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A technique is described which enables high resolution of halo in beam dynamic studies by direct simulation. The method consists in first solving the beam dynamics problem using coarse initial data. The regions of the initial data, which result in beam halo, or extremums in phase space, are identified. The dynamics are resolved by continuing the calculation using initial data points slightly offset from those that result in halo formation, thus filling in the halo structure. The solution is repeated with appropriate scaling of such things as charge per orbit etc. This process may be continued indefinitely. The method can also shed some light on the halo generation in weakly chaotic systems. The scheme is essentially different from the Δf method in that no assumption is made about fo. As an example, a bifurcation in a non-trivial space charge dominated homomorphic problem is resolved self-consistently using minor computational resources, rather than having to perform the calculation for 250 trillion effect...

Nonlinear self consistent high resolution beam halo algorithm in homomorphic and weakly chaotic systems