Focusing characteristics of intense beam solenoid lens

Abstract

In this article, by solving the nonlinear envelope equation of the intense beam in the cylindrical coordinate system, we have obtained the varying relations of the beam radius and the beam divergent angle with the paramedics (the magnetic induction strength in solenoid lens, the characteristic quantity of beam intensity, the beam emittance, the initial beam radius, and initial beam divergent angle). By theoretical analysis for the relations, we have obtained the beam peak radius and beam peak position in solenoid lens, the beam waist radius and beam waist position in the case of perfect focusing. In the ideal focusing condition, the radius of intense beam solenoid lens should not be less than the beam peak radius; the length of the solenoid lens must not be less than the beam peak position; and in order to gain optimum focusing, an optimal length should be selected; the magnetic induction strength must not be less than the threshold for getting a focusing beam through solenoid lens, and its optimum value should be selected so as to obtain the minimum value of beam divergent angle at the exit port for getting an perfect focusing output beam. The conclusions in this article have some guiding significance for the design and operation of the intense beam solenoid magnetic lens.