Neutron yield measurement system of HL-2A tokamak

1.   Introduction

The ultimate goal of fusion energy research is to obtain the power output. The measurement of fusion power or neutron yield is basic requirement for large and medium tokamaks. There are two types of technologies: detector-based measurement and activation measurement [1–3]. This research focuses on the detector-based neutron yield measurement of HL-2A tokamak because it can provide time-resolved results.

When tokamak operates, plasma generates a mixed radiation of hard x-rays, gamma rays and neutrons. The gas ionization detector has a strong anti-interference ability against hard x-rays and gamma rays due to its small ionization cross-section, and is a good choice for neutron detection. ²³⁵U fission chamber and BF₃ and ³He proportional counters are widely used in the neutron flux measurement. The principles of three types of detectors are as follows:

(a) fission chamber, the neutron reaction with the fissile material producing fission fragments and neutrons. The energy of fission fragments is up to 160 MeV.

(b) BF₃ proportional counter

(c) ³He proportional counter

The high-energy particles produced by the above neutron reactions generate ionization signals in the gas ionization detector. Among three types of reactions, the fission reaction releases the largest reaction energy. Therefore, the fission chamber has the best performance on the anti-interference ability of hard x-rays and gamma rays, and is primary neutron yield detector in TFTR [4, 5], JET [6], JT-60U [7], LHD [8], EAST [9, 10] and ITER [11, 12]. BF₃ and ³He proportional counters can be used in lower neutron yield measurement [7, 9, 10].

In this work, we present the development of HL-2A neutron yield measurement system which is based on a 95% enriched ²³⁵U fission chamber and BF₃ and ³He proportional counters, and in situ calibration results. Section 2 starts from the theoretical derivation of the equivalent noise, describes the development of the preamplifier and the results of detectors test, and finally introduces the arrangement of neutron detectors. Section 3 gives the in situ calibration work and the HL-2A experimental results, and followed by a summary and conclusion in section 4.

2.   Development of neutron yield measurement system

2.1   Equivalent noise charge of the radiation detection signal amplification system

In previous work [13], we have developed the neutron flux detector with flat energy response and tested it on the mono-energy neutron source. However, it was found difficult to suppress the noise of the ²³⁵U fission chamber during the development process. Researches [14–16] on the fission chamber did not provide detailed information in this field. It is necessary to analyze the noise of the fission chamber. Some researchers [17] deduced equivalent noise charge (ENC) for typical detector and amplifier system, however it can be seen from the derivation here that the derivation process needs further improvement.

For a typical signal amplification system, as shown in figure 1, the transfer function of amplifier is A·T(ω), in which A is gain independent frequency and T(ω) is frequency response. The noise is equivalent to the input noise source of the spectral density:

Figure  1.  Noise equivalent circuit of a signal amplification system.

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where a and A_f are white and 1/f term of series source, respectively, and b and B_f are white and f term of parallel source, respectively. The white series noise is mainly due to the thermal noise affecting the drain current of the preamplifier input field effect transistor (FET). The 1/f series noise arises mainly from the 1/f component of the drain(collector) current noise of the preamplifier input transistor [18]. Parallel noise arises from the detector leakage current, the first input current (base current or FET gate current) and thermal noise of detector bias resistors. The spectral densities considered here are mathematical, defined on the (-∞, +∞) frequent range.

The noise voltage at input can be written as:

where C_T is total input capacitance including detector capacitance C_d and input capacitance of preamplifier C_i. Therefore, the output noise voltage can be calculated by

Substituting equations (4) and (5) into equation (6), we get:

T(ω) is a function with the dimension of a frequent. The output noise voltage provided by equation (7) can be written in a more significant way in dimensionless. For a certain amplification system, τ is characteristic time-constant or the peaking time, standard deviation or full-width at half maximum, or base width. Putting x/τ for ω in the integrals of equation (7), x is dimensionless parameter, and the output noise becomes:

When a signal with a charge of Q is generated on the detector, the voltage at the input terminal is

The radiation detection signal amplification system amplifies the input signal. Within a certain frequency range, the amplification factor is independent of frequency. The maximum signal voltage at the output terminal can be written as follows:

where k is a constant independent of frequency. Let $〈U_{\mathrm{o}}^2〉=u_{\mathrm{o},\max }^2,$ solving the equivalent noise charge at the input terminal as:

By putting:

the final form of squared equivalent noise charge becomes:

The equivalent noise charge is therefore represented through the total capacitance C_T, the noise parameter a, b, and A_f, the time-constant τ and three shape factors A₁, A₂, and A₃ of the amplification system. Table 1 provides calculated values of shape factors in various amplification systems including the widely-used CR ⁿ -RC ⁿ system.

Table  1.  Shape factors in various amplification systems.

	Description	$u_{\mathrm{o}}(t)$	k	A1	A2	A3
1	Indefinite cusp	$\exp \left({\displaystyle \frac{-\left|t\right|}{\tau }}\right)$	1	1	0.64	1
2a	Truncated cusp	$\exp \left(-{\displaystyle \frac{\left|t\right|}{\tau }}\right)-\exp \left(-1\right),\left|t\right|\le \tau$	0.63	2.16	0.77	0.51
2b	Truncated cusp	$\exp \left(-{\displaystyle \frac{\left|t\right|}{\tau }}\right)-\exp \left(-2\right),\left|t\right|\le 2\tau$	0.87	1.31	0.71	0.78
2c	Truncated cusp	$\exp \left(-{\displaystyle \frac{\left|t\right|}{\tau }}\right)-\exp \left(-3\right),\left|t\right|\le 3\tau$	0.95	1.10 a	0.67	0.91
3	Triangular	$\left\{\begin{array}{c}{\displaystyle \frac{t}{\tau }},0\le t\le \tau \hfill \\ 2-{\displaystyle \frac{t}{\tau }},\tau \le t\le 2\tau \hfill \end{array}\right.$	1	2	0.88	0.67
4	Trapezoidal	$\left\{\begin{array}{c}{\displaystyle \frac{t}{\tau }},0\le t\le \tau \hfill \\ 1,\tau \le t\le 2\tau \hfill \\ 3-{\displaystyle \frac{t}{\tau }},2\tau \le t\le 3\tau \hfill \end{array}\right.$	1	2	1.38	1.67
5	Piecewise parabolic	$\left\{\begin{array}{c}{\displaystyle \frac{2}{{\tau }^2}}{t}^2,0\le t\le \tau /2\hfill \\ -{\displaystyle \frac{2}{{\tau }^2}}{\left(t-\tau \right)}^2+1,\tau /2\le t\le 3\tau /2\hfill \\ {\displaystyle \frac{2}{{\tau }^2}}{\left(t-2\tau \right)}^2,3\tau /2\le t\le 2\tau \hfill \end{array}\right.$	1	2.67	1.15	0.77
6	Sinusoidal lobe	$\sin \left({\displaystyle \frac{\pi t}{2\tau }}\right),0\le t\le 2\tau$	1	2.47	1.22	1
7a	CR-RC	${\displaystyle \frac{t}{\tau }}\exp \left(-{\displaystyle \frac{t}{\tau }}\right),t\ge 0$	0.37	1.85	1.18	1.85
7b	CR-RC2	${\displaystyle \frac{t^2}{2{\tau }^2}}\exp \left(-{\displaystyle \frac{t}{\tau }}\right),t\ge 0$	0.27	0.85	1.09	2.56
7c	CR-RC3	${\displaystyle \frac{t^3}{6{\tau }^3}}\exp \left(-{\displaystyle \frac{t}{\tau }}\right),t\ge 0$	0.22	0.62	1.06	3.11
7d	CR-RC4	${\displaystyle \frac{t^4}{24{\tau }^4}}\exp \left(-{\displaystyle \frac{t}{\tau }}\right),t\ge 0$	0.20	0.51	1.04	3.58
8a	CR2-RC	${\displaystyle \frac{t}{2{\tau }^2}}\left(2\tau -t\right)\exp \left(-{\displaystyle \frac{t}{\tau }}\right),t\ge 0$	0.2306	3.53	1.5	1.18
8b	CR2-RC2	${\displaystyle \frac{t^2}{6{\tau }^3}}\left(3\tau -t\right)\exp \left(-{\displaystyle \frac{t}{\tau }}\right),t\ge 0$	0.13	1.83	1.56	1.83
8c	CR2-RC3	${\displaystyle \frac{t^3}{24{\tau }^4}}\left(4\tau -t\right)\exp \left(-{\displaystyle \frac{t}{\tau }}\right),t\ge 0$	0.09	1.44	1.63	2.40
8d	CR2-RC4	${\displaystyle \frac{t^4}{120{\tau }^5}}\left(5\tau -t\right)\exp \left(-{\displaystyle \frac{t}{\tau }}\right),t\ge 0$	0.069	1.25	1.69	2.91
9	Gaussian	$\exp \left(-{\displaystyle \frac{t^2}{2{\tau }^2}}\right)$	1	0.89	1	1.77
10	Clipped approximate integrator	$\left\{\begin{array}{c}1-\exp \left(-{\displaystyle \frac{t}{\tau }}\right),0\le t\le {\displaystyle \frac{\tau }{2}}\hfill \\ \left(1-\exp \left(-0.5\right)\right)\exp \left(-{\displaystyle \frac{t}{\tau }}+0.5\right),{\displaystyle \frac{\tau }{2}}\le t\hfill \end{array}\right.$	0.39	2.54	0.85	0.69 a
11	Bipolar triangular	$\left\{\begin{array}{c}{\displaystyle \frac{t}{\tau }},0\le t\le \tau \hfill \\ 2-{\displaystyle \frac{t}{\tau }},\tau \le t\le 3\tau \hfill \\ {\displaystyle \frac{t}{\tau }}-4,3\tau \le t\le 4\tau \hfill \end{array}\right.$	1	4	2	1.33
Corrected Gatti's results [17].

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2.2   Design of preamplifier in fission chamber

The fission chamber is a type of gas ionization chamber which is based on collection of the charges created by direct ionization within the gas. Its electrode is coated with fissile materials. Fissile materials are radioactive and mainly emit alpha particles with MeV energy, which causes additional parallel noise. In order to reduce the impact of parallel noise, time-constant τ of signal amplification system should be small according to equation (13). The small τ is also benefit to increase the counting rate.

The detector capacitance C_d of fission chamber is very large. Then it can be concluded from equation (13) that the ENC mainly comes from the series white noise. It is necessary to decrease the white series noise figure which is mainly due to the channel resistance noise of FET. With reference to the results of other researchers [19, 20], the FET with low white series noise figure is used as the input stage, and the commercial operational amplifier is used as the amplifying stage and output stage, thus a compact charge preamplifier has been developed [21].

Then the preamplifier and the ²³⁵U fission chamber detector were tested together. In the test, a 5-meter RG-59 cable, which is low capacitance (52 pf/m), is used to connect the detector and the preamplifier. The total input capacitance reached 810 pF. The output of the preamplifier is shaped by a specially designed CR-RC amplifier and sent to a multi-channel analyzer (Canberra Multiport Ⅱ) in order to observe the pulse height spectrum. The noise amplitude spectrum is obtained when no bias voltage is applied to the ²³⁵U fission chamber. When the ²³⁵U fission chamber is biased by high voltage, the alpha signal amplitude spectrum is obtained. The acquisition time of the noise spectrum and the alpha signal amplitude spectrum is one minute. The neutron signal amplitude spectrum was obtained by placing the ²³⁵U fission chamber in a ²⁵²C_f neutron source for 72 h. The amplitude spectra of noise, α and neutron signals obtained at different time-constant are shown in figure 2 [21]. The value of the pulse height is obtained by converting the charge into energy by the argon ionization energy (26.4 eV). The three time-constants of the upper, middle and lower graphs are respectively 0.1 μs, 1 μs and 10 μs. From these amplitude spectrums, it can be found that when the time-constant is 1 μs, the noise is the lowest. It is because that the 10 μs time-constant case increases the parallel noise contribution, and 0.1 μs time-constant case increases the series noise contribution. Figure 2 also shows that alpha signal is the lowest in the 0.1 μs time-constant case. It is considered that the short time-constant decreases the probability of alpha signal accumulation. In the HL-2A experiment, the time-constant of ²³⁵U fission chamber system is set to 0.1 μs.

Figure  2.  Pulse amplitude spectrum of noise, alpha and neutron, time-constant: top, 0.1 μs; middle, 1 μs, bottom, 10 μs. Reprinted from [21], Copyright (2020), with permission from Elsevier.

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2.3   Proportional counter

Proportional counter is a type of gas ionization detector which relies on the phenomenon of gas multiplication to amplify the charge produced by the primary ion pairs within the gas. Therefore, pulses are larger than those from ionization chambers under the same conditions, and the effect of noises is slightly.

Compared with the ³He proportional counter, the BF₃ proportional counter has a larger reaction energy, so it has a better performance in anti-interference ability against hard x-rays and gamma rays. In addition, the ³He proportional counter can obtain greater sensitivity and can be used for lower neutron flux measurements. Three proportional counters with different sensitivities are installed on the HL-2A, and their parameters are shown in table 2.

Table  2.  Positions and parameters of HL-2A neutron yield detectors.

Detector indicator	Manufacture	Parameter	Moderator	Major radius (m)
1 g 235U fission chamber	Beijing Nuclear Instruments Factory, China	Φ50 mm×500 mm	Polyethylene, 50 mm Cadmium, 1 mm	11.10
0.005 mol BF3 proportional counter	Centronic LTD, UK	Φ25 mm×500 mm, 0.5 atm	Polyethylene, 62 mm	6.58
0.02 mol 3He proportional counter	Centronic LTD, UK	Φ25 mm×500 mm, 2 atm	Polyethylene, 62 mm	6.58
0.1 mol 3He proportional counter	Wuhan Newradar Special Gas Co., LTD, China	Φ57 mm×230 mm, 4 atm	Polyethylene, 71 mm	4.01

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The capacitance of the proportional counter is small due to and its very thin anode. Therefore, series noise is not serious. The signal amplification of the proportional counter is simple. It should be noted that the time-constant of the signal amplification system cannot be too small to avoid ballistic loss.

Three proportional counters were tested in a polyethylene moderator housing irradiated by a neutron source. The same preamplifier, amplifier and MCA as in the above test were used. The pulse amplitude spectrum is shown in figure 3. The top one is BF₃ counter, and shows two branch reactions. The middle one is ³He counter. The full energy peak and the so-called wall effect can be clearly seen. The bottom one is ³He counter, and its wall effect is very slight due to its large radius and high gas pressure.

Figure  3.  Pulse amplitude spectrum of BF₃ and ³He proportional counters.

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2.4   Arrangement of neutron yield detector

All detectors are placed inside polyethylene moderator housings to achieve flat energy response [13]. In order to increase the measurement range, the most sensitive detector is placed at the position closest to the HL-2A tokamak, and the least sensitive detector is placed at the farthest position from the HL-2A tokamak, as shown in figure 4. All detectors are placed at the mid-plane of HL-2A tokamak. 1 g ²³⁵U represents the ²³⁵U fission chamber which is arranged between the toroidal field coils (TFC) 10 and 11; the 0.005 mol BF₃ and 0.02 mol ³He proportional counters are arranged between TFC 9 and 10; the 0.1 mol ³He proportional counter is arranged near to TFC 4.

Figure  4.  Schematic diagram of HL-2A neutron yield detectors arrangement.

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3.   In situ calibration and HL-2A experimental results

The absolute detection efficiency of the neutron flux monitor needs to be calibrated so that the output of the detector can provide the information of the neutron yield, or the fusion power. Large devices such as JET [1, 6], JT-60U [7], TFTR [4, 5, 22] and LHD [23] have carried out in situ neutron calibration, and obtained good experimental results.

In the spring of 2021, the detection efficiency of the neutron flux detectors was calibrated using a ²⁵²C_f neutron source with an intensity of 2.2×10⁷ neutrons per second. The ²⁵²C_f neutron source is always located at magnetic axis. With reference to the support plate in the vacuum vessel, 16 homogeneous points are calibrated in the toroidal direction. The amplifier outputs of four detectors are recorded and processed online by Keysight M3100 digitizer (FPGA programmable, 14 Bits, 100 MSa/s).

The detection efficiency varies with toroidal angle between detectors and neutron source, as shown in figure 5. When the detector and the neutron source are at the same toroidal angle, the detection efficiency is high, and it decreases as the toroidal angle increases. The ratio of maximum efficiency to minimum one for a detector is in the range of 10–100. It is shown that the detection of neutrons is localized. In order to obtain reliable neutron yield results, it is necessary to arrange multiple detectors in the toroidal direction. The detector efficiency is calculated directly by averaging the efficiency of each detector, as shown in table 3.

Figure  5.  Detection efficiency as a function of toroidal angle between detectors and neutron source.

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Table  3.  Detection efficiency of HL-2A neutron yield detectors.

Detector	Detection efficiency (Detector count/Neutron source)
1 g 235U fission chamber	2.86×10-8
0.005 mol BF3 proportional counter	2.87×10-6
0.02 mol 3He proportional counter	1.13×10-6
0.1 mol 3He proportional counter	1.64×10-5

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The charge collection time of the ²³⁵U fission chamber, ³He and BF₃ proportional counters are different, and the measured values are 0.1 μs, 2 μs and 0.2 μs, respectively. Therefore, it can be assumed that the maximum counting rates in the counting mode are 500, 10 and 100 kHz. The calculated measurement range of the four detectors is shown in figure 6. It can be seen that the four detectors can cover a total neutron yield range of approximately 7 orders of magnitude from 6×10⁶ to 2×10¹³ n s^-1.

Figure  6.  Measurement range of HL-2A four neutron detectors.

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We revisited the results of HL-2A 37012 experiments in 2019. As shown in figure 7, the plasma current is about 180 kA, the average electron density of the center chord is (2–2.5)×10¹⁹ m^-3, the neutral beam heating power is 1.4–1.5 MW, and the maximum neutron yield measured by ²³⁵U fission chamber is 7×10¹² n s^-1.

Figure  7.  Measurement results of the neutron yield of HL-2A 37012 experiment.

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4.   Conclusions

This work presents the neutron yield measurement system of HL-2A tokamak which is based on the gas ionization detectors, including ²³⁵U fission chamber for high neutron yield measurement and BF₃ and ³He proportional counters for low neutron yield measurement. All detectors were in situ calibrated using ²⁵²C_f neutron source. The HL-2A experiment in 2019 was analyzed based on the calibration results. When HL-2A is heated by the 1.5 MW neutral beam injection, the maximum neutron yield reaches to 7×10¹² n s^-1.

Since the detection of the neutron flux detector is localized, further work is to develop multiple fission chamber neutron detectors symmetrically distributed in the toroidal direction, and proportional counter detector will be used to study the HL-2A Ohmic heating experiment.