# FPGA Implementation of an Efficient Algorithm for the Calculation of Charged Particle Trajectories in Cosmic Ray Detectors

This paper presents an FPGA implementation of an algorithm, previously published, for the the reconstruction of cosmic rays’ trajectories and the determination of the time of arrival and velocity of the particles. The accuracy and precision issues of the algorithm have been analyzed to propose a suitable implementation. Thus, a 32-bit fixed-point format has been used for the representation of the data values.Moreover, the dependencies among the different operations have been taken into account to obtain a highly parallel and efficient hardware implementation. The final hardware architecture requires 18 cycles to process every particle, and has been exhaustively simulated to validate all the design decisions. The architecture has been mapped over different commercial FPGAs, with a frequency of operation ranging from 300 MHz to 1.3 GHz, depending on the FPGA being used. Consequently, the number of particle trajectories processed per second is between 16 million and 72 million. The high number of particle trajectories calculated per second shows that the proposed FPGA implementation might be used also in high rate environments such as those found in particle and nuclear physics experiments.

keywords: Charged particles trajectory, fixed-point representation, FPGA implementation