Optimization of the Magnetic Field Homogeneity Area for Solenoid Type Magnets

Homogeneous magnetic fields are important requisites in modern physics research. In this paper we discuss the problem of magnetic field homogeneity area maximization for solenoid magnets. We discuss A-model and B-model, which are basic types of solenoid magnets used to provide a homogeneous field, and methods for their optimization. We propose C-model which can be used for the NICA project. We have also carried out a cross-check of the C-model with the parameters stated for the CLEO II detector.