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Abstract
Ultrafast microchannel plate (MCP) photomultiplier tubes are under active development. To obtain high gain, high spatial resolution, and good time performance, we comprehensively investigate the effects of the gap distances and voltages from cathode to MCPin and MCPout to anode in a systematic study using the finite integral technique and Monte Carlo method. A three-dimensional model is introduced to simplify the calculations. From the simulation results, a short gap distance and high gap voltage were determined to achieve good time performance, high spatial resolution, and high gain.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Ultrafast microchannel plate (MCP) photomultiplier tubes (FPMTs) [1–9] are under active development by the Institute of High Energy Physics of the Chinese Academy of Sciences and Northern Night Vision Technology Co., Ltd. With a fast response time, high spatial resolution, small size, and stable and high gain, FPMTs seem promising for high-energy physics projects [10–12] such as the Large Hadron Collider beauty experiment [13] and Circular Electron Positron Collider [14,15].
An FPMT is a vacuum device consisting of a photocathode, which absorbs light and emits photoelectrons, at least one MCP for multiplying the electrons from the photocathode, and an anode, which can be single or segmented depending on the application to collect the output bunches of electrons. The FPMT response is substantially affected by operation and geometric parameters. The MCP performance regarding the bias voltage, length to diameter ratio (L/D), channel bias angle, and electrode penetration depth has been thoroughly investigated [16]. We comprehensively study the FPMT performance, including the gain, response time characteristics, and spatial resolution according to the gap distances and voltages from cathode to MCPin and MCPout to anode.
2. Theory and simulations
We developed a three-dimensional FPMT model with an MCP. The gain, time performance, and spatial resolution according to varying operation and geometric parameters were simulated. The electric fields, electron trajectories, energies, and velocities were calculated based on the finite integral technique and Monte Carlo method.
The simulation of secondary electron emission in the MCP is essential yet difficult. Inspired by previous studies [17–22], our simulation considered the following aspects:
- 1) The edge effect of the electric field was simulated in detail in the presence of electrode end-spoiling.
- 2) The space charge effect that prevails in microchannel electron multiplication is usually omitted in MCP simulations but included in our simulation.
- 3) The Furman model [23] is a relatively mature secondary electron emission model and implemented in the simulation.
- a) Three types of secondary electrons: backscattered, rediffused, and true secondary electrons.
- b) Emitted angle: cos θ distribution, independent of the primary incident angle and energy, fully uncorrelated.
- c) Emitted energy: energy conservation, does not exceed the primary electron energy, and the aggregate energy does not exceed the primary energy.
- d) Secondary electron yields (SEY) are well defined:$${\delta _{ts}}({E,\theta } )= \hat{\delta }(\theta )D\left( {\frac{E}{{\hat{E}(\theta )}}} \right)$$where δbs, δrd and δts are backscattered yield, rediffused yield and true secondary yield, respectively. E and θ are incident energy and angle of primary electrons. δbs(E, 0) and δrd(E, 0) are yields at normal incidence (θ = 0°). Scaling function D(x) ensures that δts reaches peak value $\hat{\delta }$ at energy $\hat{E}$. ${e_1}$, ${e_2}$, ${r_1}$, ${r_2}$ and s are adjustable parameters which determine the yield trends. The adjustable parameter values employed in our simulation are listed in Table 1.
Table 1. Default model parameters
Implementing millions of MCP channels using a three-dimensional FPMT model is impossible. Hence, a simplified model based on an MCP with hundreds of channels was adopted in our simulation, as shown in Fig. 1. To avoid the edge electric field distortion affecting the electron trajectories in the cathode to MCPin and MCPout to anode gaps, a FPMT model with diameter of 2600 µm which is much larger than the light spot, even the electronic speckle on the anode was built. We considered a channel diameter of 6 µm, bias angle of 7°, channel length of 320 µm, and electrode penetration depth of 3 µm. The maximum total secondary yield of the MCP leaded glass wall is
for primary energy E = 320 eV (shown in Fig. 2) at normal incidence. These parameters were consistent with the MCP designed by Northern Night Vision Technology Co., Ltd. (NNVT) for their FPMT. A 20 µm diameter light spot illuminated the FPMT photocathode. Two hundred photoelectrons sampled using the Monte Carlo method were emitted from the illuminated spot on the photocathode. As shown in Fig. 3 that the initial energy of photoelectrons obeyed a β(1,4) distribution in the range 0.0–0.6 eV for the input photon wavelength of 410 nm, which is the data of the FPMT photocathode from NNVT. The initial elevation followed the Lambert cosine distribution from 0° to 90°. The azimuth obeyed a 0–2π uniform distribution. The initial positions were uniformly distributed. The applied voltage on MCP was 1000 V. The gap distances and voltages from the cathode to MCPin and MCPout to anode were denoted by Din, Uin, Dout, and Uout, respectively. In the simulations, only one of the four adjustable parameters was varied at a time, whereas the others were fixed to the values listed in Table 1.
Fig. 2. SEY as a function of primary electron energy over the range of 0-1000 eV at normal incidence.
3. Results and discussion
3.1 Effects of voltage Uin and distance Din
The dependence of the gain, time characteristics, and spatial resolution on Uin and Din was thoroughly investigated. Owing to mass computing, the time characteristics include only the transit time, time resolution, and rise time. A transit time spread (TTS) will be reported in future work. Din was varied from 100 µm to 500 µm for Uin of 100 V, 200 V, 300 V, and 400 V. The other parameters were set as listed in Table 1.
As shown in Fig. 4, Uin had a significant impact on the FPMT gain. With an increase in Uin, the gain increased and reached its maximum of 226035 at 400 V. On one hand, higher Uin could penetrate the MCP channel deeper as an “additional voltage” applying on the MCP and helping to obtain a higher gain. On the other hand, it is well known that the MCP gain is proportional to the SEY of the first collision, and SEY is a function of primary electron incident energy which depends on Uin. Thus, the MCP gain is related to Uin. Although the SEY for MCP at incident energy of 400 eV was lower than that at 300 eV (exhibited in Fig. 1), as a result of the slight difference and the “additional voltage” effect, the gain for 400 eV was even higher.
The time distribution of the output electrons (TDOE) was then simulated, obtaining the results shown in Fig. 5. The theoretical rise time ranged from 35 ps to 42 ps, but Din and Uin had negligible effects. The rise time was idealized in the simulation, ignoring the time delay of the oscilloscope. The time resolution was defined as the full width at half maximum of the TDOE. It ranged from 43 ps to 55 ps with no clear trend.
A decreased transit time (theoretical) by increasing Uin (or decreasing Din) was observed in the statistical transit time distribution shown in Fig. 6. A higher Uin (or shorter Din) strengthened the electric field, which accelerated the input electrons and reduced the transit time. The minimum transit time was expected to be 216 ps at Uin = 400 V and Din = 100 µm, being 1 ps faster than that at Uin = 300 V and Din = 100 µm. Hence, 216 ps was close to the transit time limit for Din = 100 µm.
The electron output distributions along the X and Y axes were obtained as shown in Fig. 7. The full width at half maximum of the pulse corresponded to the spatial resolution. The diameter of the illuminated spot was 20 µm. As the electron flow spread during multiplication from the photocathode to the anode, the spatial resolution measured at the anode broadened to 161 µm along the X axis and to 135 µm along the Y axis. Owing to the 7° bias angle of the MCP channels in the X-Z plane (as shown in Fig. 1), the output distribution was symmetric with respect to 0 µm along the Y axis but not along the X axis, and the MCP channel cross section in the X-Y plane at the output face was elliptical (X was the major axes), not round. Thus, the electronic speckle on the anode which was parallel to the MCP output face was oval, and the spatial resolution along the X axis was larger than that along Y axis. Parameters Din and Uin had no notable effects on the spatial resolution owing to the small illuminated spot on the photocathode (20 µm in diameter) and small dispersion of the photoelectrons on the MCP input face.
Fig. 7. Electron output distributions along X and Y axes for Din = 200 µm, Uin = 100 V, Dout = 200 µm, and Uout = 100 V.
3.2 Effects of voltage Uout and distance Dout
The gain, time characteristics, and spatial resolution resulting from the variations in voltage Uout and distance Dout were also simulated. Dout was varied from 100 µm to 500 µm for Uout of 100 V, 200 V, 300 V, and 400 V. The other parameters were set as listed in Table 1.
For the output side, the gain was affected by the electric field intensity Eout (Uout /Dout). The gain variation according to Eout is shown in Fig. 8. With an increase in Eout, the gain increased until reaching its maximum of 235163 at 4 V/µm (Uout = 400 V, Dout = 100 µm). We counted the gains for various cross sections along the MCP channel for Dout = 100 µm, Uout = 100 V (Eout = 1 V/µm) and 400 V (Eout = 4 V/µm). As shown in Fig. 9, the particle number for Eout = 4 V/µm was larger than Eout = 1 V/µm for each section of the whole channel. Stronger electric field between the MCPout and anode just like an “additional voltage” applied on the MCP and helped to obtain a higher gain. In Fig. 9, the particle number first increased along the channel, and then decreased at the output electrode domain. The reduction was attributed to the low SEY of the MCP nickel-chromium electrode (the maximum SEY at normal incidence is 1). Electrons striking at the electrode had a strong possibility of being absorbed without emission, which resulted in the gain decline. It is not difficult to find that the downward trend for Eout = 1 V/µm was greater, which can be ascribed to the “suction effect”. Figure 10 shows the electric field distributions of 30 V potential difference near the MCP output face for Dout = 100 µm, Uout = 100 V (Eout = 1 V/µm) and 400 V (Eout = 4 V/µm). It is exhibited that Eout = 4 V/µm penetrated the MCP channel deeper and would suction more output electrons directly preventing them from being absorbed by the MCP output electrode. To sum up, for the output side, strong electric field has two positive effects on the gain. On one hand, it offers an “additional voltage” on MCP. On the other hand, it provides a “suction effect” which prevents electrons from being absorbed by the MCP electrode.
Fig. 9. Gains versus the distance from the MCP input face to the monitor section for Dout = 100 µm, Uout = 100 V and 400 V respectively. The blue area is the MCP output penetrating electrode domain.
Fig. 10. the electric field distributions for 30 V potential difference near the MCP output face for Dout = 100 µm, Uout = 100 V (left side) and 400 V (right side), respectively.
The TDOE for varying Dout and Uout was also simulated. The rise time results are shown in Fig. 11. Dout and Uout considerably affected the rise time. A shorter Dout (or higher Uout) strengthened the electric field intensity Eout, which increased the consistency of the electronic motion and shortened the rise time. In addition, the reduction tended to flatten with increasing electric intensity (increasing Uout or decreasing Dout). The minimum rise time was 25 ps at Uout of 400 V and Dout of 100 µm, being close to the rise time limit.
As shown in Fig. 12, Dout and Uout drastically affected the time resolution, which decreased with increasing electric intensity. The reason for this is the same as that for the rise time. In addition, with increasing electric intensity, the effect gradually weakened. The minimum time resolution was 42 ps at Uout of 400 V and Dout of 100 µm.
Figure 13 shows the transit time distribution. A decreased transit time was observed with increasing electric intensity. For Dout of 500 µm, Uout had a small impact on the transit time. The electric field intensity weakened with increasing Din, thereby mitigating the declining tendency. The minimum transit time was 221 ps at Uout of 400 V and Dout of 100 µm.
Distance Dout and voltage Uout notably affected the spatial resolution. Figure 14 shows the spatial resolutions along the X and Y axes. The spatial resolution was inversely proportional to Uout and directly proportional to Dout. The declining tendency was mitigated with increasing electric intensity. The best spatial resolution was 41 µm along the X axis and 49 µm along the Y axis at Uout of 400 V and Dout of 100 µm. Strong electric intensity shortened the electron flight time between the MCP output face and anode, thus narrowing the spread.
Fig. 14. Spatial resolution according to Uout for Dout of 100–500 µm along (A) X and (B) Y axes (FWHM, full width at half maximum).
Overall, to obtain a short transit time and a high gain, a short Din (unnecessary for the high gain) and Dout and high Uin and Uout should be employed in FPMT design. A short Dout and high Uout can also shorten the rise time and time resolution as well as narrow the spatial spread of the output electrons on the anode.
4. Conclusion
A computer model was developed to investigate the performance of an FPMT under a wide range of operation and geometric parameters based on the finite integral technique, Monte Carlo method, and Furman secondary emission model. Simulation results showed that the gain, time characteristics, and spatial resolution depended on distances Din and Dout as well as on voltages Uin and Uout. Short Din and Dout and high Uin and Uout were beneficial for good time performance, high spatial resolution and high gain. Our findings can be used as guidelines for the design and development of FPMTs and other MCP-based detectors.
Funding
National Natural Science Foundation of China (12005083); Jinling Institute of Technology (jit-b-201837).
Acknowledgments
Lin Chen thanks the National Natural Science Foundation of China (Grant No. 12005083) and Ph.D. Project supported by the Jinling Institute of Technology (Grant No. jit-b-201837).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data availability. Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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