A Novel Method for Rigorously Analyzing Beam Loading Effect Based on the Macro-Particle Model

The beam loading effect is a considerable issue for a high average current beam. We apply a novel method without utilizing the specious beam current value to rigorously analyze the beam loading effect in S-band linacs. By tracking every macro-particle's state and using the energy conservation law, power dissipated from the beam is calculated in each cell. In the new particle-based algorithm, the concept of equivalent beam current is proposed. Its value is not constant and it has a small variation through the accelerating structure. Also, we introduce the iteration algorithm as comparison and we find that the two algorithms coincide with each other very well.