Magnetic Lens Made of a Single Solenoid for Controlling Bending of Two-Dimensional Ion Beam

The magnetic field inside an ideal solenoid cavity with an arbitrary cross-section is always constant, while it is always zero outside the solenoid. We can make a solenoid lens that can focus a parallel beam to a point behind it by adjusting the curvature of the solenoid circumference. In this paper, we discuss the design of magnetic lenses ranging from simple geometries to the general ones. We discovered that there are an infinite number of curvatures that can be used to focus the parallel beam to a specific focal point. Using this property, we also present the concept of a simple mass spectrometer by measuring the intensity of the ion captured by a detector placed at the focal point. This result is expected to enrich learning material in undergraduate courses, especially for the topic of electricity and magnetism.