Paul trap: axial ejection by auxiliary radio frequency voltage connection to the end-caps or by pure dipole field

The ion motion during resonant ejection from Paul traps has been described by simple expressions. They were derived for a supplementary radio-frequency voltage applied as a dipole field or connected to the trap end-caps. These expressions were derived for the ion axial motion by using Mathieu functions of fractionary order and perform well in the operating parameter range known as ensuring good mass resolutions. For ions uniformly distributed in the phase space, peak shapes were calculated by a computer program.