Final Focus Spot Size in a Solenoid Focusing System

Abstract

A linear lens can focus a cold beam to a singular point. Unfortunately, this ideal situation would never occur in the real world. Besides nonlinearity of the lens, any deviation of the beam parameters from the ideal beam's nominal beam parameters would lead to nonzero final spot size. In other words, the final spot size of a beam focused by a focusing lens with a given focusing strength depends on its beam parameters, such as the emittance, variations in beam current, energy, envelope and envelope slopes, and nonlinearity of the focusing lens. There are many types of final focusing systems. We consider only the system using a ''thin'' solenoid lens in this notes. Generally, the net focusing force in a solenoid focusing system is not sensitive to the beam current for an emittance dominated beam. For simplicity, we will ignore the space charge forces in the discussion, and focus on the contributions of beam emittance, energy variation and nonlinearity of the lens to the final spot size here.