THEORETICAL MASS AND ENERGY UPPER LIMITS FOR THERMAL IONS IN FOURIER-TRANSFORM ION-CYCLOTRON RESONANCE MASS-SPECTROMETRY

Analytic expressions for the probability of radial or axial loss of thermal ions from a hyperbolic ion trap are developed, as a function of trap dimensions, trapping potential, magnetic field strength, ion mass-to-charge ratio, and ion Boltzmann temperature. These equations are readily evaluated to yield ion cyclotron resonance (ICR) upper mass and energy limits above which a mass-dependent fraction of thermal ions will be lost prior to any ICR excitation event. Non-interacting ions are assumed to be formed initially along the trap z axis with a Maxwell-Boltzmann velocity distribution, and trapped by a quadrupolar electrostatic potential. Under these approximations, the probability of radial ion loss increases strongly and monotonically with ion mass-to-charge ratio and trapping potential, whereas the probability of axial loss is independent of ion mass and inversely related to trapping potential. Both axial and radial ion loss increase with increasing ion thermal energy. For radial ejection (which dominates at high mass-to-charge ratios), an ion "stability" diagram shows boundaries of a constant fraction of ions trapped as a function of ion mass-to-charge ratio and trapping voltage for a given magnetic field strength. Since the electrostatic potential in all common ICR ion traps is approximately quadrupolar near the trap center, the present results can be extended semi-quantitatively to those ICR trap geometries (e.g., cubic, tetragonal, cylindrical, etc.), Elongated or screened traps should significantly extend the upper mass-to-charge ratio limit.