Optimum solution of dual-ring double-scattering system for an incident beam with given phase space for proton beam spreading

A systematic method is given for deriving optimum scatterer parameters for the dual-ring double-scattering system for the incident proton beam with the given phase space parameters. This is accomplished by relating it to the known optimum solution for zero-emittance beam. Limitations on the phase space parameters of the beam incident on the first scatterer have been clarified to obtain such valid solutions. It is shown that the dual-ring double-scattering method can be applied to an incident beam with emittance as large as 100–200π mm mrad. The effect of the change of phase space parameters on the lateral distribution has been investigated. It was found that the larger the emittance of the beam, the more sensitive the fluence distribution is to the change of phase space parameters. The effect of the different emittances of the incident beam in x–θ, y–φ spaces is discussed. It is shown that lateral distribution is sensitive to the misalignment of the beam.