Understanding the focusing of charged particle beams in a solenoid magnetic field

The focusing of a charged particle beam in a solenoid is typically explained by invoking the concept of a Larmour frame and using Busch’s theorem. Often, there is some confusion about how a uniform magnetic field of a long solenoid focuses the electron beam because it is generally understood that a uniform magnetic field can only guide charged particles. We perform a simple analysis of the dynamics of a charged particle beam in a solenoid and emphasize an intuitive understanding of some of the interesting features.