Detector and radioactive source

A CLLB crystal detector from Saint-Gobain ^[24] was used; the scintillator crystal has a diameter of 2 in. and is sealed inside an aluminum housing. It was coupled directly to a photomultiplier tube (PMT) (Hamamatsu R6231-100), as shown in Fig. 1. An ORTEC 556 high-voltage power supply was used during the experiment to supply a voltage of 800 V to the detector. A ¹³⁷Cs gamma source was used as the energy calibration source for the detector, and a ²⁵²Cf source was selected to provide the neutron/gamma hybrid radiation field.

Fig. 1Full-screen View

Neutron/gamma signal discrimination system based on CLLB detector

Data acquisition system

A data acquisition system developed by our research group was used for the experiment; it includes a PXIe chassis with an embedded controller and an electronics card. The signal input of the main electronics card was directly connected to the CLLB detector. The main electronics card consists mainly of analog signal conditioning components, high-speed analog-to-digital converters (ADCs) (14 bits and 500 Msps), a clock jitter cleaner, and a field-programmable gate array (FPGA) (type xc7k325tffg900). As shown in Fig. 4, the rise time of the electrical signal of the CLLB detector is $t_r\ge 30\text{ ns}$. If the signal is processed directly by a 500 Msps ADC, there are no fewer than 15 sampling points on the rising edge. A signal with a rising edge $t_r\ge 30\text{ ns}$ corresponds to the frequency spectrum of 16.7 MHz, which is much lower than the sampling rate of the waveform digitization module for 500 Msps ADCs. The hardware of the main electronics card is almost identical to that of the main electronics card for neutron flux monitoring in the Experimental Advanced Superconducting Tokamak ^[25], except that the gain of the analog signal conditioning component is 8 V/V to accommodate the signal amplitude of the CLLB detector and PMT output (<100 mV), and the FPGA code is different. Data processed by the FPGA algorithm are transmitted to the chassis-embedded controller through the PXIe bus in direct memory access mode for display or storage ^[26].

Fig. 4Full-screen View

Schematic diagram of discrimination methods

The pulse acquisition mode of the FPGA is shown in Fig. 2. $L_r$ is the length of the entire recorded pulse; $L_b$ is the length of the sliding average of the baseline calculation; $L_o$ is the offset of the pulse trigger, which determines the starting point of the baseline calculation; and $T_g$ is the moment at which the pulse is triggered. In this experiment, the average value of 48–64 ns sampling points before pulse triggering was defined as the baseline of the pulse, and the total recording time of the pulse was 1008 ns.

Fig. 2Full-screen View

Pulse recording mode

Pulse preprocessing

First, the detector was energy-calibrated using a ¹³⁷Cs gamma source. Then, a pulse waveform with an equivalent gamma energy of 3.1–3.3 MeV (the energy band containing the thermal neutron peak) was extracted from the ²⁵²Cf source; therefore, we investigated the neutron/gamma discrimination performance in this energy band. A total of 33,782 waveforms were measured. Pulse width and amplitude analysis was used to remove severely overlapped or chopped waveforms; 33,246 pulse waveforms remained after this process. Finally, each pulse baseline value was subtracted from the sampled pulse sample data.

SK filter

In 1955, the SK filter based on discrete components was first proposed by R.P. Sallen and E.L. Key, and the Gaussian shaping of pulse signals was successfully realized. SK filters are widely used for signal filtering and pulse shaping, where they outperform other methods in terms of energy resolution and computational workload ^[27]. The SK filter has a second-order filter circuit with a simple structure and is widely used in nuclear signal pulse shaping^[28,29]. Fig. 3 shows the SK low-pass filter. When R1 = R2 = R= 3.99 kΩ and C1 = C2 = C= 1.5 pF, the corresponding bandwidth is 16.7 MHz.

Fig. 3Full-screen View

Schematic diagram of SK low-pass filter

Real-time discrimination method

The CC method uses the different integration values of the neutron and gamma pulse tails as the basis for discrimination. The principle is illustrated in Fig. 4a; the discrimination is calculated using Eq. (1): $P_{\text{CI}}=\frac{Q-Q_{\text{f}}}{Q}=\frac{Q_{\text{s}}}{Q_{\text{f}}+Q_{\text{s}}}$ (1) where $Q$ is the total pulse integral, and Q_f and Q_s represent the pulse front and tail integrals, respectively. The range of the integration intervals of Q_f is determined by t_s and t_m, and the integration interval of $Q$ is determined by t_s and t_e. If the interval between t_s and t_m is set too large, it will cause a loss of the difference between the falling portions of the neutron and gamma pulse signals in Eq. (1), where P_CI thus tends to 0. By contrast, if the interval between t_sand t_m is set too small, the information on useless pulses in Eq. (1) will increase, causing P_CI to tend to 1. Therefore, the integration interval needs to be selected according to the pulse waveform of the detector response in practical applications. In the CLLB detector, the neutron pulse will have smaller P_CI values than the gamma pulse because neutrons decay faster than gammas, unlike the typical case of liquid scintillators.

The principle of the AC method is shown in Fig. 4b, where t_c after the peak is selected as the moment of amplitude comparison. The different amplitudes of neutrons and gammas at this moment are used as the basis for discrimination, where $A_{\text{γ}}$ and $A_{\text{n}}$ represent the amplitude of the gamma and neutron pulses, respectively, at the $t_{\text{c}}$ moment. This method requires the calculation of only one sampling point but is very susceptible to the effects of noise. Therefore, the amplitudes were normalized before comparison with the other methods.

The principle of the TC method is shown in Fig. 4c. It can be considered as the inverse function of the AC method. A fixed A_c threshold line is chosen, and the difference in the time it takes for neutron and gamma pulses to decay from their peaks to the threshold line is used as the basis for discrimination. $T_{\text{γ}}$ and $T_{\text{n}}$ represent the time from the intersection of the decaying portion of the gamma and neutron pulse, respectively, with the threshold line A_c to the peak.

The PG method selects peak and post-peak sampling points for gradient calculation; the principle is illustrated in Fig. 4d. It can be written as Eq. (2): $P_{\text{G}}=\frac{A_{\text{p}}-A_{\text{b}}}{t_{\text{p}}-t_{\text{b}}}$ (2) where $P_{\text{G}}$ is the pulse gradient, $A_{\text{p}}$ is the pulse peak amplitude, and $A_{\text{b}}$ is the amplitude at a specific time interval after the pulse peak. In addition, $t_{\text{p}}$ and $t_{\text{b}}$ are the corresponding moments of the pulse peak and post-peak sampling points, respectively. Similarly, the gradient is susceptible to strong amplitude effects and is calculated using normalized amplitudes.

Evaluation criteria

The FOM was introduced as an evaluation criterion to objectively assess the performance of the discrimination method, as shown in Fig. 5. The FOM is defined ^[30] as shown in Eq. (3): $\text{FOM}=\frac{D}{{\text{FWHM}}_{\text{n}}+{\text{FWHM}}_{\gamma }}$ (3) ${\text{FWHM}}_n$ and ${\text{FWHM}}_{\gamma }$ are the half-height widths of the neutron and gamma peaks, respectively, and D is the distance between the neutron and gamma peaks. A larger FOM indicates that the method exhibits better neutron/gamma discrimination.

Fig. 5Full-screen View

Criteria for evaluating neutron/gamma discrimination

MDDM

Among the four methods described above, only the CC method uses all the waveform information. Therefore, it has better noise immunity. The discrimination performance of the CC method depends on three parameters, t_s, t_m, and t_e. The values of t_s and t_e are usually taken as the moments of the upper edge of the pulse and the end of pulse decay, respectively, and the parameter t_m is the most difficult to determine. We propose a model that maximizes the difference used for discrimination to determine the parameter t_m and achieve excellent performance by the CC method. When neutrons and gamma rays deposit energy in the CLLB detector, the photon pulse generated by the scintillation crystal can be written as shown in Eq. (4). $I\left(t\right)=I_{\text{f}}{e}^{-t/{\tau }_f}+I_{\text{s}}{e}^{-t/{\tau }_s}$ (4) where ${\tau }_{\text{f}}$ and ${\tau }_{\text{s}}$ are the fast and slow components of the decay time constant, respectively. $I_{\text{f}}$ and $I_{\text{s}}$ represent the proportions of the fast and slow components, respectively.

In the linear region, the pulse output from the CLLB detector can be represented by the convolution of the photon pulse with the response function of the PMT and readout electronics. However, the final expression of $V\left(t\right)$ still contains the factors $e^{-t/{\tau }_{\text{f}}}$ and $e^{-t/{\tau }_{\text{s}}}$ ^[31]. Because the pulse rises rapidly, this part of the output can be replaced by a linear function; thus, the gamma and neutron pulse response described above can be written as shown in Eqs. (5) and (6), respectively. $V_{\text{CLLB}\gamma }\left(t\right)=\{A(I_{\text{f}\gamma }{e}^{-\left(t-t_1\right)/{\tau }_f}\stackrel{K_{\gamma }t, t<t_1}{+I_{\text{s}\gamma }{e}^{-\left(t-t_1\right)/{\tau }_{\text{s}}})},t\ge t_1$ (5) $V_{\text{CLLBn}}\left(t\right)=\{A(I_{\text{fn}}{e}^{-\left(t-t_1\right)/{\tau }_{\text{f}}}\stackrel{K_{\text{n}}t,\text{}t<t_1}{+I_{\text{sn}}{e}^{-\left(t-t_1\right)/{\tau }_{\text{s}}})}, t\ge t_1$ (6) $K_{\gamma }=K_{\text{n}}=A/t_1$ (7)

$I_{\text{f}\gamma }$ and $I_{\text{s}\gamma }$ represent the fast and slow components, respectively, of the pulse response to gamma rays. $I_{\text{fn}}$ and $I_{\text{sn}}$ represent the fast and slow components, respectively, of the response to neutrons. $A$ is the response amplitude, which is proportional to the ray energy. In the actual detector impulse response, the pulse first rises and then decays, as shown in Fig. 6.

Fig. 6Full-screen View

Model of output pulse response of CLLB detector

The rise time of the CLLB response pulse to the peak is the same for rays of different energies. $t_0$, $t_1$. and $t_2$ represent the moments at which the pulse starts to rise, reaches its peak, and is completely decayed, respectively. S_a represents the pulse integration area of the neutron and gamma pulses from $t_0$ to $t_1$. Neutrons and gammas of the same energy in the rising phase of the pulse can be considered to have the same integration area. S_b represents the integration area of the neutron pulse from $t_1$ to $t_2$. Because the slow component of the gamma response pulse is more significant in the decaying part of the pulse, S_c represents the excess integration area of the gamma pulse from $t_1$ to $t_2$ compared to theeutron pulse. The $P_{\text{CI}}$ values of gammas and neutrons in the CC method are calculated as shown in Eqs. (8) and (9), respectively: $P_{\text{CI}\gamma }=\frac{S_b+S_c-S_{\gamma \delta }}{S_a+S_b+S_c}$ (8) $P_{\text{CIn}}=\frac{S_b-S_{\text{n}\delta }}{S_a+S_b}$ (9)

The difference in $P_{\text{CI}}$ between neutrons and gammas is strongly correlated with $D$ in Eq. (3). Therefore, the FOM of the CC method is expected to be highest when $\delta =t_1+{\tau }_{\text{m}}$ reaches the moment at which the difference in $P_{\text{CI}}$ between neutrons and gammas is maximum. $D\left(\delta \right)=\left(P_{\text{CIγ}}-P_{\text{CIn}}\right)=\frac{S_{\text{n}\delta }(S_a+S_b+S_c)-S_{\gamma \delta }\left(S_a+S_b\right)+S_a{S}_c}{(S_a+S_b+S_c)\left(S_a+S_b\right)}$ (10)

If $I_{\text{f}\gamma }<I_{\text{fn}}$, $I_{\text{s}\gamma }>I_{\text{sn}}$ and $0<{\tau }_{\text{m}}<t_2-t_1$, ${\tau }_{\text{m}}$ is the moment at which the difference between the $P_{\text{CI}}$. values of gammas and neutrons is largest, as shown in Eq. (11). ${\tau }_{\text{m}}=\frac{{\tau }_{\text{f}}{\tau }_{\text{s}}}{{\tau }_{\text{s}}-{\tau }_{\text{f}}}\text{ln}\left(\frac{I_{\text{fn}}p-I_{\text{f}\gamma }q}{I_{\text{sγ}}q-I_{\text{sn}}p}\right)$ (11) $p=S_a+S_b+S_c,q=S_a+S_b,p<q$ (12)

By calculating ${\tau }_{\text{m}}$, the parameters the CC method that will yield the best FOM can be obtained.

Comparison of methods

The discrimination effects of the time-domain methods discussed above are all related to the parameter values. To objectively evaluate each method, the definition domain of the discrimination parameters of each method is first given. Then the best FOM using these parameters is obtained as the discrimination performance of the method by a trial-and-error approach. Let t_s be 10% of the time required for the pulse to rise to its peak, t_p be the moment of the pulse peak, and t_e be 700 ns after t_s. For the CC method, t_m satisfies Eq. (13); for the AG method, t_c satisfies Eq. (14); for the PG method, t_b satisfies Eq. (15); and for the TC method, the A_c range is taken from 0.1 to 1 peak, at intervals of 1% of the peak. $t_{\text{s}}<t_{\text{m}}<t_{\text{e}}$ (13) $t_{\text{p}}<t_{\text{c}}<t_{\text{e}}$ (14) $t_{\text{p}}<t_{\text{b}}<t_{\text{e}}$ (15)

The FOM of the methods without filtering is shown in Fig. 7. Only the CC method can distinguish between neutron and gamma pulses at the current noise level, where the parameter t_m is taken as 212 ns after t_s to obtain the best FOM for this method.

Fig. 7Full-screen View

Discrimination performance of different methods without filtering

As show in Fig. 3, the shaping effect of the SK low-pass filter is affected by the value of $RC$. With increasing $RC$, the cutoff frequency decreases, the attenuation of the stop-band increases, and the filtering effect is improved.

The AC method is more strongly affected by noise, which is strongly correlated with the filtering effect. The overall FOM of the TC method is low; it is challenging to distinguish neutron and gamma signals correctly because the shaped pulse has a large oscillation with time. Therefore, the TC method is not suitable for neutron/gamma discrimination.

The PG method is also more strongly affected by noise. The FOM of the PG method is strongly correlated with the filtering effect. In addition, the FOM of the PG method is similar to that of the AC method because of the amplitude difference in Eq. (3) in the calculation, which indicates that the amplitude difference is the dominant factor in discrimination by the PG method.

Therefore, the CC method is the most suitable processing method for real-time neutron/gamma discrimination.

Effect of MDDM

When the t_s and t_e parameters of the CC method are fixed as described in Sect. 4.1, we take $t_{\text{m}}=\left\{t\right|t=60+20*a,a=0,1,2,3,\mathrm{...},28\}$. The FOM of the CC method for these values of t_m is shown in Fig. 8. The FOM curve is convex, which indicates the best FOM can be obtained by considering the FOM as a function of the single parameter t_m, and confirms the suitability of the MDDM proposed in Sect. 3.4. Let $e_0–e_1$ be the $R_0$ region, $e_1–e_2$ be the $R_1$ region, and $e_2–{\text{e}}_3$ be the $R_2$ region. The slope of the curves in the $R_0$ and $R_1$ regions is larger, indicating that the FOM improves more rapidly when t_m is close to $e_1$. By contrast, the FOM decreases rapidly when t_m is close to $e_3$. The slope of the curve in the $R_2$ region is smaller, indicating a slower decrease in the FOM in this region, although the range is large. Thus, the performance of the CC method is somewhat independent of the t_m value.

Fig. 8Full-screen View

Effect of t_m on FOM of CC method

To solve Eq. (11) for t_m, only $I_{\text{fn}}$, $I_{\text{sn}}$, $I_{\text{f}\gamma }$, $I_{\text{s}\gamma }$, ${\tau }_{\text{f}}$, ${\tau }_{\text{s}}$ and $t_1$ need to be calculated. They were obtained by fitting the neutron/gamma pulse waveform by Eqs. (5) and (6), as follows:

1. The neutron/gamma pulse signals were extracted separately by the CC method (using the parameters that were used to achieve the performance shown in Fig. 7), where 2000 pulse waveforms each were extracted for neutrons and gammas.

2. The average waveforms of neutron and gamma pulses were calculated and fitted with Eqs. (5) and (6) for neutrons and gammas, respectively, to obtain ${\tau }_{\text{fn}},{\tau }_{\text{sn}},{\tau }_{\text{f}\gamma },\text{ and}{\tau }_{\text{s}\gamma }$.

3. The average of the rise times of the fitted neutron and gamma waveforms is obtained as $t_1=30$ ns.

4. The average of ${\tau }_{\text{fn}}\text{ and }{\tau }_{\text{f}\gamma }$ is taken as ${\tau }_{\text{f}}=81.51$ ns, and the average of ${\tau }_{\text{sn}}$ and ${\tau }_{\text{s}\gamma }$ is taken as ${\tau }_{\text{s}}=451.27$ ns.

5. By substituting ${\tau }_{\text{f}}$ and ${\tau }_{\text{s}}$ into Eqs. (5) and (6), we obtained $I_{\text{fn}}=0.868,I_{\text{sn}}=0.132,I_{\text{f}\gamma }=0.837,\text{ and }{I}_{\text{s}\gamma }=0.163$.

We confirm that the above parameters satisfy Eq. (11). For a fixed value of t_s, we take $t_{\text{e}}=\left\{t\right|t=300+20*a,a=0,1,2,3,\dots ,30\}$. Fig. 9 compares the FOM obtained using the t_m values calculated using the MDDM with the potentially optimal FOM for different t_e values. The potentially optimal FOM versus t_m curve (black dots) is still convex, indicating that t_e does not need to cover the entire pulse to obtain the best discrimination performance of the CC method, and thus the calculation time required for integration can be reduced. Experimental tests show that t_e can be set between 640 and 740 ns after t_s, where the potentially optimal FOM exceeds 1.46. In addition, when t_e is set in this range, the difference between the FOM obtained using the t_m value calculated using the MDDM and the potentially optimal FOM is less than 3.9%, confirming that it can improve the performance of the CC method.

Fig. 9Full-screen View

Comparison of FOM obtained using MDDM and optimized parameters. The black dots represent the potentially optimal FOM for different values of t_e. The red dots represent the FOM obtained using the t_m values calculated using the MDDM for different values of t_e.