Light Guide Design

Requirements

Given the dimensions of the individual paddles of 60mm x 2.54mm x 2520mm and the dimensions of the photo multiplier tube (PMT) including necessary magnetic shielding it is necessary to have light guides. Further arguments for the use of light guides are the rectangular shape of the paddle cross section versus the round shape of the PMT entrance window that does not favor a direct coupling of the readout to the scintillator. In addition particles that pass very close to the end of the paddle would generate a disproportionate large signal in the PMT because of the highly non linear light absorption at short distances for short wave lengths (UV). The PMT H10534 is a 10 stage tube with a quoted 2 inch window. Measurements indicate a total diameter of the tube of 50mm. The H10534 is a full assembly including shielding and base as received from the manufacturer. At this point this assembly has an outer diameter of 60mm. Because of the expected high magnetic field in the region of the PMT of the order of 100 Gauss additional iron shielding is necessary. At this point a total outer diameter including such a shielding is estimated to be of the order of 66mm. As a consequence this dimension becomes larger than the paddle height of 60mm requiring the light guide to be bend in order the provide enough space to tack the paddles on top of each other.

Geometrical Considerations

1. The following picture shows the situation with having 66mm outer diameter readout systems coupled to the end of 60mm high paddles in terms of space as viewed for the end. In this figure tof_paddle_setting.pdf one can see that because of the additional space required by the PMT plus shielding the paddles could not be put on top of each other unless there is a light guide with a bend. Also one sees that staggering the paddles with not solve the problem because of the rather large impact angles tracks can have at the location of the TOF. The red line indicates the largest possible impact angles of tracks. The distribution of impact angles can be found here.
2. In the following an estimation is done of what bend angle is required. As an arbitrary number it is assumed that the light guide has a total length of 200mm. The picture tof_lightguide_bend1.pdf assumes a bend of 10 degree and shows that this is sufficient to provide enough space for the PMT and shielding on only at the end of the light guide but also at a location more than 50mm toward the paddle which is necessary as the shielding has to extend beyond the PMT entrance window by at least 50mm and additional space for the holding structure is needed as well. As one can see on the bottom right side of the picture a 5 degree bend will not be sufficient given a light guide length of 200mm.
3. Given the parameters from above a light guide design based on a total length of 200mm is drawn here with the emphasis to make the tapering from the rectangular cross section of the paddle to the round cross section of the PMT as shallow as possible. This is shown in tof_lightguide20cm.pdf where the transition from square to round with established over 110mm. This is also the same region where the 10 degree bend needs to happen because once the light guide is in its cylindrical shape no additional bending should be present.
4. Assuming a bend over the tapering length 110mm tof_lightguide_bend10deg.pdf shows the available space at the end of the light guide which is sufficient with a 10 degree bend having 60mm high paddles. However 10 degrees is not enough if the paddle would be only 30mm high. Because the innermost paddles see a much higher rate it might be necessary to reduce the vertical size of some paddles by a factor of two. In such a case the light guide needs a bend of about 16 degree as shown in tof_lightguide_bend16deg.pdf.

Light Guide Prototypes

1. A prototype light that has been constructed at FSU is shown in TOF-Light-Guide.pdf.

GEANT4 Simulation

GEANT4 is used in a first attempt to simulate the light loss in the light guide. A very easy way to introduce a bend is to use a toroid solid volume in GEANT4 and have the bend only in the round section of the light guide. The tapered section where the light guide goes from a rectangular cross section to a round cross section is done with a trapezoid and a cone volume using GEANT4 volume subtraction method. A picture of a light guide with a 11cm long tapered section and a 10 degree bend is shown below:

Magenta indicates the beginning of the light guide and the green part is the tapered section to move from a rectangular cross section to a round cross section. The red part is the bend of the circular part of 10 degree while the blue part is a strait section of cylinder 7cm long. The yellow part indicates the glass entrance window of the PMT.
In the following there are four links to pdf files for four different light guide configurations. 10 degree and 20 degree bend with short and long tapered sections. In all cases 1000 photons were generated in the scintillator section in 2pi and transported through the scintillator. At each interface to a new section of the light guide volume the photons were counted and plotted in a histogram. The ratio of histogram entries provide the information about who much loss is expected at each section and through the whole light guide.

• Light Guide 10deg bend with short tapered section
• Light Guide 20deg bend with short tapered section
• Light Guide 10deg bend with long tapered section
• Light Guide 20deg bend with long tapered section

The resulting numbers and ratios for the four tested configurations are shown below:

The light loss through the whole light guide is of the order of 25%.
Each row contains the number of photons arriving at the next volume interface. First row is at the entrance to the light guide then to the tapered section then to the bend section then to the strait section then to the PMT glass and finally to the PMT photo cathode. The fractional numbers are the photon counts divided by the previous number of photons subtracted from 1. This is the % in loss of photons through the previous section of light guide. The number at the end is the total loss of photons through the full light guide in % normalized to 1.