The dependence of CE and TTS on the applied voltage (UI) and the inner diameter (DI-in) of the electrode I is well investigated. UI and DI-in are varied from − 600 V to 600 V and 40 mm to 100 mm. Results are graphically represented in Fig. 2 and Fig. 3.
CE versus UI and DI-in over the ranges of − 600 V ≤ UI ≤ 600 V and 40 mm ≤ DI-in ≤ 100 mm.
TTS versus UI and DI-in over the ranges of − 600 V ≤ UI ≤ 600 V and 40 mm ≤ DI-in ≤ 100 mm.
As can be seen in Fig. 2, the tendencies of CE vs. UI and DI-in are similar. With the increases of UI and DI-in, CEs gradually increase until the maximum of 100% at UI = − 200 V and DI-in = 70 mm and then remain constant. Obviously, negative voltage weakens the electric field upon the dynode, which repels a portion of photoelectrons and makes them be attracted by the electrode II. Owing to the 0 V bias voltage, small DI-in not only weakens the electric field upon the dynode, but also interrupt the collection process, which results in the low CE.
TTS vs. UI also has the similar change trend as TTS vs. DI-in. With the increasing UI and DI-in, TTSs gradually decrease until the minimum and then increase slightly, whose reason can be ascribed. As mentioned above, low UI generates weak electric field in which TTS is more affected by the initial momentum of photoelectrons. On the contrary, high UI generates strong field upon the dynode, which enlarges the speed difference between the photoelectrons from the top and other areas of the photocathode, and thus widens TTS. Results show that at UI = 0 V, TTS reaches the minimum value of 5.3 ns. Similarly, DI-in determines the field strength in the PMT and finally affects TTS. The minimum TTS is 4.9 ns at DI-in = 70 mm.
Based on the consideration of both high CE and short TTS, UI = 0 V and DI-in = 70 mm are studied out as the optimized values of electrode I, assuming that other parameter values are fixed as listed in Table 1.
CE and TTS performances for the bias voltage (UII) and diameter (DII) of the electrode II over the ranges of 0 V ≤ UII ≤ 2000 V and 90 mm ≤ DII ≤ 250 mm are studied. Results are exhibited in Fig. 4 and Fig. 5.
CE versus UII and DII over the ranges of 0 V ≤ UII ≤ 2000 V and 90 mm ≤ DII ≤ 250 mm.
TTS versus UII and DII over the ranges of 0 V ≤ UII ≤ 2000 V and 90 mm ≤ DII ≤ 250 mm.
Two similar tendencies are observed in Fig. 4. CEs keep 100% until UII = 1600 V and DII = 170 mm, then decrease slightly. It can be seen form the electron trajectories that with the increase of UII and DII, more photoelectrons tend to be attracted by the electrode II, which deteriorates CE.
A declining TTS is observed for increasing UII in Fig. 5. At UII = 2000 V, TTS is the minimum which is 4.6 ns. With the increase of DII, TTS gradually decreases until the minimum of 4.9 ns at DII = 170 mm and then increases. As analyzed in the UI part, DII affects the electric field intensity in the PMT, and thus TTS.
Considering both high CE and short TTS, UII = 1600 V and DII = 170 mm are supposed to be the optimized values, assuming that other parameter values are fixed as listed in Table 1.
Diameter of the dynode (Dd) affects the electric field distribution in and upon the dynode. The dependence of CE and TTS on the bias voltage of the dynode (Ud) and Dd is systematically investigated over the ranges of 0 V ≤ Ud ≤ 2000 V and 70 mm ≤ Dd ≤ 130 mm.
Results in Fig. 6 show that Dd has no significant effect on CE. CE remains 100% in the whole interval 0 mm ≤ Dd ≤ 2000 mm. CE stayed at 100% for various Ud except 0 V which is 99.2%.
CE versus Ud and Dd over the ranges of 0 V ≤ Ud ≤ 2000 V and 70 mm ≤ Dd ≤ 130 mm.
It is shown in Fig. 7 that TTS gradually decreases to a minimum of 5.3 ns at Ud = 1000 V and then increases to some extent with increasing Ud. The reason is the same as UI’s as mentioned above. In addition, Dd has the similar effects on TTS as DI-in ≥ 70 mm. An increasing TTS (the minimum is 5.3 ns) is observed for the increasing Dd.
TTS versus Ud and Dd over the ranges of 0 V ≤ Ud ≤ 2000 V and 70 mm ≤ Dd ≤ 130 mm.
Based on above discussion, Ud = 1000 V and Dd = 70 mm are employed as the optimized values for the dynode, assuming that other parameter values are fixed as listed in Table 1.
Glass envelop handle
The inner surfaces of the bottom hemisphere and the handle of the glass envelope are coated with the aluminum thin layer which is electrically connected with the cathode (0 V). Diameter of the glass envelope handle (Dh) impacts the electric field distribution, and thus the time properties and CE. Effects of Dh on CE and TTS are studied in the interval of 180 mm ≤ Dh ≤ 340 mm.
As exhibited in Fig. 8 that CE remains 100% first and then decreases after 300 mm. The reason is similar as DII’s. Besides, a decreasing TTS is observed. The electric field shielded by the glass handle is gradually released with the increase of Dh, which enhances the electric field in the PMT. The strong field reduces the momentum difference of photoelectrons and narrows TTS. Therefore, Dh should be optimized into 300 mm.
CE and TTS as functions of Dh over the range of 180 mm ≤ Dh ≤ 340 mm.
The optimized design
Inspired by above simulations, a set geometry and operating parameters of the Dynode-MCP-PMT are proposed for better performance as summarized in Table 2.
Table 2 Parameters of the optimized 20-in. Dynode-MCP-PMT.
Results show that CE of the optimized model is 100%. TTS is 3.7 ns which is less than 5 ns and almost cut the 7.2 ns (before optimization) in half. Besides, the gain of the first dynode is 6.4 which is benefit for the total gain.”