Abstract
A brief overview is given of the recent work done by the beam-physics group of Hiroshima University on resonant beam instabilities in high-intensity hadron rings. Emphasis is placed upon two essentially different instability mechanisms, namely, coherent and incoherent resonances that occur respectively in the beam core and in the beam tail. On the basis of a semi-empirical coherent resonance condition, a simple rule is introduced to construct a new type of stability map. The proposed diagram enables one to find the optimum operating region of any circular machine in the betatron tune space very easily and quickly.
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