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This paper has the motivation to understand the role of field inhomogeneties in altering stability boundaries in nonlinear Paul traps mass spectrometers. With the inclusion of higher order terms in the equation of motion, the governing equation takes the form of a nonlinear Mathieu equation. The harmonic balance technique has been used to obtain periodic solutions which represents the transition curves, beta(u) = 0 and beta(u) = 1. A continuous fraction expression, similar in form to the linear case, has also been derived to plot iso-beta(u) lines within the stability region. The expression qualitatively reflects experimental observations in literature related to ion stabilities in nonlinear traps. The role of hexapole and octopole superposition in shifting the stable region as well as ion secular frequencies in nonlinear Paul traps has been discussed using the analytical expression derived in this paper. |
