I am trying to find the required specifications of an paul RF trap, in which a proton can be confined.(trap dimensions,voltage frequency and amplitude used, etc). I have to solve the equations of motion numerically because the potential doesn't have a closed form for this specific geometry and equations of motion can not be solved analytically (indeed , only a series solution can be obtained for potential using Legendre polynomials and this series is present in the system of equations of motion) .
for this purpose, I solve this system of ODEs numerically (Runge-Kutta) and see if the ion leaves the trap. you know, I can simulate the motion for a limited time span (typically about some milliseconds at most). So if the ion happen to leave the trap after a longer time span , I can't notice that.
The question is that how and when I can claim that the ion is confined in the trap?(using numerical methods)