With a three-dimensional (3D) quadrupole ion trap running in a Fourier transform operating mode, the detected signal is an image of the collective motion of the confined ions. Consequently, it is assumed that the image signal is the sum of the axial trajectories of the simultaneously confined ions. The resulting frequency spectrum after Fourier transformation comprises frequency peaks at the axial secular frequencies of the confined species according to their mass/charge ratio. With a singly confined species, the maximal amplitude of the image signal is proportional to the amplitude of the secular axial frequency peak. The matrix method is employed to express the axial trajectory sampled at the confinement field period. In that case, the expression of the image signal, as well as its maximal amplitude, is calculated as a function of the trap operating conditions and initial axial positions and axial velocities of the ions. The initial position and velocity distributions are connected to the injection mode. With the steady ion flow injection mode (SIFIM) and an initial phase of the confinement field equal to kπ, the maximal amplitude of the image signal is proportional to either the sum of the initial axial positions or the number of confined ions and the mean value of the initial axial positions. By simulation, amplitude fluctuation of the frequency peak is then calculated for a number of ions ranging between some tens to some thousands of ions injected by SIFIM. The peak amplitude fluctuations induced by the fluctuations of the number of ions are seven times greater than those induced by the fluctuations of the distribution of the initial axial positions.
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