Optical physics¶

As with EM physics, the optical physics models in Celeritas are closely related to those in Geant4. Unlike Geant4, optical photon generation and stepping in Celeritas takes place in a drastically different manner.

Here is a flowchart depicting the creation of optical photons in the optical tracking loop:

        flowchart TB
  gun["Gun or external"]
  geant4-direct["Direct Geant4 offload"]
  geant4-scint["Geant4 scintillation"]
  geant4-ceren["Geant4 cherenkov"]

  classDef not-impl stroke-width:2px,stroke-dasharray: 5 5
  class geant4-direct,geant4-scint,geant4-ceren not-impl

  subgraph main-celeritas-loop["Main celeritas loop"]
    offload-gather
    scintillation-offload
    cherenkov-offload
  end

  offload-gather -->|pre-step| scintillation-offload
  offload-gather -->|pre-step| cherenkov-offload

  subgraph photon-gen["Optical photon generation"]
    scintillation-gen
    cherenkov-gen
  end

  scintillation-offload -->|generator dist| scintillation-gen
  cherenkov-offload -->|generator dist| cherenkov-gen
  geant4-scint -->|generator dist| scintillation-gen
  geant4-ceren -->|generator dist| cherenkov-gen


  photons["Optical tracking loop"]
  gun -->|inits| photons

  geant4-direct -->|inits| photons
  scintillation-gen -->|inits| photons
  cherenkov-gen -->|inits| photons

Optical materials¶

Each “physics material” (see celeritas::ImportPhysMaterial) can have an associated “optical material.” When importing from Geant4, each optical material corresponds to a single “geometry material” (see celeritas::ImportGeoMaterial) that has a RINDEX material property, and all physical materials that use the geometry material share the same optical material.

class MaterialParams : public celeritas::ParamsDataInterface<MaterialParamsData>¶

Manage properties for optical materials.

Each “physics material” (the combination of a geometry-specified material and a user-specified region) can map to a single optical material. Many materials—especially those in mechanical structures and components not optically connected to the detector—may have no optical properties at all.

Optical volume properties are imported from Geant4 into the ImportData container. The celeritas::MaterialParams class loads the mapping of PhysMatId to OptMatId and makes it accessible via the main loop’s material view. By combining that with the GeoMaterialParams which maps volumes to PhysMatId, this class maps the geometry volumes to optical materials for use in the optical tracking loop.

When surface models are implemented, surface properties will also be added to this class.

Offloading¶

During the main stepping loop, the celeritas::OpticalCollector class adds a pre-step hook to store each track’s speed, position, time, and material; at the end of the step, the track’s updated properties and within-step energy distribution are used to “offload” optical photons by generating distribution parameters to be sampled in the stepping loop. The generator distribution data is analogous to the “genstep” data structure in Opticks [Blyth, 2019].

class OpticalCollector¶

Generate and track optical photons.

This class is the interface between the main stepping loop and the photon stepping loop and constructs kernel actions for:

gathering the pre-step data needed to generate the optical distributions,
generating the scintillation and Cherenkov optical distributions at the end of the step, and
launching the photon stepping loop.

The photon stepping loop will then generate optical primaries.

The “collector” (TODO: rename?) will “own” the optical state data and optical params since it’s the only thing that launches the optical stepping loop.

Todo:: This doesn’t do anything but set up the optical tracking loop: move to setup namespace

class CherenkovOffload¶

Sample the number of Cherenkov photons to be generated.

This populates the GeneratorDistributionData used by the CherenkovGenerator to generate optical photons using post-step and cached pre-step data.

The number of photons is sampled from a Poisson distribution with a mean

\[ \langle n \rangle = \ell_\text{step} \difd{N}{x} \]

where \( \ell_\text{step} \) is the step length.

class ScintillationOffload¶

Sample the number of scintillation photons to be generated.

This populates the GeneratorDistributionData used by the ScintillationGenerator to generate optical photons using post-step and cached pre-step data.

The mean number of photons is a product of the energy deposition and a material-dependent yield fraction (photons per MeV). The actual number of photons sampled is determined by sampling:

for large (n > 10) mean yield, from a Gaussian distribution with a material-dependent spread, or
for small yields, from a Poisson distribution.

struct GeneratorDistributionData¶

Input data for sampling optical photons.

This contains all the data needed to sample optical photons directly generated by tracks in the main stepping loop.

Generating¶

Depending on the process that emitted a photon, the generator classes sample from the distribution of photons specified by the generator distribution to create optical photon initializers which are analogous to secondary particles in Geant4.

class CherenkovGenerator¶

Sample Cherenkov photons from a generator distribution.

Cherenkov radiation is emitted when a charged particle passes through a dielectric medium faster than the speed of light in that medium. Photons are emitted on the surface of a cone, with the cone angle, \( \theta \), measured with respect to the incident particle direction. As the particle slows down, the cone angle and the number of emitted photons decreases and the frequency of the emitted photons increases.

An incident charged particle with speed \( \beta \) will emit photons at an angle \( \theta \) given by \( \cos\theta = 1 / (\beta n) \) where \( n \) is the index of refraction of the matarial. The photon energy \( \epsilon \) is sampled from the PDF

\[ f(\epsilon) = \left[1 - \frac{1}{n^2(\epsilon)\beta^2}\right] \]

class ScintillationGenerator¶

Sample scintillation photons from optical property data and step data.

The optical photons are generated evenly along the step and are emitted uniformly over the entire solid angle with a random linear polarization. The photon energy is calculated by the scintillation emission wavelength

\[ E = \frac{hc}{\lambda}, \]

where \( h \) is the Planck constant and \( c \) is the speed of light, and \( \lambda \) is sampled by the normal distribution with the mean of scintillation emission spectrum and the standard deviation. The emitted time is simulated according to empirical shapes of the material-dependent scintillation time structure with one or double exponentials.

Note

This performs the same sampling routine as in G4Scintillation class of the Geant4 release 11.2 with some modifications.

Volumetric processes¶

Like other particles, optical photons undergo stochastic interactions inside optical materials.

class AbsorptionModel : public celeritas::optical::Model¶: Set up and launch the optical absorption model interaction.

class RayleighModel : public celeritas::optical::Model¶: Set up and launch the optical Rayleigh scattering model interaction.

class RayleighMfpCalculator¶

Calculate the Rayleigh MFP for a given set of material properties.

Uses the Einstein-Smoluchowski formula to calculate the mean free path at a given energy. In [Landau and L\'ıfsh\'ıts, 1884] , the mean free path is given by equation (120.2):

\[ l^{-1} = \frac{1}{6\pi} k^4 \rho k_B T \left(\frac{\partial \rho}{\partial P}\right)_T \left(\frac{\partial \varepsilon}{\partial \rho}\right)_T^2 \]

where we only consider density fluctations at constant temperature. The first partial derivative may be rewritten in terms of the isothermal compressibility \( \beta_T \):

\[ \left(\frac{\partial \rho}{\partial P}\right)_T = \rho \beta_T. \]

The latter partial derivative may be calculated via the Clausius-Mossetti equation

\[ \frac{\varepsilon - 1}{\varepsilon + 2} = A \rho \]

for constant \( A \), giving

\[ \left(\frac{\partial \varepsilon}{\partial \rho}\right)_T = \frac{(\varepsilon - 1)(\varepsilon + 2)}{3\rho}. \]

The final equation for the MFP in terms of energy:

\[ l^{-1} = \frac{k_B T \beta_T}{6\pi} \left(\frac{E}{\hbar c}\right)^4 \left[ \frac{(\varepsilon - 1)(\varepsilon + 2)}{3} \right]^2. \]

The scale factor is a unitless user customizable factor that is multiplied to the inverse MFP.

Surface processes¶

Optical photons also have special interactions at material boundaries, specified largely by user-provided material properties. The surface definitions are translated from Geant4 “skin” and “border” surfaces to Celeritas “boundary” and “interface” surfaces, respectively (see Geometry). The “boundary” of a volume is currently defined, from Geant4 input, as a directional property.

Celeritas surface physics currently uses the following heuristic to reproduce Geant4 boundary physics behavior. Given a pair of old→new volume instances P0→P1 corresponding to volumes L0→L1, the surface properties are determined in decreasing precedence by:

The interface surface from P0 to P1
If L1 is the child of L0 (crossing into an “enclosed” volume), then the boundary surface of L1
The boundary surface of L0
The boundary surface of L1
The volumetric material properties of L0 and L1