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AGATA: comparison of the A120, A180 configurations

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For more information on the simulation code and to obtain the actual code contact Enrico Farnea

Last updated: June 3rd 2004

The configurations

The configurations for AGATA which will be compared below are "spherically symmetrical" configurations, based on encapsulated tapered coaxial detectors, grouped into clusters within a single cryostats, arranged around the target position and pointing to the target position.

As outlined in the AGATA Technical Proposal (see p.41 and following), a method for tiling the spherical surface with a few elementary shapes is to project a pattern drawn on each of the faces of an enclosed regular polyhedron. In the case of AGATA, it is convenient to start with an icosahedron, which has 20 equilateral triangular faces and is the platonic polyhedron with the largest number of faces; this will ensure the maximum degree of symmetry. Covering the icosahedron faces with a pattern of regular hexagons, the final polyhedron will be composed of 12 regular pentagons (the tips of the icosahedron) and of a number of hexagons, which in general will be slightly irregular and of a few different shapes.

The actual shape of the single capsule is given by the intersection of a cylinder (80 mm diameter, 90 mm length) with an irregular polyhedron having two parallel irregular hexagonal faces and it is shown in the following picture:



A 1 mm thick passivated area is considered at the back part of the detector and around the coaxial hole. The detectors are encapsulated in an Aluminium capsule 0.7 mm thick, with a 0.5 mm capsule-crystal spacing.

Only a few of the resulting polyhedra (that is, number of hexagons) have been taken into consideration as a possible configuration for AGATA, given the requirements that only a small as possible number of hexagonal shapes should be used and that there should be a  free space of reasonable size around the target to host ancillary devices. The polyhedra with 120 or 180 hexagons satisfy these conditions. The 180 hexagons can be grouped into triple clusters in a natural way and no space is left in between the neighbouring clusters. This arrangement will be referred to as A180 configuration. To achieve the same result with 120 hexagons using triple clusters, one needs six different crystal shapes, obtaining what will be referred to as A120F configuration. However, accepting a small spacing in between the triple clusters, the number of different shapes can be reduced to two, with an obvious gain in development cost and modularity of the array. This arrangement will be referred to as A120 configuration. Actually, a more natural way to group the detectors in the case of 120 hexagons would be to consider clusters of 2 or 4 detectors; in both cases, one ends with two different crystal shapes and one cluster type. In the following, only the configuration with quadruple clusters will be considered, which will be referred to as A120C4 configuration. It should be noted that the latter configuration is less attractive than the others from the practical point of view, due to the extra complication of handling more objects within a single cryostat (148 signal feedthroughs instead of 111).

The A120 configuration is built out of 2 different capsule shapes, grouped into 2 different triple cluster types. These clusters can be arranged in two different ways around the target position, depending on the way the icosahedron is "unpacked" on a plane; in the following, only the arrangement having the higher degree of symmetry around the beam axis will be discussed. The performance of the other arrangement as a whole is similar, but it lacks the required symmetries to build partial sections of the array, that is groups of clusters having a border as "sharp" as possible. In the case of the symmetrical A120 configuration, the possible sections are as following:

1
5 clusters
Demonstrator
VRML image
2
15 clusters
"1pi" VRML image
3
25 clusters
"2pi" VRML image
4
35 clusters
"3pi" VRML image
5
40 clusters
4pi VRML image

Each section covers more solid angle than suggested by its name, which is the price to pay to obtain "compact" sections. Notice that in order to simplify the drawing, the intersection of each polyhedron with the cylinder has not been sketched in the VRML files (a nice VRML viewer can be downloaded at the Systems in Motion web site).


The A120F configuration is built instead out of 6 different capsule shapes, grouped into 2 different triple cluster types. The natural way to arrange the clusters is to follow the same arrangement of the A120 configuration with the highest degree of symmetry around the beam axis. This way, one obtains the same sequence of sections shown for the A120 configuration:

1
5 clusters
Demonstrator
VRML image
2
15 clusters
"1pi" VRML image
3
25 clusters
"2pi" VRML image
4
35 clusters
"3pi" VRML image
5
40 clusters
4pi VRML image


The A120C4 configuration is built out of 2 different capsule shapes, grouped into a quadruple cluster (of a single type). Given the size of the quadruple clusters, it is very difficult to build regular sections and what can be achieved is the following:

1
5 clusters
Demonstrator VRML image
2
10 clusters
"1pi" VRML image
3
20 clusters
"3pi" VRML image
4
25 clusters
"3.5pi"
VRML image
5
30 clusters
4pi VRML image

Given the underlying symmetry, it is not possible to arrange the clusters to form a compact section covering (even roughly) half of the total solid angle.


The A180 configuration is built out of 3 capsule shapes (grouped into a single triple cluster type). In this case, the sequence of sections is the following:

1
5 clusters
Demonstrator VRML image
2
15 clusters
1pi VRML image
3
45 clusters
3pi VRML image
4
55 clusters
"3.5pi"
VRML image
5
60 clusters
4pi VRML image

Also in this case, given the underlying symmetry, it is not possible to arrange the clusters to form a compact section covering half of the total solid angle.

In the calculations, the pentagonal elements were not considered. Given the cost to develop the pentagonal encapsulated segmented detectors, it was felt that the increase in performance brought by these detector would not be worthwhile.



Performance considering the tracking

In the following, the performance of the AGATA array in its various proposed configurations will be presented. The results were obtained considering the proper amount of passive materials (capsules and cryostats) and performing a full reconstruction with the mgt tracking code developed in Padova. Of course the quoted performance depends on the performance of the tracking algorithms. The performance of the array in the (unrealistic) case of perfect gamma-ray tracking is called response function and is given for reference purposes in the next section.

Response function as a function of energy and recoil velocity

Demonstrator

In the demonstrator phase, 5 triple (or quadruple) clusters will be employed. The following table summarizes the expected photopeak efficiency and P/T ratios for 1 MeV photons at various multiplicities and zero recoil velocity.

Multiplicity
1
10
20
30
A120 Efficiency (%)
3.6
3.1
2.8
2.5
A120F Efficiency (%)
4.0
3.4
3.0
2.8
A120C4 Efficiency (%) 5.7
4.7
4.2
3.8
A180 Efficiency (%) 2.8
2.4
2.2
2.0
A120 P/T (%) 47.6
49.8
49.5
48.7
A120F P/T (%)
50.0
50.2
49.2
48.1
A120C4 P/T (%) 50.3
50.1
49.2
47.9
A180 P/T (%) 49.5
49.6
49.2
48.6

The response of the array to a regular rotational cascade at zero recoil velocity is shown in the following plot:
The same quantity is shown in the case of various recoil velocities:
Positioning the demonstrator in its "standard" position along the z axis, the FWHM of a 1 MeV peak as a function of the recoil direction (assumed to be sharply defined) is shown in the following plots for various recoil velocities:
The same data are displayed comparing the various configurations at various recoil velocities, which should be compared to the reference values at zero recoil velocity summarized in the following table:


A120
A120F
A120C4
A180
FWHM (keV)
2.46
2.48
2.49
2.46

The case of variable recoil velocity is discussed in more detail in the following report, where it is shown that, measuring on an event-by-event basis the direction of the recoils within 0.3 degrees and their velocity module within 0.3%, the performance of the array is kept to a reasonable value up to a 50% recoil velocity.


1pi array

As explained above, 15 triple clusters are needed to build this section for both the A120 and A180 configurations, while 10 quadruple clusters will be needed for the A120C4 configuration. Also in this case the table summarizes the expected photopeak efficiency and P/T ratios for 1 MeV photons at various multiplicities and zero recoil velocity.

Multiplicity
1
10
20
30
A120 Efficiency (%)
11.5
9.6
8.5
7.5
A120F Efficiency (%) 12.8
10.2
9.0
8.3
A120C4 Efficiency (%) 11.2
8.9
8.0
7.3
A180 Efficiency (%) 8.8
7.3
6.6
6.2
A120 P/T (%) 52.0
53.2
50.0
47.2
A120F P/T (%) 52.0
51.0
49.2
47.3
A120C4 P/T (%) 50.7
50.0
48.5
46.6
A180 P/T (%) 51.6
51.6
51.0
50.2

The response of the array to a regular rotational cascade at zero recoil velocity is shown in the following plot:
The same quantity is shown in the case of various recoil velocities:


2pi array

As explained above, in the case of the A120C4 and A180 configurations it is not really meaningful to build this section and only the data relative to the A180 configuration are presented for completeness. In order to build this section, 25 or 30 triple clusters are needed respectively for the A120 and A180 configurations. Also in this case the table summarizes the expected photopeak efficiency and P/T ratios for 1 MeV photons at various multiplicities and zero recoil velocity.

Multiplicity
1
10
20
30
A120 Efficiency (%)
19.8
15.8
14.2
13.0
A120F Efficiency (%) 21.9
17.2
15.2
13.8
A180 Efficiency (%) 18.3
14.7
13.4
12.4
A120 P/T (%) 52.6
51.0
49.0
47.1
A120F P/T (%) 51.9
50.1
47.5
45.0
A180 P/T (%) 52.6
51.3
50.3
48.8

The response of the array to a regular rotational cascade at zero recoil velocity is shown in the following plot:
The same quantity is shown in the case of various recoil velocities:


3pi array

As explained above, in order to build this phase 35 or 45 triple clusters are needed respectively for the A120 and A180 configurations, while 20 quadruple clusters are needed for the A120C4 configuration. Also in this case the table summarizes the expected photopeak efficiency and P/T ratios for 1 MeV photons at various multiplicities and zero recoil velocity.

Multiplicity
1
10
20
30
A120 Efficiency (%)
28.0
21.7
19.4
17.7
A120F Efficiency (%) 31.6
24.0
21.1
19.2
A120C4 Efficiency (%) 23.4
18.3
16.2
14.9
A180 Efficiency (%) 28.0
21.9
20.0
18.6
A120 P/T (%) 52.6
49.4
47.3
45.2
A120F P/T (%) 52.4
48.5
46.0
44.3
A120C4 P/T (%) 51.0
49.4
47.2
45.4
A180 P/T (%) 52.6
49.6
48.3
47.3

The response of the array to a regular rotational cascade at zero recoil velocity is shown in the following plot:
The same quantity is shown in the case of various recoil velocities:


Full array

In this phase, 40 or 60 triple clusters are needed respectively for the A120 and A180 configurations. The following table summarizes some of the relevant geometrical characteristics of the configurations:



A120
A120F
A120C4
A180
Number of crystals
120
120
120
180
Number of crystal shapes
2
6
2
3
Number of cluster types
2
2
1
1
Covered solid angle (%)
70.97
77.79
78.0
78.36
Volume of Germanium (cm3)
43590
42225
43160
70243
Mass of Germanium (kg)
232
225
230
374
Initial mass of Germanium (kg)
289
289
289
434
Fractional loss of Germanium (%)
19.7
22.1
20.4
13.8
Centre to Detector face distance (cm)
19.7
18.0
18.5
24.6


The values for the partial sections can be obtained by scaling to the number of clusters composing the section.

The following table summarizes the expected photopeak efficiency and P/T ratios for 1 MeV photons at various multiplicities and zero recoil velocity:


Multiplicity
1
10
20
30
A120 Efficiency (%)
32.9
25.2
22.4
20.5
A120F Efficiency (%) 36.9
27.7
24.3
22.0
A120C4 Efficiency (%) 36.4
27.5
24.3
22.1
A180 Efficiency (%) 38.8
29.6
27.0
25.1
A120 P/T (%) 52.9
48.8
46.5
44.9
A120F P/T (%) 53.0
48.4
45.9
43.7
A120C4 P/T (%) 51.8
47.5
45.3
43.4
A180 P/T (%) 53.2
48.4
47.3
46.1

The response of the array to a regular rotational cascade at zero recoil velocity is shown in the following plot:
The same quantity is shown in the case of various recoil velocities:


Response function

In the following, the response function of the AGATA array in its various proposed configurations will be presented for comparison with the data obtained with the tracking procedure. The response function is obtained by considering individual photons (multiplicity 1) interacting with the array as a whole and considering the total energy deposition (that is, using the array as a single "conventional" detector). The response function gives the performance of the array in the limit of perfect gamma-ray tracking. The results were obtained considering the proper amount of passive materials (capsules and cryostats).


Response function at 1 MeV

The response function at 1 MeV for the different sections of the four considered configurations is given in the following two tables. For the exact meaning of the different rows please refer to the numbering used in the first section of this document.


Photopeak efficiency (%)

A120G
A120F
A120C4
A180
1
3.8
4.2
5.9
2.8
2
12.2
13.5
11.8
9.1
3
21.5
23.7
25.1
30.0
4
30.8
34.6
32.0
-
5
36.5
40.4
39.6
42.2


Peak-to-total ratio (%)

A120G
A120F
A120C4
A180
1
46.5
46.3
46.9
46.6
2
49.3
48.9
47.8
49.2
3
51.4
50.9
50.0
53.2
4
53.0
52.7
51.0
-
5
54.2
53.7
52.1
55.5



Response function as a function of energy and recoil velocity

In the following plots, the response function is given as a function of energy (in the 80 keV - 2.7 MeV range) and recoil velocity (in the 0%-50% range).

Demonstrator

The response of the array to a regular rotational cascade at zero recoil velocity is shown in the following plots:
The same quantities are shown in the case of various recoil velocities:


1pi array

The response of the array to a regular rotational cascade at zero recoil velocity is shown in the following plots:
The same quantities are shown in the case of various recoil velocities:


2pi array

The response of the array to a regular rotational cascade at zero recoil velocity is shown in the following plots:
The same quantities are shown in the case of various recoil velocities:


3pi array

The response of the array to a regular rotational cascade at zero recoil velocity is shown in the following plots:
The same quantities are shown in the case of various recoil velocities:


Full array

The response of the array to a regular rotational cascade at zero recoil velocity is shown in the following plots:
The same quantities are shown in the case of various recoil velocities: