The analysis of cyclotronic integrator in cylindrical coordinates for simulation of Penning ion source of DECY-13 cyclotron

An analysis of Cyclotronic Integrator in Cylindrical Coordinates for penning ion source simulation as a particle mover algorithm with parameters relevant to DECY-13 cyclotron has been carried out. The simulation is done with a typical setup of a Penning ion source simulation using a single negative hydrogen ion. The domain of simulation is a two dimensional axially symmetric r-z plane that is mirrored in the z = 0 plane. The result is then compared with the standard non-relativistic Boris algorithm in cylindrical coordinates for the same set of parameters. The error for both methods is calculated by comparing the components position and velocity vector for each time step with the standard non-relativistic Boris algorithm in cylindrical coordinates but with an infinitesimal time step width. The result shows that while the cyclotronic integrator is generally slower than the standard non-relativistic cylindrical Boris algorithm, it gives a better long term accuracy. For the same step width, it is observed that the numerical damping for particle trajectories are not as significant as the particle trajectories obtained using the standard Boris algorithm in cylindrical coordinates. Thus the integrator is suitable for a Penning ion source simulation which generally requires a relatively long period of simulation.