E.Farnea Monte Carlo Simulations Monte Carlo Simulations for AGATA for AGATA
Problems with an analytical solution ... Problems with an analytical solution ... • A two-body collision between rigid bodies can be described analytically. Once the initial conditions are fixed, the status of the system at any time can be predicted.
Problems with a numerical solution ... Problems with a numerical solution ... • There is no analytical solution to the three- body problem. • However, we are able to find numerical solutions to the problem and send a probe to another planet (if American and European engineers agree on the system of units!). Once the initial conditions are fixed, the status of the system at any time can be predicted.
Problems! Problems! • There is no way to predict the sequence of results from a series of roulette tosses, nor the result of a single toss. • However, given the probability for a single result, we are able to predict with good approximation the distribution of results over a large number of tosses.
What is a Monte Carlo simulation? What is a Monte Carlo simulation? • A Monte Carlo simulation is a technique to face problems where analytical or numerical solutions to a problem are not available. • In a Monte Carlo simulation, the evolution of the system (e.g. the response of detectors to the radiation) is obtained by assigning probabilities to the elementary stochastic processes; the path for each event is chosen by picking up random numbers each time a new choice is requested. • The results depend critically on the input (number of elementary processes and their description) and on the total number of events.
Arrays from TESSA0 to AGATA Arrays from TESSA0 to AGATA EUROBALL III EUROGAM TESSA ESS30 GaSp EUROBALL IV
Idea of γ -ray tracking Idea of γ -ray tracking Compton Shielded Ge Efficiency loss due to ε ph the shield; poor energy ~ 10% resolution at high recoil N det ~ 100 θ ~ 8º velocity because of the Ω ~40% large opening angle Ge Sphere ε ph Too many detectors ~ 50% are needed to avoid N det ~ 1000 θ ~ 3º summing effects Ge Tracking Array Combination of: ε ph ~ 50% •segmented detectors N det ~ 100 •digital electronics θ ~ 1º Ω ~80% •pulse processing •tracking the γ -rays
γ -ray tracking detectors γ -ray tracking detectors γ -ray tracking Segmented cathode Pulse Shape Analysis
Benefits of the γ -ray tracking Benefits of the γ -ray tracking scarce Detector Doppler correction photon direction Definition of the capability Segment Pulse shape analysis + good tracking γ
AGATA AGATA • High efficiency. • Good position resolution on the individual γ interactions . • Capability to stand a high counting rate. • High granularity. • Capability to measure the 120 hexagonal crystals 180 hexagonal crystals 6 shapes 3 shapes 60 triple clusters 60 triple clusters 2 types all equal Compton scattering angles of Inner radius Inner radius 18 cm 24 cm the γ -rays within the Amount of germanium Amount of germanium 225 kg 374 kg Solid angle coverage Solid angle coverage 78 % 79 % detectors. 4320 segments 6480 segments Efficiency at 1MeV: 37% (M γ =1), 22% (M γ =30) Efficiency at 1MeV: 39% (M γ =1), 25% (M γ =30) Peak/Total: Peak/Total: 53% (M γ =1), 44% (M γ =30) 53% (M γ =1), 46 % (M γ =30)
We need simulations to ... We need simulations to ... • Optimize the geometry of the array • Evaluate the expected performances • Test the tracking algorithms with “standard” datasets • Test the analysis programs with “standard” datasets • .......
Geant4 Geant4 • Geant4 is a software package which includes advanced tools to describe complex geometries and the interactions of radiation with matter and to handle the information within a program. • Based on the C++ programming language
The Agata simulation code The Agata simulation code • Flexible description of the possible configurations of the array • Emission of various particle type under different spectra/source conditions • Particles are emitted one at a time to have better control of the results, high multiplicity events are emulated • Main goal: production of a list-mode output file for the tracking algorithms
Monte Carlo List-mode file: simulation -101 0.05005 -0.00000 -0.00056 1.00000 based on -102 0.466 -1.660 0.000 -1 993.359 -0.48689 -0.86533 -0.11889 36 GEANT4: 131 150.495 -12.660 -26.164 -3.122 40 132 155.894 -10.057 -25.571 -1.729 34 Agata 132 1.402 -10.088 -25.595 -1.801 34 Reconstruction of the events with the Analysis of the spectra γ -ray tracking: mgt
Class structure of the program Class structure of the program Agata *Agata *Agata Agata Agata Agata SteppingAction RunAction EventAction PhysicsList VisManager Agata *Agata GeneratorOmega CSpec1D Agata Agata Analysis GeneratorAction SteppingOmega CSpec2D *Agata Emitted *Agata *Agata InternalEmission ExternalEmission *Agata Agata Detector *Agata Emitter *Agata *Agata Shell Detector InternalEmitter ExternalEmitter Construction *Agata Detector Simple * Possibility to *Agata *Agata *Agata change parameters DetectorAncillary DetectorArray SensitiveDetector via a messenger class CConvex Agata Messenger classes are not shown! Messenger classes are not shown! Polyhedron HitDetector
AGATA Detectors AGATA Detectors Hexaconical Ge crystals 90 mm long 80 mm max diameter 36 segments 3 encapsulated crystals Al encapsulation: 111 preamplifiers with cold FET 0.6 mm spacing ~230 vacuum feedthroughs 0.8 mm thickness LN 2 dewar, 3 liter, cooling power ~8 watts 37 vacuum feedthroughs Germany & Italy ordered 3 symmetric encapsulated crystals (2 delivered). Cryostat will be built by CTT in collaboration with IKP-Köln. Cluster ready by end 2004.
Geodesic Tiling of Sphere using 60–240 hexagons and 12 pentagons 60 80 110 120 150 200 240 180
Building a Geodesic Ball (1) Building a Geodesic Ball (1) Start with a On its faces, draw a regular platonic solid pattern of triangles grouped Project the faces on e.g. an icosahedron as hexagons and pentagons. the enclosing sphere; E.g. with 110 hexagons and flatten the hexagons. (always) 12 pentagons
Building a Geodesic Ball (2) Building a Geodesic Ball (2) Al capsules 0.5 mm spacing 0.7 mm thick Al canning 2 mm spacing 2 mm thick A radial projection of the spherical tiling generates Space for encapsulation and the shapes of the detectors. canning obtained cutting the Ball with 180 hexagons . Add encapsulation and crystals. In the example 3 part of the cryostats for crystals form a triple cluster realistic MC simulations
Building a Geodesic Ball (3) Building a Geodesic Ball (3)
Two candidate configurations Ge crystals size: Length 90 mm Diameter 80 mm 120 hexagonal crystals 6 shapes 180 hexagonal crystals 3 shapes 40 triple-clusters 2 shapes 60 triple-clusters all equal Inner radius (Ge) 18 cm Inner radius (Ge) 24 cm Amount of germanium 225 kg Amount of germanium 374 kg Solid angle coverage 78 % Solid angle coverage 79 % 4320 segments 6480 segments Efficiency: 37% (M γ =1) 22% (M γ =30) Efficiency: 39% (M γ =1) 25% (M γ =30) Peak/Total: 53% (M γ =1) 44% (M γ =30) Peak/Total: 53% (M γ =1) 46% (M γ =30)
Comparison of various configurations A120G, A120F : triple clusters A180 : triple clusters Ge crystals size: length 90 mm, diameter 80 mm Passivated areas: 1 mm at the back and around the coaxial hole A120G A120F A120C4 A180 Number of crystals 120 120 120 180 Amount of germanium (kg) 232 225 230 374 Solid Angle (%) 71 78 78 79 ε ph / PT at M = 1 (%) 33 / 53 37 / 53 37/52 39 / 53 ε ph / PT at M = 30 (%) 21 / 45 22 / 44 22/44 25 / 46 Efficiency and P/T values at E γ = 1 MeV and recoil velocity β = 0. Values obtained after tracking with standard position resolution (5 mm @ 100 keV). Cryostats and capsules included in the simulation.
Photopeak efficiency Photopeak efficiency 30 photon rotational cascade E γ = E 0 +n ∆ E γ Recoil velocity β = 0
Response function Response function Individual γ -rays are fired and the energy releases within the array are summed. Passivated areas, cryostats and capsules are considered. Photopeak efficiency Peak-to-total ratio
Effect of the scattering chamber Effect of the scattering chamber In addition to cryostats and capsules, a scattering chamber (2 mm aluminium thick) is considered in the simulation. Absolute photopeak Peak-to-total ratio efficiency (response function)
Effect of ancillary devices Effect of ancillary devices In addition to cryostats, capsules and scattering chamber, an “ancillary” sphere is considered in the simulation. Only the results for A180 are shown. Absolute photopeak Peak-to-total ratio efficiency (response function)
High-energy peaks High-energy peaks 14 photon rotational cascade + 10 MeV γ Recoil velocity β = 0
Effect of the recoil velocity - 1 Effect of the recoil velocity - 1 Photopeak efficiency 30 photon rotational cascade E γ = E 0 +n ∆ E γ A180 configuration (no scattering chamber) Recoil direction: z axis β : constant (event by event) Recoil velocity perfectly known when recostructing
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