ANALYTIC POTENTIAL IN A LINEAR RADIOFREQUENCY QUADRUPOLE TRAP WITH CYLINDRICAL ELECTRODES

We have analyzed a linear radio-frequency ion trap of finite length employing a four-sectored hollow cylinder enclosed between two end caps. Solutions to Laplace's equation determine the effective potential inside the trap due to the rf trapping field, the static confining potential from dc-biased end caps, and the potential arising when a dc bias is present on the cylinder sectors. The finite length of a linear trap results in field distortion at the trap ends due to fringing effects. We have demonstrated that near the ends, the effective potential arising from the rf fields acts to propel ions out of the trap. We have further shown that the addition of a dc bias on two neighboring cylinder 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. An exact analytic determination of the potential can be used to determine the profile of the trapped ion cloud.