TESLA Report 2004-13 Calculation of 3D Space-Charge Fields of Bunches of Charged Particles by Fast Summation

The fast calculation of space-charge fields of bunches of charged particles in three dimensional space is a demanding problem in accelerator design. Since particles of equal charge repel each other due to space-charge forces, it is difficult to pack a high charge in a small volume. For this reason, the calculation of space-charge forces is an important part of the simulation of the behaviour of charged particles in these machines. As the quality of the charged particle bunches increases, so do the requirements for the numerical space-charge calculations. In this paper we develop a new fast summation algorithm for the determination of the electric field generated by N charged particles. Applying the nonequidistant Fast Fourier Transform (NFFT) the fast summation requires only O N logN operations. The numerical test cases confirm this behaviour.