Theoretical fractional formulation of a three-dimensional radio frequency ion trap (Paul-trap) for optimum mass separation

Sarkhosh Seddighi Chaharborj,Pei See Phang,Zahra Seddighi Chaharborj,Shahriar Seddighi Chaharborj

doi:10.1177/14690667211026790

Abstract

We investigate the dynamics of an ion confined in a Paul–trap supplied by a fractional periodic impulsional potential. The Cantor–type cylindrical coordinate method is a powerful tool to convert differential equations on Cantor sets from cantorian–coordinate systems to Cantor–type cylindrical coordinate systems. By applying this method to the classical Laplace equation, a fractional Laplace equation in the Cantor–type cylindrical coordinate is obtained. The fractional Laplace equation is solved in the Cantor–type cylindrical coordinate, then the ions is modelled and studied for confined ions inside a Paul–trap characterized by a fractional potential. In addition, the effect of the fractional parameter on the stability regions, ion trajectories, phase space, maximum trapping voltage, spacing between two signals and fractional resolution is investigated and discussed.

Highlights

A brief summary of ion traps and fractional calculus techniques are presented here
Quadrupole ion traps were invented at the beginning of the 1950s1,2,3 by Paul et al, demonstrating to be excellent tools to perform mass spectrometry.4– 10Other applications of quadrupole ion traps include quantum computing, ultraprecise atomic clocks, ion crystals, high–precision spectroscopy, fractional ion traps, and etc.[3,4,5,6,7,8,9,10,11,12]
Experiments show that the cylindrical ion trap has a good resolution so as to perform mass separation of ions

Summary

Introduction

A brief summary of ion traps and fractional calculus techniques are presented here. Ion trapsQuadrupole ion traps were invented at the beginning of the 1950s1,2,3 by Paul et al, demonstrating to be excellent tools to perform mass spectrometry.4– 10Other applications of quadrupole ion traps include quantum computing, ultraprecise atomic clocks, ion crystals, high–precision spectroscopy, fractional ion traps, and etc.[3,4,5,6,7,8,9,10,11,12] the combined (Paul and Penning) trap[13,14] or the Kingdon trap[15] can be successfully used to achieve mass spectrometry with very good results. Keywords Paul–trap, cantor-type, cylindrical coordinate, fractional parameter, fraction ion motion, mass separation Ion motion inside a Paul-trap with fractional potential in the cantor-type cylindrical coordinates is modelled.

Results

Conclusion