udo Schröder, 2003

18

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.

Rad

In

ter

Neu

tron

s

W. Udo Schröder, 2003

19

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