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In this paper we explore the two dimensional system describing trapped ionicsystem in the quadrapole field with a superposition of rationally symmetrichexapole and octopole fields for meromorphic integrability. We use theLyapunov's and Ziglin-Morales-Ramis classical methods for the proofs. Theinaccuracies from the previous such paper have been removed.

Non-Integrability of the Trapped Ionic System II