Structural Energy Distribution and Particle Phase Stability Study of Longitudinal Dynamics of a Simple Linear Proton Accelerator

This paper presents the study of longitudinal beam dynamics of a simple linear proton accelerator and simulation results for a model linear accelerator (LINAC) using MATLAB. The study part of the transition energy, particle acceleration, transit time factor, RF factor, and momentum compaction are discussed. For the simulation, the model LINAC is built using unit cells and the unit cell consists of Quadrupole doublet and acceleration cavity. Model LINAC’s basic setup is present and the simulation is based on the single-particle analysis. The robustness of the model LINAC tested to operate varying different parameters like initial arrival phase and input energy. The criteria to measure the robustness of the model LINAC are to check the kinetic energy at the end of the LINAC and the transverse stability of the transfer matrices of each cell. The paper also presents the theoretical analysis of phase stability at both below and above transition energy. The stability of small and larger amplitude oscillations are present and simulation results for different particles each starting with different amplitudes observed, where the large amplitude oscillation falls outside of the separatrix.