Detector simulation & Geant4

Nam Tran Boston University

1Vietnam School on Neutrino 2020

Outline• Simulation in high energy physics

• Why? • What is simulated? • How simulation is done?

• (Short) Introduction to Geant4

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Why?• HEP detectors are very complex machines

• Expensive, and take long time to build • Once built, will stay in operation for many years

• The gap between R&D to full detector is huge • 2-3 orders of magnitude in terms of dimensions, number of

readout channels • Cannot afford to build a full detector without careful

evaluation of mechanical, electronic and physics performance

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Why?• New physics, enhanced/suppressed processes

• Can introduce new physics, • Or tweak branching ratio of a specific process • Simulation is not magic! Cannot invent/create physics

that you are not including • Also very important in data analysis and

interpretation of the physics measurements

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Needed in all stages• First ideas about an experiment

• Given the physics goals, what kind of detectors are needed? What level of performance?

• Formal proposal • More detailed simulation show feasibilities of the

experiment • R&D and construction

• Optimize detectors & development and test algorithms • Running & analysis

• Test reconstruction algorithms, study backgrounds, … • More understanding of detector performance, inputs for

next R&D, …5

What are simulated?• Particle generation • Interaction with materials & transportation in

detectors • Digitization

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How?

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Particle generation Detector simulation Digitization

Particles from collision, beam, or cosmic ray, …

-Geometry, material,

- Electric & magnetic field

- Particle transportation

- Physics interactions

-Electronic signal modeling

- Pile up/overlap

Raw data to physics

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https://indico.cern.ch/event/656460/timetable/#47-introduction-to-geant4-1

Physics to simulated data

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https://indico.cern.ch/event/656460/timetable/#47-introduction-to-geant4-1

Types of simulation• Toy simulation

• Simple analytical equations without detailed geometry/field descriptions

• Zeroth order detector or physics studies • Very fast: small fraction of a second per event

• Parameterized simulation • Approximate geometry/field descriptions • Parameterized energy response, shower shapes, … • Relative fast: ~second per event

• Full simulation • Detailed, as close as possible to real geometry/field • Can be really slow …

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Event generation• Use knowledge about particle physics to simulate a

known process • Or use alternative models/theories

• E.g.: Mu2e • Can be simple

• Particle beam with mono-energetic particles • Or complicated

• Heavy ion collisions

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An example• An event:e+e− → μ+μ−

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https://indico.cern.ch/event/656460/timetable/#47-introduction-to-geant4-1

Detector simulation• Input: particles from event generation stage • Next question: how those particles would interact

with our detector? • Need

• Description of detector materials • Description of electric and magnetic fields • Knowledge about particle-material interactions

• Most popular simulation package in HEP: Geant4 toolkit • Also widely used in other fields: nuclear physics,

medical, space, …13

Digitization• Convert results of interactions to detector signals

• Charges/voltages: similar to what we can readout from real detectors

• Apply pile-up, overlapping if needed

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Monte Carlo method• Computational algorithms which use repeated

random sampling to obtain numerical results • Example: integral calculation

f(x) = 1.5 [sin4 (x) cos5 ( x2

5 ) + sin6 ( x4 )] exp (− x2

16 )

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MC method example• Randomly

generated points in the x-y plane • Orange: accepted • Blue: rejected

• Result: accepted

accepted + rejected× area

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MC in particle tracking• Track a particle in medium, one of the most common

applications of MC in particle physics • Assume that all the possible interactions are known • The distance s between two subsequent interactions is

distributed as • is a property of the medium, proportional to the

probability of an interaction per unit length and density

• where is partial cross section of process ,

p(s) = μexp(−μs)μ

μ = Nσ = N∑i

σi = ∑i

μi

σi i μi = Nσi

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MC in particle tracking• Divide the particle trajectory in “steps”

• Straight free-flight tracks along the step • Could be limited by geometry boundaries

• Sampling the step length accordingly to • Sampling the interaction at the end of the step • Sampling the interaction accordingly to • Sampling the final state using the physics model of

the interaction • Update the properties of the primary particle • Add the possible secondaries produced (to be

tracked later)

p(s)

μi/μ

i

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Geant4 simulation toolkit• Original acronym for

GEometry ANd Tracking • Developed at CERN, first

version in 1974 • Last FORTRAN version:

GEANT 3.21 • Rewritten in object-oriented

C++ in 1994-1998 • Currently maintained by the

Geant4 Collaboration • https://geant4.web.cern.ch

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https://cds.cern.ch/record/118715?ln=en

It is only a toolkit• Toolkit = collection of tools, and not a completed

application • You cannot run it out of the box • Have to provide your own code to string Geant4 tools

together in order to complete an application • Required code from you (at minimum)

• Experimental set-up (detector geometry, fields) • Primary particles input to your simulation • Decide which particles and physics models you want

to use out of those available in Geant4

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User classes in Geant4• You have to provide a main() function • Initialization classes

• G4VUserDetectorConstruction • G4VUserPhysicsList • G4VUserActionInitialization

• Action classes • G4VUserPrimaryGeneratorAction • G4UserEventAction • G4UserStackingAction • G4UserTrackingAction • G4UserSteppingAction

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Mandatory elements

An example of Geant4 application

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main()B1DetectorConstruction

concrete class, inherited from G4VUserDetectorConstruction

Instance of G4VModularPhysicsList

(Inherited from G4VUserPhysicsList)

B1ActionInitializationconcrete class, inherited from G4VUserActionIntialization

B1PrimaryGeneratorActionconcrete class, inherited from

G4VUserPrimaryGeneratorAction

Many jargons …• World volume, mother/daughter volume • Run, event, track, step, step point • Process

• At rest, along step, post step • Cut • Sensitive detector, score, hit, hits collection

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Geant4 system of units• Geant4 is aware of units

• Always use appropriate units, Don’t rely on default units! • e.g.: radius = 10.0 * cm; E = 1.0*GeV;

• To output in a specific unit

• Or use “best” unit

• Can define custom units as well

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Detector geometry components

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Materials• Different kind of materials are

available • Isotopes ↔ G4Isotope

• Elements ↔ G4Element

• Molecules ↔ G4Material

• Compounds, mixture ↔ G4Material

• Attributes • Density, temperature, pressure, state

• Lots of predefined materials • G4NistManager

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Properties of atoms A, Z, cross section, …

Macroscopic properties - temperature, pressure,

state, density - Radiation length,

absorption length, …

Defining detector geometry

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Step 1: Create geom.

object

Step 2: Assign properties:

material

Step 3: Place in a mother

volume

• A unique volume must exist and fully contains all other volumes -> world volume

Checking geometry• Geant4 does not allow malformed geometries

• Protruding • Overlapping

• Checking can be done at construction (but requires lots of CPU time!)

• Or at run time, generally less demanding than the previous one

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/geometry/test/grid_test /geometry/test/recursive_test

Sensitive detector (SD)• A specific volume that you want to read out

information from • Position, time, energy deposited, dose, … • Corresponds to active materials in real detectors (e.g.

plastic scintillator, crystal, gas volume, …) • A logical volume becomes sensitive if it has a pointer

to a sensitive detector (G4VSensitiveDetector) • Two possibilities to make a Geant4 SD

• Create your own SD: more manual coding, but highly customizable

• Use Geant4 built-in tools, namely primitive scorers

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Run• A collection of events which share the same detector and

physics configuration • Start with “beamOn”, geometry is optimized for navigation

and cross section tables are (re)calculated • G4RunManager • G4UserRunAction is the optional user hook

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Interactions hadron

Run

Event• An event is the basic unit of simulation in Geant4 • Represents by G4Event class, • At the beginning of processing, primary tracks are

generated, and pushed into a stack • A track is popped from the stack one-by-one and tracked

• Secondaries are also pushed into the stack • When the stack is empty, the processing of the event is

completed • Output: hits and trajectory collections • G4EventManager• G4UserEventAction

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Step• Has two points (pre and post step points) • Ends when a physics process is invoked • Or at volume boundaries

• In case a step is limited by a boundary, the end point stands on the boundary, and it logically belongs to the next volume

• Boundary processes such as transition radiation or refraction could also be simulated

• Information can be extracted at the end of each step • G4SteppingManager • G4UserSteppingAction

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Track• A Track is a snapshot of a particle, represented by the

G4Track class • Keeps current info about the particle: energy, momentum,

position, … • Is updated after every G4Step

• A track object is deleted when • It goes outside of the world volume • It disappears in an interaction (decay, inelastic scattering) • It is slowed down to 0 kinetic energy and there are no

'AtRest' processes • It is manually killed by the user

• No track object persists at the end of an event33

Run, event, track and step

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Particle in Geant4• 3 layers of description

• G4Track: geometrical information (position) • G4DynamicalParticle: dynamic physical properties

• Energy, momentum, polarization, … • G4ParticleDefinition: characteristic properties of the

particle • Charge, mass, lifetime, …

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Flowchart of an event

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MC sampling at each step• Each particle has its own list of applicable

processes. At each step, MC sampling is performed to determine • Step length • A particular process which would be invoked

• The process which requires the shortest interaction length limits the step

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Geant4 process kinds• At rest

• e.g. muon decay • Along the step

• e.g. Cherenkov radiation • Post step

• e.g.: decay in flight, hadron interactions

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Physics list• A class which collects all the particles, physics

processes and production thresholds needed for your application

• It tells the run manager how and when to invoke physics • It is a very flexible way to build a physics environment

• user can pick the particles he wants • user can pick the physics to assign to each particle

• But, user should have a good understanding of the physics required • omission of particles or physics could cause errors or poor

simulation

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Predefined physics lists• Geant4 provides ~20 reference physics list

• Used by larger experiments like CMS, ATLAS, … • These are routinely validated and updated with each

release • Should only be considered as starting points which you

may need to validate or modify for your application • Production cuts on secondary particles set to a

default 1 mm threshold • Secondary particles with Ekin < Eneeded to travel 1 mm are

stopped

40https://geant4-userdoc.web.cern.ch/UsersGuides/PhysicsListGuide/fo/PhysicsListGuide.pdf

Don’t forget about the production cut!

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Geant4 examples• Extensive examples demonstrate how to use

Geant4 tools • https://gitlab.cern.ch/geant4/geant4/tree/master/

examples • With different levels: “basic”, “extended”, “advanced”

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Summary• Simulation is an important part of doing

experimental HEP • The most widely used toolkit is Geant4

• It is a very flexible tool • Can be complicated … • There are lots of example code to learn/start

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