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In particle accelerators, particle losses to surrounding components must beminimized. These particles usually have been driven into an undesired "halo"outside the desired distribution before being lost. The processes involved andphysical identification of such halo is an intense research topic especiallywhen the nonlinear space charge effect is taken into account. In order topresent a method, firmly based on the physics of the transient beam state, fordetermining when a particle may be defined as being in a halo, the particularexample of an initially rms matched beam injected into a resonance of analternating-gradient (AG) focusing lattice is studied, in which the resonancebetween the collective mode and single particle motion pushes some particlesinto a halo defined by extending the halo description to the action-angleframe. In this new frame of description, the halo particles can be physicallydefined as those with larger actions affected by the outer quasi hyperbolictori, which contains the halo particles observed in the traditional approacheson projected 2D phase space, as well as some particles still hidden in thecore.

A new description of space charge induced beam halo