Light Concentrators

From: Steve Biller (
Date: Wed Jun 08 2005 - 11:02:58 CDT

  It doesn't seem to us that there should be any problems with
light concentrators. In fact, preliminary investigations suggest
that these ought to work extremely well for Braidwood. Here
are some details:

  The optimal shape of a light collectors for hemispherical
PMTs is not a flat cone, but can be best described as approximately
segments of a Winston cone arranged in a ring about the perimeter of
the PMT. In accordance with Lioville's theorem, the effective gain
in light collection (or 'concentration factor'), has several terms:
First, 1/sin^2(theta), where theta is the half-angle of the cone opening.
Secondly, the transmission function at a given incident angle
(i.e. cone reflectivity and probablity to release a photoelectron
at a given incidence angle on the PMT). Thirdly, because the PMT surface
is curved, there is an extra factor for the ratio of the actual
area to the projected area at zero incidence angle. For typical, 8-inch,
hemispherical tubes, this last factor amounts to a gain of about 30%.

  The SNO concentrators were optimised for a cut-off half-angle
of about 56 degrees, so as to include 1m of light water outside
of the acrylic vessel. For Braidwood, if we just wanted to set this
angle at the acrylic vessel (which may be very reasonable),
the angle is almost identical. Obviously, these concentrators have
worked extremely well in SNO (we couldn't have done without them),
so there is a clear proof of principle that this does all work.

  The theoretical maximum concentration factor (taking the transmission
function as being 1) for a 56 degree opening angle and standard 8-inch,
hemispherical PMTs is therefore:

         C_max = (1/sin^2(56 deg))*(1.0)*(1.33) = 1.9
  In practise, light cones have something closer to a 90% transmission
function averaged over angles with an angular response that rolls-off
at the edges. In SNO, we managed to achieve an average concentration factor
of about 1.7. There is every reason to believe that a similar factor
can be achieved for Braidwood. If we wished to extend the cut-off angle
to encorporate a view of 20cm into the buffer region, this concentration
factor would go down to about 1.5.

  Two issues that arise in the use of concentrators are: 1) the fact that
the angular acceptance of the PMTs is clearly affected and needs to be
modelled, and 2) some photons will bounce off the reflectors, into the
detector to produce late light. In the case of the former, PMTs have
a wavelength-dependent angular response that has to be considered in any
case, and this is all part of what you see from your calibration data.
In SNO, while we've gone through the process of modelling and questioning
and re-modelling etc. the angular response function of cones, the fact is
that this really hasn't been a problem as the calibrations nail things
And, in the case of Braidwood, we're talking about a relative measurement
of identical detectors so all this is second order in any case.
Regarding the
late light issue, once again, reflections off the PMT glass etc. are there
anyway. The additional light, whether late or not, improves the calorimetric
measurement of total charge. Also, the increased sampling statistics of
each PMT+concentrator improves the resolution of the prompt-light peak and,
thus, enhances the ability to reconstruct events based on timing.
The late-timing tail due to reflections will only last tens of nanoseconds
and, again, while there a some aspects of this tail which are not perfectly
modelled in SNO, this has not really affected us and the concentrators have
definately been a positive (in fact, necessary) gain.

  Preliminary simulations of the Braidwood geometry using the SNO
Monte Carlo both confirm a concentration factor in the expected
regime and indicates that the additional late-light tail based on the
arrival time of the 1st photon at each PMT appears to be minimal.
However, we are still studying details of the timing and charge
resolutions and particularly need to look more closely at these
near the edge of the fiducial volume. We hope to produce a more detailed
report of all this in the near future.

  A final note: the context in which we discussed the use of light
concentrators previously was not as a means to necessarily decrease the
number of PMTs used, but to enhance the light collection for the same
number of tubes in a cost-efficient manner so as to further improve the
vertex reconstruction and energy resolution of the detector (after all,
a gain of 1.7 in light yield stands to improve our energy resolution
by up to 30%). In addition, they may allow us to potentially pick up the
weaker Cherenkov signal for use in additional background discrimination.

                                              - Steve

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