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The use of nonlinear lattices with the large betatron tune spreads can increase instability and space charge thresholds by orders of magnitude compared to typical linear accelerator lattices. Unfortunately, strong nonlinear fields create, in general, strong resonances and chaotic motion. This shrinks the dynamic aperture to impractical values, thus erasing all benefits from their use. Previously known examples of stable and regular accelerator motion with special nonlinear lenses were related to one-dimensional motion or round beams. However, no solution has been realized with real 2D transverse magnetic fields to produce stable, close to regular 2D motion with the large dynamic aperture and betatron tune spread comparable to the betatron tune itself. This paper presents possible solutions for such 2D lattices. They consist of straight sections with short linear and nonlinear lenses with transverse magnetic fields

Practical solutions for nonlinear accelerator lattice with stable nearly regular motion