Model calculation of amplitudes for FT-ICR ion detection in a cylindrical Penning trap

A Green’s function strategy first proposed by Grosshans et al. is used to calculate the electric charges induced by trapped ions on the 4-fold or 8-fold segmented ring electrode of a cylindrical Penning trap. The ions are assumed to move in the central region of the trap where the harmonic approximation holds. The electric charges induced on each detection segment of the ring electrode are obtained in the form of a triple Fourier series with coefficients that describe the contribution of each frequency combination m ₊ ν ₊+m _? ν _?+m _z ν _z as a function of R ₊, R _?, Z, where ν ₊, ν _?, ν _z are the characteristic frequencies and?R ₊, R _?, Z the corresponding amplitudes of the ion motion. The sideband structure is analyzed and the origin of the sidebands is tracked. Finally, single-electrode, differential, and additive detection are discussed.