MODELING COULOMB EFFECTS IN FOURIER-TRANSFORM ION-CYCLOTRON RESONANCE MASS-SPECTROMETRY BY CHARGED DISKS AND CHARGED CYLINDERS

A two-dimensional charged-disk model is proposed to explain Coulomb-induced frequency shifting in Fourier-transform ion cyclotron resonance (FT-ICR) mass spectrometry. This model corresponds more closely to the actual FT-ICR experiment than does the charged-point model,1 which we recently developed. The model consists of a uniformly charged disk of ions of mass m1, whose excited cyclotron motion is perturbed by a second uniformly charged disk of ions of mass m2, whose cyclotron motion is also excited. By looking in a rotating coordinate frame which rotates at the cyclotron frequency of the first disk, it is seen that the second disk creates an average radial force on the first disk which lowers the cyclotron frequency of the first disk. This radial force is numerically evaluated and found to be a function of the cyclotron radius, the ratio of the cyclotron radius to the disk radius, and the charges of the two disks. Unlike the charged-point model, which was flawed by having an infinite average radial Coulomb force, the average radial Coulomb force for the charged-disk model is finite. This average Coulomb force allows the use of formulae which permit characterization of a given set of model parameters in terms of an ’apparent Coulomb distance’, for which a model consisting of point charges with a fixed location in a rotating frame would give the same frequency shift. It is argued that the same ’apparent Coulomb distance’ would apply for a charged cylinder model, which accounts for Coulomb-induced line broadening in addition to Coulomb-induced frequency shifting. It is suggested that the treatment in this paper, together with the use of elongated cells equipped with trapping screens, could permit absolute mass calibrations of FT-ICR spectra.