Calculation of 3D Space-Charge Fields of Bunches of Charged Particles by Fast Summation [chapter]

G. Pöplau, D. Potts, U. van Rienen
2006 Mathematics in Industry  
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
more » ... s 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 log N ) operations. The numerical test cases confirm this behaviour.
doi:10.1007/978-3-540-32862-9_34 fatcat:5mq6jq5qijd2feiydqrqe74ip4