Dynamics of charged particles in a solenoid and the accurate determination of the magnetic axis of a solenoid using measured field data.

A fundamental understanding of the theory and measurement procedures for characterizing a solenoid is crucial for making a project cost-effective and achieving the desired performance for its use in a LINAC. This paper attempts to comprehend the beam dynamics of charged particles by considering the conservation of canonical angular momentum, which can take on positive, negative, and zero values. The analytical expression to generate a parallel beam using a solenoid is derived. The effect of the final beam size on the values of a solenoid's spherical aberration coefficient and the position of the minimum beam size with respect to the focal length is studied using electron trajectories. A practical procedure to tune the above two parameters of a solenoid is demonstrated by simply modifying the demountable disks connected at each end. A mathematical model is proposed to accurately determine the axis of a solenoid and the magnetic centre using the measured magnetic field data, which is validated experimentally. Several solenoids, used in the 9.5 MeV 10 kW electron LINAC suitable for sterilizing medical products and food irradiation, have been characterised using this procedure.