Space-charge dynamics in Orbitrap mass spectrometers

The paper deals with space-charge interactions in the ion population trapped in the OrbitrapTM mass analyzer where the ions perform multiple quasi-harmonic oscillations in the axial direction. The many-particle problem for interacting ions is mathematically complicated and its solution, even numerical, is obstructed by the required precision of one per million to be maintained on a large number (10(5)-10(6)) of oscillation periods. We develop a perturbation method based on the Bogoliubov-Krylov-Mitropolsky theory and derive averaged Hamiltonian equations in perturbations, which describe the evolution of the ions' oscillation amplitudes and phases in so-called slow time. This approach provides a semi-analytical comprehensive model of resonant and nonresonant spacecharge effects and allows fast and accurate numerical computation. Practical mitigation strategies for most deteriorating space-charge effects like coalescence and frequency shifts are considered.