Power series expansion of axially symmetric toroidal harmonics for toroidal ion trap

Kotana, AN and Mohanty, AK (2020) Power series expansion of axially symmetric toroidal harmonics for toroidal ion trap. In: International Journal of Mass Spectrometry, 448 .

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Abstract

This study presents a method to obtain power series expansions of toroidal harmonics in terms of radial and axial distances from the trapping circle. In order to obtain the power series expansion of individual toroidal harmonics, three-term recurrence relations are derived, which involve toroidal harmonics of order n−1, n, n+1 and derivative of toroidal harmonic of order n. Using these three-term recurrence relations a systematic procedure is presented to obtain the power series expansion for a toroidal harmonic of arbitrary order, up to the desired number of terms. With this procedure, the power series expansions of toroidal harmonics till order 5 are presented. Verification of this theory was carried out on an arbitrary toroidal ion trap. The potential and the trajectory of a singly charged ion of 78 Th obtained by the power series were compared with those computed using the Boundary Element Method (BEM). The match was found to be very good

Item Type:	Journal Article
Publication:	International Journal of Mass Spectrometry
Publisher:	Elsevier B.V.
Additional Information:	The copyright for this article belongs to the Elsevier B.V.
Keywords:	Power series; Three-term recurrence relation; Toroidal harmonic; Toroidal ion trap; Toroidal multipole coefficient
Department/Centre:	Division of Physical & Mathematical Sciences > Instrumentation Appiled Physics
Date Deposited:	02 Feb 2023 09:29
Last Modified:	02 Feb 2023 09:29
URI:	https://eprints.iisc.ac.in/id/eprint/79751

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