A six-dimensional (6D) phase-space is formed by the positions (x,y,z) and the corresponding momenta (px,py,pz) of the particles. All particles in a beam occupy a finite volume in the 6D phase space. It is often desirable to manipulate the phase-space of a particle beam into the most suitable distribution for a particular application. For example, a transversely symmetric (round) electron beam can be made flat for applications in linear colliders, or certain types of accelerator-based light sources with planar radiation devices. In this minicourse, we will discuss the principles of beam 6D phase-space manipulations which include the round-to-flat beam transformation, and transverse-longitudinal phase-sapce exchange etc.. The experimental demonstrations of these techniques will also be presented.
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