Optical Stochastic Cooling is a potential candidate of beam cooling techniques for high energy storage rings and colliders. Theoretical study of the damping dynamics of Optical Stochastic Cooling with the transit-time method is presented. We discovered a necessary condition for particle beam bypass in transverse cooling. The required amplification factor and laser power and properties of amplified signal distortion in the cooling section are reported. Alternatively, we also studied the effect of electron cooling on particle beams. Employing electron beam energy modulation, we study the cooling dynamics for ion beams with large momentum spread. The analytical and numerical study of the instabilities and chaos owing to energy modulation of the electron beam is addressed. A method to eliminate a specified betatron harmonic, which can cause the resonance between the beam envelope and the betatron function for high intensity beams, is developed.
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