| Process | K+ | K- | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| BCAL | FTOF | BCAL | FTOF | |||||||||
| hits | ⟨P⟩ | R<0.1 | hits | ⟨P⟩ | R<0.1 | hits | ⟨P⟩ | R<0.1 | hits | ⟨P⟩ | R<0.1 | |
| GeV/c | GeV/c | GeV/c | GeV/c | |||||||||
| X(2.2)+→K°(890)K°(890)π+ | 22% | 1.9 | 24% | 48% | 2.4 | 74% | 22% | 1.9 | 24% | 48% | 2.4 | 74% |
| X(2.2)+→K+K°(890) | 52% | 2.6 | 8% | 32% | 5.0 | 5% | 38% | 2.3 | 10% | 34% | 3.4 | 38% |
| X(2.175)°→φ(1020)f°(980)→K+K-π+π- | 12% | 1.7 | 8% | 48% | 2.0 | 93% | 12% | 1.7 | 7% | 46% | 2.0 | 93% |
The influence of the Cherenkov detector on the identification of the 1-st process is not dramatic. At most, it would allow to double the identifiable sample. It would be more important for the 2-nd sample increasing the number of identifiable events by a factor of about 4. It turns out that the decay mode 2) provides one relatively energetic kaon, however it is emitted at large angles and often hits BCAL. Additionally, a Cherenkov detector would add a benefit of redundancy to the PID system, which helps to calibrate it. Another observation - the extra coverage provided by aerogel helps to identify the 1-st process if a strong rejection power is needed.
The lowest pion/kaon thresholds
that gases at atmospheric pressure and room temperature provide is about 2.5/8.9 GeV/c
It would help to push
the threshold as low as reasonable.
Potential options to lower the threshold are:
So far, a gas threshold detector has been considered, but investigations have been also done for a single aerogel detector 2) and for a DIRC-type detector 5). The conclusion is in favor of a gas detector against the option 2). DIRC 5) seems to be expensive and difficult to build.
The goal of this study is to optimize the design of the threshold counter at atmospheric pressure, as well as to evaluate the options 3) and 4).
The gas Cherenkov detector location and size have been fixed. It has been suggested to split the volume into 16 sectors and use 2 mirrors in each sector, in order to move the light spot to a special place, where the field is about 200 Gs and the photodetector can be positioned perpendicular to the field direction, in order to provide an effective shielding. I tried to optimize the optics and simulated the Cherenkov light detection with GEANT. The general geometry was taken from the HDDS simulation code.
The radiator is about 200~cm long, filled
with C4F10.
The refractive index is 1.00141 at 300 nm and the pion threshold is 2.64 GeV/c. This gas has the highest
refractive index for available gases which do not need heating and a very good transparency down to 160 nm.
The gas dispersion is shown on the next picture.
It has been suggested to use elliptical mirrors.
The Cherenkov radiation angle is about
0.05 at γ=1 and 0.02-0.04 for pions at 3-4 GeV/c. The trajectories bite in θ is about ±0.07,
which would smear the light spot in the focal planes stronger than the Cherenkov
radiation angle. For threshold detectors the goal is to minimize the size of the photodetector. Elliptical mirrors, therefore,
are a reasonable choice since the practically straight trajectories are emitted from a small area. However, such
a mirror would not focus Cherenkov light into a thin ring and for a RICH one should use different
mirrors.
The photon detector hit scatter plots are shown on the next picture. Pions evenly populating
a momentum range from
2.5 to 6.5 GeV/c were simulated, uniformly in the angular phase space. The left/right plot
shows the photons from pions below/above 4 GeV/c.
It turns out that this optics design leaves holes in the acceptance. The light from particles,
which hit boundaries between two 1-st mirrors is properly collected up to polar angles of
particle emission of about 0.13 rad. For larger angles the light reflected by the 1-st mirror
misses the 2-nd mirror of the same sector, hits the 2-nd mirror of the neighbor sector
and is lost. The next picture illustrates this effect.
The picture shows one sector of the detector, the sector's boundaries are presented by green lines.
The 1-st mirror is blue, the second mirror is black. The line of sight is along Z.
Three trajectories for pions at 2.7 GeV/c are shown, simulated at θ=0.13 (bottom)
and θ=0.15 (top), which hit the boundaries, and a trajectory at θ=0.13 closer
to the mirror center. While the light from the first and the last trajectories
is properly collected, the light from the second one goes to the neighbor sectors and is lost.
A flat mirror between the neighbor sectors would not help to recover this light.
Apparently, the focal length of the 1-st mirror is too short.
This picture also shows that the trajectories azimuthal component, imposed by the central
solenoidal field, is reduced at the Cherenkov detector and particles move nearly radially.
This is a result of the radial field component at the solenoid exit.
Another drawback of this geometry is a too fine mirror structure at low radii,
leading to splitting of light radiated by trajectories at θ<0.04 between typically 4 channels.
The photon detector hit scatter plots are shown on the next picture. Pions evenly populating
a momentum range from
2.5 to 7.5 GeV/c were simulated, uniformly in the angular phase space. The left/right plot
shows the photons from pions below/above 4 GeV/c. The next plot uses a narrower phase space
of 3.8<P<4.0 GeV/c, 0.09<θ<0.11. The axis X on these plots points along a radius.
The observed number of photoelectrons depends on the radiation angle, the radiator length
and the detector figure of merit No:
Npe=No L(cm) sin²θ.
Typically, with one mirror reflection, one can reach values
No≅50 for normal PMTs and No≅100
for PMTs with quartz windows.
The simulation result for the figure of merit are given in the next table. In order
to compare the results with other detectors, which typically use one reflection,
one of the mirrors was changed to ideal reflection.
It follows from the table that simulation overestimate the typical figure of merit
by a factor of about 2. Therefore, I apply an additional reduction factor 0.5
for the number of simulated photons.
The full number of photoelectrons produced by a pion in the whole detector is
presented on the next plot, for the regular borosilicate window, UV-enhanced borosilicate
window and the quartz (fused silica) window (all taken from Photonis specs).
The quartz window result is well described by a conventional formula with a figure of merit of
No=100.
One can also compare this calculation to
the measurements from CLAS, which observed about 15 p.e. at γ=1, from 60 cm of the same radiator,
2.5 reflections and a UV-enhanced window. It would be projected to about 45 p.e. for
our case, which is slightly larger than my estimate of ≅40.
The number of channels hit by one track depends on the trajectory angles and is about
1.3. At this level I assume that the full signal is analyzed, adding signals from
2 adjacent sectors, if needed. The 1 photoelectron signal was simulated using
Photonis specs. The next plots show the 1-p.e. signal shape and the efficiency
to detect a pion if the threshold corresponds to the average amplitude from 3 photoelectrons.
At this threshold no 1-p.e. signal should be detected.
Optics Optimization
General approach
The trajectories of particles at P>3 GeV/c look nearly straight in r-projection.
Interestingly, in the Cherenkov detector area, the trajectories have very small azimuthal
component, which is illustrated by the next plot. Three trajectories are shown,
at the same momentum of 3 GeV/c and emitted at different polar angles. The view is along the beam.
The reason for turning the trajectories opposite to the main solenoidal bend
is a high radial field at the solenoid exit.
I used the following constraints:
There are two free parameters:
First iteration
For the 1-st try I selected the 1-st focal length at 0.3 of the distance between the
two mirrors.
This minimizes the photodetector size, but requires
a large 2-nd mirror.
The azimuthal space is divided into 16 sectors.
In order to use these considerations I wrote a script which
calculates the optimal parameters and positions of the mirrors.
I ran it from the interactive GEANT. The script
plotted the results overlaying them with the setup layout from GEANT.
The following plot shows these results with blue lines, while the
optimized geometry has been already set in GEANT. Several pion trajectories
with a momentum of 4.5 GeV/c, produced at various polar angles have been
simulated.
The 2-nd mirror is in fact practically spherical.
#
RZ, cm
RX=RY, cm
Zcenter, cm
Rcenter, cm
angle
1
321.1
143.6
283.4
46.2
9.2°
2
103.2
101.3
582.9
111.2
72.4°
GEANT definitions
I used my version of GEANT (which had elliptical shapes included), using HDDS as a guidance to
the geometry. The geometry was much simplified in comparison with HDDS.
The mirrors were defined as several sectors of ellipsoids, set with the option "MANY",
to be clipped properly by the borders of the mother volume (a 22.5° sector). Defining several
sectors per mirror was done mainly to make drawn pictures less populated.
A sector is displayed on the next plot.
Problems with this geometry
Second iteration
For the second try I selected a larger 1st focal focal length at 0.45 of the distance between the
two mirrors.
The following plot shows the result of the optics calculation.
The mirror parameters are shown in the next table.
#
RZ, cm
RX=RY, cm
Zcenter, cm
Rcenter, cm
angle
1
335.2
179.1
277.5
57.3
11.6°
2
93.3
92.2
567.0
122.3
33.1°
Azimuthal segmentation
A different azimuthal segmentation is proposed in order to reduce the light splitting at the center:
Each internal sector overlaps in φ with 3 external sectors and reflects
light to the 2-nd mirror/PMT of the central sector out of these three.
The 2-nd mirrors become smaller and are defined in GEANT using the flag "ONLY".
A sector is displayed on the next plot.
Light focusing
In summary, this second iteration of geometry is free of the problems of the first iteration.
No light cross talk between sectors appears. The cost of this is a larger light spot on the
photodetector, but still within a 10 cm diameter.
Efficiency
In this simulation I used
the optical parameters depending on the wavelength:
The optical properties are presented on the next plot.
PMT
regular
UV-enhanced
Fused silica
No, cm-1
90
160
240
EM background
The electromagnetic background (mainly e+e- pairs) produced by
the photon beam was simulated. About 0.05% of beam photons give signals (>3p.e.)
in the gas Cherenkov detector, exclusively in the central area of the 1-st mirror ring (R<25 cm).
For a beam of 108 Hz this would give about 50 kHz of background hits.
With a time resolution of 50 ns the accidental background would be about 0.25%, further reduced
by the detector segmentation.
E-Mail :
gen@jlab.org
Last updated: Mar 26, 2007