Fine-mesh photomultiplier tubes

Since ACC is placed in a high magnetic field of 1.5 T in the Belle detector, we decided to use fine-mesh photomultiplier tubes (FM-PMTs) for the detection of Cerenkov lights, taking advantage of its large effective area and high gain [44]. Other candidate photo-sensors such as microchannel-plate photomultiplier tubes (MCP-PMT) and hybrid photodiodes (HPD) were still at R&D stages or extremely expensive when this decision was made. The FM-PMTs were produced by Hamamatsu Photonics [49].
A sectional view of an FM-PMT is shown in Fig. . Each FM-PMT has a borosilicate glass window, a bialkali photo-cathode, 19 fine-mesh dynodes, and an anode. Three types of FM-PMTs of 2, 2.5, and 3 inches in diameter are used in ACC. The effective diameters ($\phi$) of these FM-PMTs are 39, 51, and 64 mm. The cathode-to-anode distance ($L$) is about 20 mm. The average quantum efficiency of the photo-cathode is 25 % at 400 nm wavelength. The optical opening of the mesh is about 50 %.

Figure: Sectional view of FM-PMT.

The FM-PMTs with 19 dynode stages of fine mesh have high gain ($\sim 10^8$) with moderate HV values ($<$ 2500 V). The gain of FM-PMT decreases as a function of field strength as shown in Fig. . The gain reduction is $\sim 10^{-3}$ for FM-PMTs placed parallel to the direction of magnetic field and slightly recovers when they are tilted. The FM-PMTs used for ACC were produced with dynodes with a finer mesh spacing than conventional products at that time, to give approximately 10 times higher gain as shown in in Fig. .

Figure: Relative gains of conventional and improved FM-PMTs in magnetic fields. The tubes were placed parallel (0$^o$) or tilted by 30$^o$ with respect to the field direction.

Effects of a magnetic field on the pulse height resolution have been evaluated by tracing the change of a quantity $N_{eff}$, which is defined as $N_{eff} = (\mu /\sigma)^2$, by using the mean ($\mu$) and sigma ($\sigma$) of the recorded ADC spectrum. The quantity $N_{eff}$ represents the effective photostatistics for the spectrum, which is a convolution of a single-photoelectron (pe) response of the device and the Poisson statistics with $N_{pe}$, the average number of photoelectrons emitted from the photo-cathode. For FM-PMTs, the ratio $N_{pe}/N_{eff}$ is about 2 at $B$ = 0. The relatively large excess noise factor is due to the fact that a single-photoelectron spectrum does not have any characteristic peak [50]. Reduction of $N_{eff}$ in a magnetic field has been measured for 2 in., 2.5 in. and 3 in. FM-PMTs, with $N_{eff}$ at $B$ = 0 ($N^0_{eff}$) of about 20. Table shows the ratio $N_{eff}/N^0_{eff}$ at $B$ = 1.5 T for two ranges of applied HVs. As the field $B$ increases, the resolution deteriorates and the quantity $N_{eff}$ decreases. The decrease in $N_{eff}$ is larger when the field is at a large angle such as 30$^o$ than the case of $\theta = 0^o$, and the decrease in $N_{eff}$ at a large angle is more significant for smaller FM-PMTs. However, it is noticed that, in a magnetic field, the resolution improves, namely the quantity $N_{eff}$ increases, by applying higher voltage, while no significant change is found in absence of the field.

Table: Measured ratio $N_{eff}/N^0_{eff}$ at B = 1.5 T. The number of tested samples for each condition is shown in parentheses.

PMT	2000 - 2200 V		2600 - 2800 V
diam.
	$\theta$ = 0$^o$	$\theta$ = 30$^o$	$\theta$ = 0$^o$	$\theta$ = 30$^o$
2	0.74 (7)	0.64 (10)	0.75 (10)	0.73 (10)
2.5	0.80 (5)	0.73 (5)	0.85 (8)	0.85 (8)
3	0.79 (2)	0.77 (4)	0.87 (6)	0.99 (7)