E.Farnea Monte Carlo Simulations Monte Carlo Simulations for AGATA - - PowerPoint PPT Presentation

E.Farnea

Monte Carlo Simulations for AGATA Monte Carlo Simulations 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
• f elementary processes and their description) and
• n 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

εph

~ 10% Ndet ~ 100 Too many detectors are needed to avoid summing effects Combination of:

• segmented detectors
• digital electronics
• pulse processing
• tracking the γ-rays

Compton Shielded Ge Ge Sphere Ge Tracking Array

εph

~ 50% Ndet ~ 1000

θ ~ 8º θ ~ 3º θ ~ 1º

Efficiency loss due to the shield; poor energy resolution at high recoil velocity because of the large opening angle

Ω ~40%

εph ~ 50% Ndet ~ 100

Ω ~80%

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 good

Definition of the photon direction Doppler correction capability

Detector Segment Pulse shape analysis + tracking γ

120 hexagonal crystals 6 shapes 60 triple clusters 2 types Inner radius 18 cm Amount of germanium 225 kg Solid angle coverage 78 % 4320 segments Efficiency at 1MeV: 37% (Mγ=1), 22% (Mγ=30) Peak/Total: 53% (Mγ=1), 44% (Mγ=30) 180 hexagonal crystals 3 shapes 60 triple clusters all equal Inner radius 24 cm Amount of germanium 374 kg Solid angle coverage 79 % 6480 segments Efficiency at 1MeV: 39% (Mγ=1), 25% (Mγ=30) Peak/Total: 53% (Mγ=1), 46

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

Compton scattering angles of the γ-rays within the detectors.

% (Mγ=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 simulation based on GEANT4: Agata

List-mode file:

• 101 0.05005 -0.00000 -0.00056 1.00000
• 102 0.466 -1.660 0.000
• 1 993.359 -0.48689 -0.86533 -0.11889 36

131 150.495 -12.660 -26.164 -3.122 40 132 155.894 -10.057 -25.571 -1.729 34 132 1.402 -10.088 -25.595 -1.801 34

Reconstruction of the events with the γ-ray tracking: mgt Analysis of the spectra

Class structure of the program Class structure of the program

Agata

*Agata RunAction *Agata EventAction Agata PhysicsList Agata VisManager Agata

SteppingAction

*Agata Analysis Agata

GeneratorAction

CSpec1D Agata

GeneratorOmega

Agata

SteppingOmega

*Agata Detector Construction *Agata Detector Shell *Agata Detector Simple *Agata

SensitiveDetector

*Agata

DetectorArray

Agata HitDetector CConvex Polyhedron

Messenger classes are not shown! Messenger classes are not shown! * Possibility to change parameters via a messenger class

*Agata

DetectorAncillary

CSpec2D *Agata

Emitted

Agata

Emitter

*Agata

ExternalEmission

*Agata

ExternalEmitter

*Agata

InternalEmission

*Agata

InternalEmitter

AGATA Detectors AGATA Detectors

Hexaconical Ge crystals 90 mm long 80 mm max diameter 36 segments Al encapsulation: 0.6 mm spacing 0.8 mm thickness 37 vacuum feedthroughs 3 encapsulated crystals 111 preamplifiers with cold FET ~230 vacuum feedthroughs LN2 dewar, 3 liter, cooling power ~8 watts 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 80 120 110 150 200 240 180

Building a Geodesic Ball (1) Building a Geodesic Ball (1)

Start with a platonic solid e.g. an icosahedron On its faces, draw a regular pattern of triangles grouped as hexagons and pentagons. E.g. with 110 hexagons and (always) 12 pentagons Project the faces on the enclosing sphere; flatten the hexagons.

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 the shapes of the detectors. Ball with 180 hexagons. Space for encapsulation and canning obtained cutting the

• crystals. In the example 3

crystals form a triple cluster Add encapsulation and part of the cryostats for 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 40 triple-clusters 2 shapes Inner radius (Ge) 18 cm Amount of germanium 225 kg Solid angle coverage 78 % 4320 segments Efficiency: 37% (Mγ=1) 22% (Mγ=30) Peak/Total: 53% (Mγ=1) 44% (Mγ=30) 180 hexagonal crystals 3 shapes 60 triple-clusters all equal Inner radius (Ge) 24 cm Amount of germanium 374 kg Solid angle coverage 79 % 6480 segments Efficiency: 39% (Mγ=1) 25% (Mγ=30) Peak/Total: 53% (Mγ=1) 46% (Mγ=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 22/44 37/52 78 230 120

A120C4 A180 A120F A120G

22 / 44 37 / 53 78 225 120 374 232 Amount of germanium (kg) 21 / 45 33 / 53 71 120 25 / 46

εph / PT at M = 30 (%)

79 Solid Angle (%) 180 Number of crystals 39 / 53

εph / PT at M = 1 (%)

Efficiency and P/T values at Eγ = 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 Eγ = E0+n∆Eγ 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 efficiency Peak-to-total ratio (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 efficiency Peak-to-total ratio (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 Eγ = E0+n∆Eγ A180 configuration

(no scattering chamber)

Recoil direction: z axis β: constant (event by event) Recoil velocity perfectly known when recostructing

Effect of the recoil velocity - 2 Effect of the recoil velocity - 2

20% 5% 30 photon rotational cascade (Eγ = E0+n∆Eγ) A180 configuration (no scattering chamber) Velocity direction variable event-by- event (recoil opening angle: 5°) White: recoil direction perfectly known when recostructing Red: only average recoil direction known (=z axis) At β=5%:

3.824 keV @ 2710 keV 12.578 keV @ 2710 keV

At β=20%:

7.756 keV @ 2710 keV >80 keV @ 2710 keV!!! 2390 2710 keV

Additional information

• n the recoils is essential

to fully exploit the power

• f the tracking!

Additional information

• n the recoils is essential

to fully exploit the power

• f the tracking!

Doppler Broadening Doppler Broadening

Causes of Doppler broadening:

• Uncertainty on the position of the

first interaction;

• Uncertainty on the position of the

source;

• Uncertainty on the direction of the

source;

• Uncertainty on the speed of the

source.

The present tracking algorithm is mildly dependent on the source position as shown by the behaviour of P/T (εγ depends also on geometrical factors)

2

1 ) cos( 1 β θ β − − =

lab cm

E E

Uncertainty on the source position Uncertainty on the source position

Single 1MeV photons

Diffused source with a gaussian distribution of FWHM δs around the centre of the array The position of the emitting nucleus IS NOT known on an event-by-event basis.

Uncertainty on the source direction Uncertainty on the source direction

Single 1MeV photons

Recoil cone of 10°

half-opening around the beam axis

The direction of the emitting nucleus IS measured on an event- by-event basis with an uncertainty σdir.

Uncertainty on the source speed Uncertainty on the source speed

Single 1MeV photons

Speed of the recoiling nucleus variable with a gaussian distribution (FWHM: 10% of the average speed) The speed of the emitting nucleus IS measured on an event- by-event basis with an uncertainty ∆β.

Requirement for the beam and the ancillary detectors Requirement for the beam and the ancillary detectors

0.3 0.7 2.4 Velocity module : ∆β (%) 0.3 0.6 2 Direction: σdir(degrees) 0.3 0.5 1.5 Position: δs(cm) β = 50% β = 20% β = 5%

Performance within the reach

• f the existing technologies!

Conclusions Conclusions

• Monte Carlo simulations are an essential

tool in many fields of Physics.

• Using simulated data we can estimate the

realistic behaviour of a detection system as complex as AGATA.

• In order to fully benefit from its capabilities,

AGATA will need ancillary detectors.