Simulations for Ion Traps Methods and Numerical Implementation

Abstract

The cooling of ions in traps and RF ion guides is a powerful tool for providing cooled ion bunches with low emittance and small energy spread which are, for example, needed for high-precision mass measurements at various rare-isotope facilities. This will be outlined in the associated article “Simulations for Ion Traps – Buffer Gas Cooling” by Stefan Schwarz, in which simulations of buffer gas cooling in ion traps and ion guides are discussed in detail. Such numerical simulations are indispensable for designing efficient cooling devices and for a theoretical guidance of related experiments. Here, particular questions to be addressed are, e.g., the optimization of the applied electric and magnetic fields, tests of proposed configurations and beam manipulations, performance optimizations, the explanation of observed unexpected behavior and the influence of space-charge effects. This contribution deals with the basic concepts and the numerical realization of simulations which are commonly used for a theoretical description of various kinds of charged particle systems, like, e.g., ions in traps, ion beams or bunches of ions in accelerator structures or ions in ion sources. To this end the different approaches to the problem are introduced at first in Sect. 2: the direct particle–particle viewpoint taken in the molecular dynamics (MD) simulations and the phase-space picture underlying the frequently used particle-in-cell (PIC) scheme. In a second part, Sect. 3, we then outline the standard numerical techniques for calculating the forces, solving the Poisson equation and integrating the equations of motion which are needed for implementing these simulation methods. Concerning the integration of the equations of motion special emphasis is put in Sect. 3.4 on advanced, non-standard time integration schemes for specific applications like the ion motion in Penning traps or cases where the motion is dominated by a strong homogeneous magnetic field. The