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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)

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closed as off topic by dmckee Feb 13 '13 at 0:12

Questions on Physics Stack Exchange are expected to relate to physics within the scope defined by the community. Consider editing the question or leaving comments for improvement if you believe the question can be reworded to fit within the scope. Read more about reopening questions here.If this question can be reworded to fit the rules in the help center, please edit the question.

As per our FAQ we don't handle computational questions. There is a beta site for Scientific Computation. If you would like I can ask the moderators of that site if they would like me to migrate this there. – dmckee Feb 13 '13 at 0:14
Reposted on SciComp.SE as numerical investigation of stability of motion (confinement). – dmckee Feb 14 '13 at 14:25