Rotation Risley-prism scanner appears to be the most promising solution to high-accuracy beam scanning and target tracking. In the paper, some important issues crucial to the function implementation are thoroughly investigated. First the forming law of scan blind zone relative to double-prism structural parameters is explored by a quantitative analysis method. Then the nonlinear relationship between the rotation speeds of double prisms and the change rate of beam deviation angle is presented, and the beam scan singularity is indicated as an essential factor that confines the beam scan region. Finally, the high-accuracy radial scan theory is verified to illustrate the important application owing to the high reduction ratio from the rotation angles of double prisms to the deviation angles of the emergent beam. The research not only reveals the inner mechanisms of the Risley-prism beam scanning in principle, but also provide a foundation for the nonlinear control of various beam scan modes.