The Geometry of AGATA
The AGATA technical proposal contains a discussion of the various possible options for tiling a sphere with hexagons and pentagons. This document concluded that the optimum geometric configurations have either 120 or 180 hexagons, each with 12 pentagons. (It was realised soon that the fraction of efficiency brought by the pentagons is not worth the cost of developing and handling this crystal shape and therefore that they are not considered in this report.) The underlying geometry of the two configurations is shown in the next picture, without any assumption on how the crystals could be packed into multiple cryostats.
The actual shape of the single crystals is given by the intersection of a cylinder (80 mm diameter, 90 mm length) with an irregular polyhedron having two parallel irregular hexagonal faces, as shown in the following picture:
The final size of the 4 array depends on the number of crystals and on the way of packing them into cryostats. Clearly, the performance of the different configurations will depend on the amount of germanium they consist of and on how complete a solid angle coverage around the target point one can achieve.
In the following we present the summary of a series of Monte Carlo calculations, which have been performed in the last three months with the aim of evaluating the relative performance of the proposed configurations. Hopefully, this exercise will help in deciding the optimum choice. The calculations have been performed by Enrico Farnea, leader of the conceptual design team, who has also prepared the detailed report that can be found at:
The A180 configuration: The 180 hexagons can be grouped into 60 all-equal triple-clusters in a natural way and no space is left in between neighbouring clusters (besides of course the pentagonal holes). This arrangement is shown in the following figure and will be referred to as A180 configuration. There are 3 crystal shapes. Because of its high symmetry, modularity and solid angle coverage ( ~78 %) this was, since the beginning, the preferred choice for the geometry of AGATA.
The A120F configuration: To achieve similar solid angle coverage with 120 hexagons packed into triple-clusters, one needs 6 different crystal shapes (the 3 of each original “colour” being anyway rather similar), which can be packed into 2 different clusters shapes. This configurationwas not considered before because of the many different crystal shapes. However, the fact that its solid angle coverage is close to 78% makes it an interesting compromise between the A180 and the A120 configuration.
TheA120 configuration: Accepting a small spacing in between the triple clusters (and consequently a reduced solid angle coverage), the number of different crystal shapes can be reduced to 2, and 2 cluster shapes. This results in a deduced development cost and a gain in modularity of the array.
The A120C4 configuration: A more straightforward way to group the 120 hexagons is achieved by considering 30 all-equal quadruple-clusters. Again there are only two different crystal shapes and only one type of cluster. Although this arrangement maximises the solid angle coverage, it should be noted that due to the extra complication of handling more objects within a single cryostat (148 signal feedthroughs instead for 111 for a triple), from the practical point of view the A120C4 configuration is less attractive than those with triple-clusters.
The following table summarizes the relevant geometrical characteristics of the configurations:
Configuration / A120 / A120F / A120C4 / A180Number of crystals / 120 / 120 / 120 / 180
Number of crystal shapes / 2 / 6 / 2 / 3
Number of clusters / 40 / 40 / 30 / 60
Number of cluster shapes / 2 / 2 / 1 / 1
Covered solid angle (%) / 71.0 / 77.8 / 78.0 / 78.4
Amount of Germanium (kg) / 232 / 225 / 230 / 374
Centre to crystal-face dist. (cm) / 19.7 / 18 / 18.5 / 24.6
Electronics channels / 4440 / 4440 / 4440 / 6660
The Performance of AGATA
The performance of the 4 configurations, in terms of full energy efficiency and Peak-to-Total ratio for cascades of 1 MeV photons is summarised in the following table. The results were obtained considering a realistic amount of passive materials (capsules and cryostats) and performing the gamma-ray tracking with the mgt tracking code developed in Padova. The quoted performance depends on the performance of the tracking algorithms, however, for the purpose of our comparison we need to just compare the relative values. The calculations used the same assumptions for dead material, tracking response, position resolution, etc.
Multiplicity / 1 / 10 / 20 / 30A120 Efficiency (%) / 32.9 / 25.2 / 22.4 / 20.5
A120F Efficiency (%) / 36.9 / 36.9 / 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 4 configurations to a cascade of 30 -rays equally spaced between 80keV and 2.7 MeV, presented in the following figure renders graphically the fact that the array with 180 crystals is, as expected, superior those with 120. In the same time it shows that the performance of A120F and A120C4 is better than that of the simple A120 (labelled A120G in the figure)
Appendix 1
SD analysis by Araceli/Waely LOPEZ-MARTENS
I have been simulating 194Pb events produced in a typical fusion-evaporation reaction. I used Radware level schemes on top of which I added statistical gamma-rays taken from the appropriate distribution and in the case of the SD cascades, I have included the E2 bump transitions as well as 5 links or quasicontiuum cascades. (the links are at 2.1 MeV and above 2.6 MeV) The v/c=0.
In order to see something and not spend too much time simulating and tracking, I have boosted the SD intensity to 4% and the links to 0.3%. The total number of simulated gammas was 808800
(68000 of which are SD related and the rest correspond to sampling many times 14 different ND cascades. The spectra I am sending you are 5 SD gated spectra on the reconstructed data (with the forward tracking algorithm I have made, which gives approximately the same results as Dino's mgt)- a list of 12 gates was used.
If one integrates the same peaks (using the same channels) in all 4 configurations (A180, A120C4, A120F and A120), one gets the following results:
SD line enhancement when using A180 conf:
Factor of 2 compared with A120 conf.
Factor of 1.6 compared with A120F conf.
Factor of 1.3 compared with A120C4 conf.
SD link enhancement when using A180 conf:
Factor of 2.3 compared with A120
Factor of 1.7 compared with A120F
Factor of 1.2 compared with A120C4
I will try to simulate soon a greater number of gamma-rays, and thus keep the proper intensity relationships...to see what becomes of the intensity ratios for weaker structures.....(10-4, 10-6)
Also, I have not quantified the resolving power in each case. I could try to see how much statistics one needs with the different configurations in order to get 100 counts (above background) in a linking transition, for example.