Image charge-induced ion cyclotron orbital frequency shift for orthorhombic and cylindrical FT-ICR ion traps

Abstract

A coherently orbiting ion packet induces a distribution of image charge on the ion trap electrodes; the resultant electric field from the image charge shifts the ICR orbital frequency of the ions in the ion packet. The effect of image charges upon the cyclotron motion of a trapped ion has previously been modeled for infinite parallel plate and spherical cavity geometries. In other prior work, an analytical method to solve for the charge induced on any of the electrodes of a Fourier transforms ion cyclotron resonance (FT-ICR) ion trap has been presented. In this work, we report approximate analytical solutions for the frequency shift due to the induced image charges for both finite-size cylindrical and tetragonal traps as a function of ion axial and radial position. For a cubic trap, the mass-independent frequency shift at an ICR orbital radius equal to half the trap radius is ≈ 10 −5 Hz for one ion. Thus, image charge-induced frequency shifts in the ppm range can be expected for typical ICR experiments involving 10 3-10 5 ions at low mass-to-charge ratio (60 ⩽ m/z ⩽ 600), whereas the shift can increase to ≈ 1 u for 100 000 singly-charged 3000 u ions at 3.0 T. The image charge-induced shift for a cylindrical trap is higher than for a cubic trap of comparable size. Implications for mass calibration are discussed.