In the world there have been built five reactor based slow positron sources producing very intense beams, of which, the NEPOMUC source generates the highest intensity about 3109 e+/s after updated. The beam intensity depends on the power of the core, the converter material, and the moderator geometry. It is important to have good knowledge of the influencing factors and relevant processes for building a positron source in China Mianyang Research Reactor (CMRR). In this paper, the basic mechanism and several pivotal processes are studied and modeled, including the high energy ray induced fast positron generated in target, the moderation of fast positron to slow positron, the emission of slow positron from surface, the extraction of slow positron from surface to external grid, and finally the focusing and transport by beam optic system. The beam intensity at the end of the solenoid can be deduced as I = Emth 12, where 1 is the slow positron extraction efficiency from moderators, 2 is the efficiency of lens extraction and solenoid transportation, and Emth is the slow positron emission rate from surface. The value of Emth can be expressed as Emth= AP 2L+e+pbmod, where A is the effective surface area of the moderator, P is the generating rate of the fast positron in unit volume, L+ is the slow positron diffusion length, e+ is the branching ratio of surface positron ( 0.25), i.e. the ratio of positrons reaching the surface to that emitted freely, pbmod ( 0.4) is the probability of the emitted moderated positron. Therefore, attention should be paid to the values of P, L+, 2 and A to enhance the beam intensity. P is in proportion to the neutron absorption rate by cadmium, which requires higher neutron flux of incidence. L+ is sensitive to the moderator material and its annealing condition. For the well annealed single crystal tungsten, the value of L+ is about 100 nm, while for that annealed at 1600 ℃, it decreases to only 40 nm. The value of 1 is related to the moderator depth/width ratio, the extraction voltage, and the moderator back layout. Although deeper ring can enlarge the moderator area A, the average extraction efficiency 1 decreases obviously. Considering the product of 1 and A, the recommended depth/width ratio is 3 : 1. Validations are performed by employing two types of experimental results, including several isotope slow positron sources and the PULSTAR reactor based source. The calculated efficiencies of isotope sources match well with the experimental measured results, which verifies our basic model and parameters. With these parameters and models, the intensity of PULSTAR reactor based positron source at system exit is calculated to be 5.8108e+/s, which matches well with the reported measured value of (0.5-1.1)109e+/s. Some suggestions are made and will be considered in our future design of positron source.