Crystal LabFerrara · UniFe & INFN

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Simulation

Crystal physics in Geant4

Channeling, coherent radiation and pair production in oriented crystals, simulated in Geant4 and in our own codes.

The physics.

Planar channeling in the continuous potential of the crystal planesThe transverse potential energy of a positive particle between atomic planes forms wells, highest at each plane. A particle whose transverse energy is below the well depth is trapped and oscillates inside one channel: it is channeled. One with more transverse energy crosses the planes: it is over the barrier. U0 over the barrier: E⊥ > U₀ channeled: E⊥ < U₀ x dashed: atomic planes U₀ ≈ 20 eV for silicon (110) planes
Transverse potential energy between silicon planes. A particle below the barrier is channeled; one above it crosses the planes.

Geant4, the toolkit used to sim­u­late de­tec­tors and beam lines through­out par­ti­cle physics, treats matter as amor­phous, with atoms placed at random. In a crystal this fails when­ev­er a par­ti­cle travels close to a plane or an axis, where it feels the av­er­aged, con­tin­u­ous po­ten­tial of many atoms at once.

We follow each par­ti­cle in that con­tin­u­ous po­ten­tial, step by step along its tra­jec­to­ry. Compar­ing its trans­verse energy with the depth of the well tells whether it is trapped between planes (chan­neled), cross­ing them over the barrier, or re­flect­ed by a bent plane; in­co­her­ent scatter­ing on nuclei and elec­trons, which changes the trans­verse energy, is added along the way.

The radia­tion of an ultra­relativistic par­ti­cle on such a curved tra­jec­to­ry is com­put­ed with the Baier–Katkov quasi-clas­si­cal formula, which in­cludes the recoil of the emis­sion; the same ap­proach gives co­her­ent pair produc­tion by photons. These models, first written in our codes CRYSTALRAD and RADCHARM++, are now part of Geant4 as G4Channel­ingFastSimModel, G4BaierKatkov and G4Co­her­entPairProduc­tion, so any Geant4 user can sim­u­late ori­ent­ed crys­tals in a full setup. Two members of the group belong to the Geant4 Collabora­tion.

What we have shown.

Two group members belong to the Geant4 Collabora­tion. We im­ple­ment­ed channel­ing, co­her­ent radia­tion and co­her­ent pair produc­tion in Geant4 (G4Channel­ingFastSimModel, G4BaierKatkov, G4Co­her­entPairProduc­tion), build­ing on our CRYSTALRAD and RADCHARM++ codes.

Geant4

Channeling, Baier–Katkov radiation and coherent pair production in oriented crystals, implemented as a Geant4 simulation model.

J. Korean Phys. Soc. 83 (2023)

Python tool

Reads Geant4 simulations step by step and compares each particle’s energy with the channel potential, to tell which coherent effect is at work.

Nucl. Instrum. Methods A 1074 (2025)

Read first.

  1. Geant4 simulation model of electromagnetic processes in oriented crystals for accelerator physicsSytov A., Bandiera L., Cho K., Hwang S., et al. · J. Korean Phys. Soc. 83 (2023)
  2. Simulation code for modeling of coherent effects of radiation generation in oriented crystalsSytov A.I., Tikhomirov V.V., Bandiera L. · Phys. Rev. Accel. Beams 22, 064601 (2019)
  3. RADCHARM++: A C++ routine to compute the electromagnetic radiation generated by relativistic charged particles in crystals and complex structuresBandiera L., Bagli E., Guidi V., Tikhomirov V.V. · Nucl. Instrum. Methods B 355 (2015)
  4. A novel tool for advanced analysis of Geant4 simulations of charged particles interactions in oriented crystalsNegrello R., Bandiera L., Canale N. … Fedeli P., Guidi V., Mazzolari A. et al. · Nucl. Instrum. Methods A 1074 (2025)
  5. MBN explorer atomistic simulations of 855 MeV electron propagation and radiation emission in oriented silicon bent crystal: theory versus experimentHaurylavets V.V., Leukovich A., Sytov A. … Bandiera L., Mazzolari A., Romagnoni M. et al. · European Physical Journal Plus 137 (2022)

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