LONGITUDINAL SINGLE BUNCH STABILITY

At high intensity, a short range wake field can distort the beam's pot ential well and thereby change the stationary distribution. It is now known that if this is not taken into account, instability thresholds w ill be incorrectly predicted. A numerical method exists for solving th e linearized Vlasov equation for the self-consistent case, including t he distortion to the stationary distribution, and finding such thresho lds. We have found physical explanations for the eigenmodes and instab ility thresholds predicted in this method. As a result, a much simpler stability criterion has been found. The criterion is simple in that i t depends only on the stationary distribution and does not require sol ution of the linearized Vlasov equation.