CYCLOTRON ORBITAL RADIUS DETERMINATION IN FOURIER-TRANSFORM ION-CYCLOTRON RESONANCE MASS-SPECTROMETRY

Measurement of the cyclotron orbital radius of a coherently excited ion packet is of fundamental importance in Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometry. First, the measured ICR orbital radius provides a check on the post-excitation cyclotron radius calculated for a given excitation waveform, for determining energy thresholds in collision-induced dissociation experiments. Second, since ICR signal strength is proportional to ICR orbital radius, measurement of ICR orbital radii for ions of different m/z values leads to more accurate ion relative abundances from measurement of relative FT-ICR mass spectral peak areas. Third, combination of the measured ICR orbital radius and the measured ICR signal for an ion trap of a given geometry provides a direct determination of the number of coherently orbiting ions (and in particular the detection limit). Finally, direct knowledge of the ICR orbital radius is essential for experimental tests of various ICR signal damping mechanisms. In this paper, we investigate the measurement of ion cyclotron orbital radius, based on the ratio of the third-to-first harmonic ICR orbital frequency signals in conventional cubic or cylindrical ion traps. The sensitivity of the method to distributions in ICR orbital phase, orbital radius, and axial position is analyzed theoretically. Experimental tests of the method demonstrate that it offers a reliable and accurate means to determine moderate to large ion cyclotron orbital radii. Under optimal experimental conditions (namely, for narrow distributions in phase and axial position of ions in a given coherently orbiting packet), the present radius determination scheme yields a radius that is very close to the square root of the ratio of the average cubed radius to the average radius, i.e., r(meas.) almost-equal-to ([r3]/[r]) 1/2.