Uniformization of the transverse beam profile by means of nonlinear focusing method

It has been known that uniformization of a beam with a Gaussian profile is possible utilizing odd-order nonlinear focusing in the beam transport system, and this has recently been employed for uniform beam irradiation. Here, we have theoretically studied uniformization of the transverse beam profile using nonlinear-focusing forces produced by multipole magnets in detail. In the case where the nonlinear field of the multipole magnet is given by an infinite power series, all the odd-order multipole strengths required for uniformization of a Gaussian beam and the extent of the resultant uniform region have been expressed using the Twiss parameters. We have shown the principle of uniformization using even-order nonlinear fields. We have also actually demonstrated the transformation of a beam with an asymmetric distribution into one with a uniform distribution by utilizing nonlinear focusing, especially with the sextupole and octupole fields. The validity of the formulas presented here was confirmed through particle-tracking simulations. A practical method to realize a uniform profile using beam collimation and octupole focusing is also presented.