Conceptual design of a BackTOF neutron spectrometer for fuel ion ratio measurements at ITER

In a neutron time of flight spectrometer (TOF), information on the neutron energy is typically obtained from the time difference between elastic scattering in two sets of organic scintillator detectors. The first scattering takes place in the primary detector set (D1), and the secondary detector set (D2) subsequently catches a fraction of the neutrons that first scattered in the D1.

The back scattering time of flight spectrometer (BackTOF) works in a similar way as the traditional forward scattering TOF [9]. The difference is that the traditional TOF relies on forward scattering on hydrogen in the D1, while the BackTOF relies on backwards scattering on deuterium. The need for a deuterated D1 comes from the fact that neutron scattering on hydrogen cannot produce a backscattered recoil neutron since their masses are about equal, and the kinematics of the reaction does not allow for neutrons being scattered at angles larger than 90° in the lab frame. See figure 1 for a geometrical description of the two configurations. A forward TOF spectrometer is described in detail in [7]. We note here that a scattering angle around 30° is used, and the neutron recoil energy is therefore $E_{n}^{\prime}$  ≈  0.75 · E_n. In a BackTOF spectrometer, the scattering angle is close to 180°, and the recoil energy is $E_{n}^{\prime}$  ≈  0.11 · E_n.

Zoom In Zoom Out Reset image size

The efficiency of a TOF spectrometer is given by the fraction of the incoming neutrons that scatter in the D1, into the solid angle covered by the D2, times the catching efficiency of the D2. Design parameters that affect the efficiency are the area and thickness of the D2 (A_D2 and dx_D2, respectively) as well as the distance from the D1 to the D2 (L). Increasing A_D2 or decreasing L results in an increased solid angle covered by the D2, and hence a higher efficiency. Similarly, increasing dx_D2 increases the catching efficiency of the D2, which also results in a higher total efficiency. A similar argument can be made for the count rate capability. The limiting factor here is the rate in the D1. Therefore, any design change that increases the efficiency also increases the maximum count rate capability.

The main contribution to the resolution of a TOF spectrometer is the fact that, due to the finite size of the D1 and D2 detectors, there is no 1:1 mapping from incoming neutron energy to flight time, t_TOF. Instead, there is a distribution of flight times, which is typically simulated with Monte Carlo codes. The main contributing factors are the area and the thickness of the D2 detector. Since the velocity of a neutron (assuming classical kinematics) scales as  √E, the energy resolution of the spectrometer scales as dE/E  =  2 · dt_tof/$\langle {{t}_{\text{tof}}}\rangle$, where dt_tof is the standard deviation of flight times from incoming mono-energetic neutrons, and $\langle {{t}_{\text{tof}}}\rangle$ is the mean value of the flight times. Increasing A_D2 or dx_D2 improves the efficiency and count rate capability, but also results in a higher dt_tof and hence degraded resolution. Similarly, decreasing L improves the efficiency and count rate capability, but reduces $\langle {{t}_{\text{tof}}}\rangle$, which also degrades the resolution. This illustrates the trade-offs between resolution, efficiency and count rate capability.

The forward scattering TOF is well suited for measurements of neutrons from the DD reaction with energies around 2.5 MeV. Consider a typical example; assuming a flight path of L  =  1.25 m, the energy of the recoil neutron is around 1.9 MeV, which gives a $\langle {{t}_{\text{tof}}}\rangle$ of 65 ns. A well-designed spectrometer will have a dt_tof of about 2 ns, and the energy resolution then becomes 2 · 2/65  =  6%, which is acceptable for analysis of the DD emission. However, for 14 MeV neutrons $\langle {{t}_{\text{tof}}}\rangle$ is reduced to 27 ns, and the energy resolution degrades to 14%, which is not acceptable for analysis of the DT emission. These figures are representative of the TOFOR spectrometer [9] in operation at JET. To improve the resolution of a forward TOF without sacrificing the efficiency and count rate capability requires a significant scale up of the spectrometer size, which precludes it from being used at ITER.

On the other hand, in the backscattering geometry, a 180° scattering of a 14 MeV neutron results in a recoil energy of 1.6 MeV. With a 125 cm flight path this gives a resolution of 5.5% if dt_tof is kept at 2 ns. For 14 MeV neutrons, this is almost three times better than forward scattering spectrometer despite the same physical dimension of the instrument. Further, the geometrical contribution to dt_tof in a BackTOF is smaller than for a forward scattering TOF, and the energy resolution can be expected to improve further. The exact numbers will be examined in section 3 with Monte Carlo calculations.

The dominating background in all time of flight spectrometers of the type studied here is that due to random coincidences between uncorrelated neutrons. Since the neutron emission from a fusion plasma is random in time, the random background signal will appear as a flat line in the spectrum, see e.g. the discussion in [7] concerning the TOFOR spectrometer. Modern data acquisition systems can record both the timing and energy deposition of each elastic scattering in the D1; it is therefore possible to define adaptive energy intervals that can discriminate parts of the random background. See e.g. [13–15], where this is implemented for the TOFOR spectrometer.

Consider an example, if a coincidence between two events in the D1 and D2 detectors is recorded, there is an interval of acceptable energy depositions in the D1 that is compatible with the time difference between the two events. If the energy deposition does not fall within this interval, the coincidence can be discarded as random background. On the other hand, if the energy deposition falls within this interval, it can be either a true coincidence or a part of the random background. The part of the random background where the energy deposition in the D1 overlaps with the allowed energy deposition for a true event cannot be discriminated in this way.

The efficiency of the adaptive energy thresholds to discriminate the random background therefore scales with the width of the acceptable interval compared to the energy span of all possible events. The BackTOF has very favourable properties in this regards. In figure 2 the acceptable interval for a forward as well as a BackTOF system is illustrated for 14 MeV neutrons as a function of scattering angle α. In both cases, an interval of α  =  ±10° is assumed. In the case of the forward TOF, the acceptable interval has a width of 4 MeV, which is about 30% of the entire range (0–14 MeV). On the other hand, for the BackTOF the interval is only 0.4 MeV wide, or about 3% of the entire range (0–12.5 MeV). The possibility to discriminate the random coincidences in the BackTOF is therefore enhanced by about 10 times compared with the forward TOF. The reason is that the geometry of the BackTOF is designed around an interval in the scattering angle where the energy deposition in the D1 varies slowly with the scattering angle. The opposite is true for the forward TOF.

Zoom In Zoom Out Reset image size

Finally, measurements of the energy deposition in the D1 detector can also be used to discriminate multiple scattering events in a D1 detector. For example, if the 180° scattering of a neutron in the D1 is divided into two scatterings (each less than 180°) the total energy loss will be lower compared to a single 180° collision. This will result in a shorter t_TOF when compared to a single scattering. This can then be discriminated since the energy deposition in the D1 is no longer compatible with the shorter flight time.

In this paper, a MCNP model of a backscattering time of flight spectrometer has been used to simulate the instruments response to the neutron emission from a DT plasma. The model is based on a circular D2 detector of diameter 1.0 m and thickness 2 cm. A circular hole with diameter 15 cm is left in the middle of the D2 detector to allow for the neutron beam to reach the D1 detector. The D2 detector is further separated into 3 concentric rings. The separation of the D2 in 3 rings is in part a question of manufacturability, but it also allows for improved performance. Each ring will span a different interval of recoil angles, α in figure 1(b), and this will result in different lengths of the flight path (L), and hence different t_TOF, for the same incoming neutron energy. By compensating for this difference the energy resolution of the spectrometer can be improved somewhat. Figure 3 shows an illustration of a possible detector arrangement using hexagonal detectors. The photo multiplier tubes are assumed to be mounted on the back.

Zoom In Zoom Out Reset image size

The D1 detector is separated in 5 layers along the z-axis of the spectrometer, with each layer being 7 mm thick. To reduce the count rate in the D1 detectors, each layer was further divided in 4 equal parts. An illustration of a possible D1 assembly is shown in figure 3. The PM tubes are mounted on the side of each D1 detector with a light guide in between that converts the rectangular shape of the D1 detector to the circular shaper of the PM tube.

To simulate the spectrometer response to incoming neutrons we made use of the PTRAC option in MCNP. This allows for a detailed output of each interaction made by the Monte Carlo particles, including exactly where they interacted and with which timing. This is referred to as the neutron history. Synthetic data for the D1 and D2 detectors are subsequently made using the interactions recorded in the PTRAC file and a spectrometer response is calculated. Two different types of MCNP simulations were made.

In the first simulation, only neutron histories that contain at least one interaction in the D2 detector were written to the PTRAC file. This filters out e.g. neutrons that scatter in the forward direction in the D1 and never reaches the D2 to make a coincidence. This simulation was used to generate the instrument response function with no random background included. In each simulation 128 million particles were launched.

In the second simulation, all neutrons histories were written to the PTRAC file, even if they never interacted in the D2 to make a coincidence. This simulation was used to generate synthetic data that includes the random background between uncorrelated neutrons. This is important since the random background originates from coincidences between different neutrons. It is therefore not necessary for a neutron to interact in the D2 in order to contribute to the random background. In order to keep the size of the PTRAC file manageable, the simulation was limited to 6.4 million neutron histories. A time trace of synthetic data was then constructed by adding a random starting time to each neutron history. By adjusting the range of random starting times, different intensities of the flux on the D1 can be simulated. For example, to simulate an area integrated neutron flux at the D1 of 10⁸ s⁻¹, the simulated neutron histories are distributed randomly between 0 and 6.4 · 10⁶/10⁸ s  =  0.064 s. Subsequently, a time of flight histogram is created from all possible coincidences in the simulated data.

In figure 4, the time of flight histogram for the simulated spectrometer response to 14 MeV neutrons is shown. The results are based on an MCNP simulation with 128 million neutron histories. The total response without the kinematic energy cuts is shown in solid blue. The main peak is located at t_tof  =  74 ns, and dt_tof  =  1.6 ns. The energy resolution at full width half maximum is therefore 4.3%. As can be seen, there are prominent structures at a level of a few percent in intensity on both sides of the main peak. The structures are due to neutrons colliding multiple times in the D1 detectors, either on deuterium or on carbon.

Zoom In Zoom Out Reset image size

Also shown in figure 4 are separate t_TOF histograms from histories where the incoming neutron has either scattered on carbon-12, or multiple times on deuterium in the D1. These are shown in red dashed and green dash-dot, respectively. From this analysis it is clear that the structure on the high-energy side (tof  <  74 ns) is predominantly due to neutrons scattering on carbon. The higher mass of the carbon nuclei causes the neutrons to loose less energy in the recoil compared to scattering on deuterium. Therefore they can travel the distance from D1 to D2 faster and produce a lower time of flight. Multiple scattering on deuterium in the D1 mainly shows up on the low-energy side of the main peak. Such multiple scattering typically causes a larger energy loss compared to the single scattering, and the time of flight is therefore increased.

The response function after the kinematic cuts have been applied is also shown in figure 4 in the dotted black line. The kinematic cuts are effectively discriminating the structures on both the high- and low-energy sides of the main peak, which remains near-Gaussian for at least three orders of magnitude. Of particular importance is the lack of structures on the high-energy side (low flight time) of the main peak, which could otherwise have interfered with the determination of the beam-target component as explained in section 1. Integrating the spectrum after the kinematic cuts gives an efficiency of 1.25 · 10⁻³.

In addition to the response function shown in figure 4, d(n, 2n)p breakup reactions can also introduce a background component. In contrast to elastic scattering, where it is possible to define kinematic cuts with a 1:1 relationship between the flight time of the scattered neutron and the energy of the recoil nucleus, this is a three-body reaction, and there is a continuous spectrum of events where the flight time of one of the emitted neutrons is compatible with the energy of the recoil proton. Such reactions are not included in the MCNP model described above. Instead we have estimated the impact of this background using the methodology for three body reactions as described in chapter 47 in [16]. It was found that for incoming neutrons at 14 MeV the maximum energy of neutrons that are emitted in the backwards direction, i.e. towards the D2-detector, is about 0.9 MeV. This results in flight times longer than 100 ns. Therefore the background from d(n, 2n)p breakup reactions does not interference with the main response peak at 74 ns (figure 4). Instead the background is found on the low energy side of the spectrum, which is dominated by backscattered neutrons [17] of no relevance to the fuel ion ratio measurement. Further, if the emission of the reaction products are assumed to be isotropic in the center-of-mass reference frame, only about 0.1 percent of the total number of d(n, 2n)p reactions result in neutrons emitted towards the D2-detector. This makes this contribution from d(n, 2n)p reactions vanishingly small compared to that from backscattered neutrons.

The results from the second simulation, including random coincidences, are shown in figure 5. It was found that the saturation load on a single D1 detector (here assumed to be 2 MHz) was reached for a total area integrated neutron flux on the D1 assembly of 2.6 · 10⁸ s⁻¹. The 6.4 million events simulated are therefore equivalent to 25 ms data taking at maximum load.

Zoom In Zoom Out Reset image size

The simulated spectrum contains about 8'000 true coincidence events, which are shown in solid blue. Random coincidences without adaptive energy thresholds are shown in the dashed red line. The peak signal to background is about 3. The random coincidences after the adaptive thresholds have been applied are shown in dash-dot green. As can be seen, the energy cuts are very effective at reducing the background. On the low energy side (tof  >  74 ns) the signal to background is improved by a factor of 50, and on the high-energy side (tof  <  74 ns) the background is discriminated entirely except for a shoulder above t_TOF  =  70 ns.