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Quadrupole ion trap with dipolar DC excitation: motivation, nonlinear dynamics, and simple formulas

Tandel, DD and Chatterjee, A and Mohanty, AK (2023) Quadrupole ion trap with dipolar DC excitation: motivation, nonlinear dynamics, and simple formulas. In: Nonlinear Dynamics .

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Official URL: https://doi.org/10.1007/s11071-023-08706-1


We study the dynamics of a trapped ion in a mass spectrometer under the action of both the usual quadrupolar RF and dipolar DC excitation. The relevant governing equation, derived from electrostatic field calculations for realistic geometries, is a classical Mathieu equation perturbed with a constant inhomogeneous term and a small quadratic nonlinearity. An early paper by Plass examined the case without the quadratic term using variation of parameters. Here, we note a significantly simpler particular solution than used by Plass, include the quadratic term, and develop a second-order averaging-based approximation. The averaging results show that a particular underlying simple periodic solution is stable. We then show that a two-frequency approximation matches that solution well for practical purposes. Finally, we present and validate an easy iterative calculation for obtaining that two-frequency solution and quantify the effect of the quadratic nonlinearity.

Item Type: Journal Article
Publication: Nonlinear Dynamics
Publisher: Springer Science and Business Media B.V.
Additional Information: The copyright for this article belongs to the Springer Science and Business Media B.V.
Keywords: Dipolar DC excitation; Harmonic balance; Higher-order averaging; Periodic solutions; Quadrupole ion trap
Department/Centre: Division of Physical & Mathematical Sciences > Instrumentation Appiled Physics
Date Deposited: 25 Jul 2023 05:02
Last Modified: 25 Jul 2023 05:02
URI: https://eprints.iisc.ac.in/id/eprint/82600

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