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1

DSP algorithms for fission fragment and

prompt fission neutron spectroscopy

Sh. Zeynalov1,2, O.V. Zeynalova2, F.-J. Hambsch1, S. Oberstedt1, I. Fabry1

1)EC-JRC-Institute for Reference Materials and Measurements, Retieseweg 111, B-2440 Geel, Belgium2)JINR-Joint Institute for Nuclear Research, Dubna Moscow region, Russia

2

Data acquisition system

3

Digitized waveforms structure

Event = А1, А2, K, N

Cathode pulse used as a fission event

time reference

Energy released inside the 1st and the 2nd

half of the TGIC ND signal used for the neutron TOF

measurement after pulse shape analysis

A1

A2

K

N

The trigger pulse

L samples M samples

Waveforms sampled with 100

MHz WFD 12 bit amplitude

resolution

The actual trigger position L has the mean value (L-0.5)∆

and the dispersion σ =0.3 ∆

4

Analogue signal processing

Traditional analogue electronics approach when each module performs a dedicated signal processing.

Detector current is converted into a step pulse in a charge-sensitive preamplifier. The height of the step pulse conveys

information on the FF’s kinetic energy, released during deceleration in the working gas of the IC. The algorithm for precise

pulse height measurement is widely accepted for about 50 y in experimental nuclear physics and it is implemented in a

variety of commercially available electronic modules. In a spectroscopy amplifier the pulse undergoes first differentiation,

and then the result is integrated by a shaping filter in order to improve the SNR. The peak value of the shaped pulse is

measured with the help of an ADC and the numerical value is transferred to the PC, where the desired pulse height

distributions can be accumulated and displayed on demand.

5

DSP approach

Spectroscopic amplifier

Peak sensitive ADC

Multichannel analyser

CFD and TAC

Pulse shape analyser

And many other very useful devices….

The DSP approach uses a single waveform digitizer module and a variety of software to suit different experimental needs.

( ) (τ) ( τ) τ

0

V t I h t d∞

= −∫

0 0

( ∆) ( ∆) (( )∆)k n kn

n n

V k I n h k n V I h∞ ∞

= =

= − ⇒ =∑ ∑

Continuous and discrete form relations

between the detector current pulse (In) and the

preamplifier output signal (Vk) are as follows:

6

Basic maths for spectroscopy amplifier

0

( τ )( ), ( ) и (τ) τ ,

τ

In In O ut O ut Int In

k k k

dW kV V k V V k V V d

d

∞∆ −

= ∆ = ∆ = ∫

,1

Int Int InV V A V

k k k= × +

+.Out Int In

V V Vk k k

= −

0 0

(τ) ( τ)( ) ( τ) τ ( ) (0) (τ) τ

τ τ

t tInOut In IndV dW t

V t W t d V t W V dd d

−= − = −∫ ∫

τ 1 τ(τ ) exp , exp( )

τ

dWW

A d A A= − = × −

The differentiating formula

The kernel function describing a signal passing through an RC circuit

Sampling is the way to convert continuous signal to discrete

Matrix representation of discrete signals and equations

7

50000.00

0.01

0.02

0.03

0.04

0.05

Time [nsec]

Pu

lse h

eig

ht

[V]

RC = 800 nsec

Step function

CR-RC

RC2 - integration

RC3 - integration

RC4 - integration

RC5 - integration

4950

0

50

100

Cu

rre

nt

[arb

itra

ry]

Time [nsec]

100 2000

5000

10000

Co

un

ts

Pulse height [arb.]

100 2000

2000

4000

6000

8000

Co

un

ts

Drift time [arb.]

∑+

=

=ML

k

kIkT1

][*kknnnknk VhIIhV *)(* 1−=⇒=

Fission fragment pulse processing

8

FF angle determination

100 150 200

100

200

T90

T0(E)

Pulse height [arb.]

Drift tim

e [a

rb.]

1θ

2θ

0.0 0.5 1.00.0

0.5

1.0

CO

S(Q

2 )

COS(Q1)

FF 0 and 90for drift time the-T,T ,)cos(*))(()( 0o

09009090 ΘΕ−=− TTETT

city drift velo theis W distances;A -G theis d andG -C theis D where,*5.0

90W

dDT

+=

uesheight val pulse original and corrected are P P ,*

* OC

90

90 andTT

TPP

OC

σ+=

is the grid inefficiency factorσ

100 150 20040

60

80

100

120

140

T0(E

) [a

rb.]

FF kinetic energy [arb]

Backing side

Layer side

9

FF’s energy loss correction

80 90 100 110 120 130 140 150 160 1700

2

4

6

8

YIE

LD

[%

]

MASS [amu]

NPA617

Present measurement

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.050

75

100

125

150

175

Pu

lse h

eig

ht

[arb

.]

1/COS(ΘΘΘΘ)

Backing side

Layer side

100 150 2000.0

0.5

1.0

CO

S(Q

)

Pulse height [arb.]

50 1000

5000

10000

Co

un

ts

FF energy [MeV]

Backing side

Layer side

10

Data acquisition system

11

Event = А1, А2, K, N

Cathode pulse used as a fission event

time reference

Energy released inside the 1st and the 2nd

half of the TGIC ND signal used for the neutron TOF

measurement after pulse shape analysis

A1

A2

K

N

The trigger pulse

L samples M samples

Waveforms sampled with 100

MHz WFD 12 bit amplitude

resolution

Digitized waveforms structure

12

100 150 200 250

0.0

0.5

1.0

Pu

lse h

eig

ht

[arb

itra

ry]

Time [arbitrary]

Step pulse

Output of 4 order Butterworth filter

First the DSP signals are passed trough the 8th order

Butterworth filter in order to comply to the Nyquist criterion

The Butterworth filter of 2,4,6,8-th order

0.0 0.1 0.2 0.3 0.4 0.5

0.2

0.4

0.6

0.8

1.0

H( ΩΩ ΩΩ

)

Frequency

Betterworth 2

Betterworth 4

Betterworth 6

Betterworth 8

The band-limited continuous-time signal, with bandwidth of B Hz can be recovered from its samples provided

that the sampling speed Fs > 2B samples/sec. Thus, to assure a correct signal analysis the bandwidth of the signal

should be limited to 50 MHz.

Shannon sampling frequency

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PFN time-of-flight spectroscopy

The left hand figure illustrates how the ND signals are transformed after passing the Butterworth filter. Properly

chosen cut-off frequency of the filter guarantees the same rise time for all ND pulses. The right hand figure illustrates

how the CFTM algorithm works with pulses having the same rise time, but different pulse heights. Signals are passing

the constant fraction of their pulse height at the same time instant. So the simplest digital realisation of the CFTM is to

get time instant at the constant fraction of the pulse height

1 00 15 0 200 2 50

0 .0

0 .2

0 .4

0 .6

0 .8

1 .0

Pu

lse

he

igh

t [a

rbit

rary

]

T im e [a rb itra ry]

1 .0

0 .5

0 .1 67

0 .2 692 , 0 .13 463 , 0 .04 488

2 4 0 2 6 0 2 8 0 3 00

0

5 0 0

1 0 0 0

1 5 0 0

Cu

rren

t [a

rbit

rary

]

T im e [n s e c ]

O r ig in a l N D p u ls e

N D p u ls e a fte r 8 o rd e r B u tte rw o rth f ilte r

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Interpolation formulas:

))()((*)()( 1 kkkk tftftftf −∆+=∆++ Linear

32

2

33

12

333

12

3333

112

23

)2(*)2(*)2(*)(

))1()2((**)32()()(

2

))1(*2)2((*)()(2)(

)1(3)1(3)2(

)()(3)(3)(

)(*)(*)(*)(

+−+−+−=

+−+−+−−=

++−+−+−=

−−++−+

−+−=

+∆++∆++∆+=∆+

+

++

++

−++

kakbkctfd

kkabktftfc

kkkatftftfb

kkkk

tftftftfa

dtctbtatf

k

kk

kkk

kkkk

kkkk

ctbtatf kkk +∆++∆+=∆+ )(*)(*)( 2

2

1

2

**)(

)12(*)()(

2/))()(2)((

kakbtfc

katftfb

tftftfa

k

kk

kkk

−−=

+−−=

+−=

+

+ Parabola

Cubic parabola

)exp(*!3*

1),(

3

4τττ

τtt

tB −

= 4-th order Butterworth filter

15

300 400 500 600

1

10

100

1000

Co

un

ts

Time [0.5*nsec]

Prompt fission neutrons TOF distribution

Neutrons

Ph

oto

ns

Prompt fission neutron TOF distribution obtained using the developed CFTM

algorithm with cubic parabola interpolation. The flight path is 0.8 m and the FWHM

measured for the photon peak is 1.7 nsec

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The pulse shape separationprinciple

100 200 300 400

0.01

0.1

1

10

100

Am

plitu

de

[a

rbit

rary

]

Time [arbitrary]

Neutron pulse

Photon pulse

Narrow window

Wide window

.

1 2

0 0

( ) , y ( ) , where ( ) - is i-th ND current waveform

T T

x I t dt I t dt I t= =∫ ∫

17

Neutron – Gamma separation

0

20

40

50

100

150

200

250

0

20

40

60

50 100 150 200 250

50

100

150

200

250

Neutrons

Photons

Illustration of the neutron – gamma pulse shape separation

principle.

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Conclusions

• Digital signal processing (DSP) algorithms for FF and PFN spectroscopy have been

developed

• The algorithms are applied in an experiment with 252Cf(SF), using a fully digital

acquisition system with four 12bit/100 MHz WFD.

• DSP algorithms are developed as recursive procedures performing the signal

processing, similar to those available in various nuclear electronic modules such

as constant fraction discriminator (CFD), pulse shape discriminator (PSD), peak-

sensitive analogue-to-digital converter (pADC), pulse shaping amplifier (PSA).

• To measure the angle between FF and the cathode plane normal of the GTIC a new

algorithm is developed, having advantage over the traditional analogue pulse

processing schemes.

• Algorithms are tested by comparison of the results of the DSP data analysis for 252Cf(SF) with the data available from literature, demonstrating a superior quality of

the DSP technique over traditional analogue signal processing.

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Thank you !