A new Monte-Carlo simulator for studying particle dynamics in matter - Un simulatore Monte-Carlo per studiare la dinamica delle particelle nella materia

We present a “Monte Carlo” simulator designed to model high-energy radiation sources and radiation transport within matter. The system is implemented in both hardware and software, using commercial National Instruments tools and devices. The software employes a data acquisition board, managed by a Xilinx FPGA module for the sampling of random electronic noise.

The theoretical framework is based on the definition of the phase space of the particles involved into simulation, i.e. photons, electrons and positrons; all treated as point entities according to the semi-classical approximation model for transport.

Radiation particles (both corpuscolar and not) are fully characterized by their position in a 6-dimensional space: 3 Dimensions related to actual position, two angles (spherical coordinates for direction), and kinetic energy. X-ray or Gamma (?) photons have their state characterized in the same way, with the addition of a 3D vector for linear polarization. The choice of radiation particles source and the transporting medium is flexible for the user; the medium can be homogeneous or not.

Each particle is tracked during its journey through phase space: from its staring point within this space to the various interaction events. The state of a particle in phase space is recalculated and updated each time an interaction occurs. The mathematical relations used to compute the new states are an integral part of the model defined for the simulator; these are derived from available literature.

The history of each individual particle, i.e. flight lenght, type of interaction, determination of new state, etc … depends on the range in which a uniformly distributed random number between 0 and 1 falls. The Monte Carlo simulation is performed using an appropriate random floating-point number generator, which is the core of the system.

The programming environment includes a tool implementing multiplicative-congruential algorithm, with a pseudo-random list that recycles every 6.75*10^12 extractions. The generator routine is invoked many times throughout the simulation, approaching the recycling limit. For this reason, we have integrated real time hardware into the project. We employed an analog input channel, assigning an FPGA the task of sampling and quantizing the white-band voltage signal generated by thermal noise, output from a 100 k? commercial resistor. This setup resulted in a physical source of completely random floating numbers on an embedded module, which serves as a distinguishing feature of our system.

The simulation system is now ready for use, and we have shared a demonstration of its correct functionality. A case study has been created in which the transporting medium is the human body (modeled using CT scans) and high-energy particles-sources are those used in medical diagnostic imaging and radiotherapy. We found that the results of our simulations are consistent with data available in literature and experimental cases.

New future applications will be therapeutic planning in medicine, radiation protection, effects of radiation in space systems.