Prediction of long term stability by extrapolation

Abstract

This paper studies the possibility of using the survival function to predict long term stability by extrapolation. The survival function is a function of the initial coordinates and is the number of turns a particle will survive for a given set of initial coordinates. To determine the difficulties in extrapolating the survival function, tracking studies were done to compute the survival function. The survival function was found to have two properties that may cause difficulties in extrapolating the survival function. One is the existence of rapid oscillations, and the second is the existence of plateaus. It was found that it appears possible to extrapolate the survival function to estimate long term stability by taking the two difficulties into account. A model is proposed which pictures the survival function to be a series of plateaus with rapid oscillations superimposed on the plateaus. The tracking studies give results for the widths of these plateaus and for the seperation between adjacent plateaus which can be used to extrapolate and estimate the location of plateaus that indicate survival for longer times than can be found by tracking.