Analytic potential in a linear radio-frequency quadrupole trap with cylindrical electrodes

An analytical expression is derived for a radio-frequency ion trap of novel configuration consisting of a four-sectored hollow cylinder enclosed between two end caps. The cylindrical geometry of the sectored trap provides shielding against the buildup of charge and also makes it possible to calculate the potential within the trap by solving Laplace's equation for given boundary conditions. Equations are presented for calculating the time-averaged potential generated by the RF fields, the end-cap potential, and the potential arising from the application of a dc bias on two of the four electrode sectors. It is shown that, near the ends of this trap, the effective potential arising from the RF fields acts to propel ions out of the trap and that the addition of a dc bias on two neighboring sectors generates an inhomogeneous field in the trap which produces a force on the ions along the trap's long axis in a direction dependent on the sign of the bias.