Paper  Title  Page 

WEO2C06  A New Paradigm for Modeling, Simulation, and Analysis of Intense Beams  534 


Currently when the effects of space charge on a beam line are calculated the problem is solved using a particle in cell method of advancing a large number of macroparticles. If quantities such as space charge induced tune shifts are desired it is difficult to determine which of the many variables that make up the beam is the cause. The new method presented here adds the effects of space charge to a nonlinear transfer map, this allows us to use normal form methods to directly measure quantities like the tune. This was done using the code COSY Infinity which makes use of differential algebras, which allow the direct calculation of how the tune depends on the beam current. The method involves finding the high order statistical moments of the particles, determining the distribution function, and finally the potential. In order to advance the particles as accurately as possible a fast multipole method algorithm is used. In this talk we present the new methods and how they allow us to follow the time evolution of an intense beam and extract its nonlinear dynamics. We will also discuss how these methods can improve the design and operation of current and future high intensity facilities. 

