A method of operating an electrostatic trapping mass analyzer, comprising: (a) introducing a sample of ions from a population of ions into a trapping region of the mass analyzer having a central longitudinal axis, the trapping region defined by: an inner spindle electrode having an outer surface that is axially symmetric about the central longitudinal axis and that is symmetric about a central equatorial plane that is perpendicular to the central longitudinal axis; and a pair of outer electrodes (8a, 8b) disposed at either side of the equatorial plane and having respective inner surfaces, wherein the outer surface of the inner spindle electrode and the inner surfaces of the outer electrodes (8a, 8b) are shaped such that a trapping potential corresponding to the trapping field is a quadro-logarithmic potential that is established by application of an electrostatic voltage difference between the inner spindle electrode and the outer electrodes (8a, 8b), wherein an established trapping field within the trapping region is such that ions of the introduced sample of ions are caused to exhibit radial motion with respect to the central longitudinal axis of the trapping region while undergoing harmonic motion in a dimension z defined by the central longitudinal axis, the frequency of harmonic motion of a particular ion being a function of its mass-to-charge ratio, wherein the population of ions is introduced into the trapping region through an injection aperture that is offset from a minimum of a z-axis harmonic potential; (b) superimposing a periodic modulation field onto the trapping field within the trapping region, the modulation field acting to either increase or reduce the harmonic motion amplitudes (34, 38) of the ions by an amount varying according to the frequency of harmonic motion; and (c) acquiring a mass spectrum of the ions in the trapping region by measuring a signal representative of an image current induced by the harmonic motion of the ions; the method CHARACTERIZED IN THAT the periodic modulation field is a multi-frequency periodic modulation field such that the harmonic motion amplitudes of the ions are spread as a function of mass to charge of the ions. (a) introducing a sample of ions from a population of ions into a trapping region of the mass analyzer having a central longitudinal axis, the trapping region defined by: an inner spindle electrode having an outer surface that is axially symmetric about the central longitudinal axis and that is symmetric about a central equatorial plane that is perpendicular to the central longitudinal axis; and a pair of outer electrodes (8a, 8b) disposed at either side of the equatorial plane and having respective inner surfaces, wherein the outer surface of the inner spindle electrode and the inner surfaces of the outer electrodes (8a, 8b) are shaped such that a trapping potential corresponding to the trapping field is a quadro-logarithmic potential that is established by application of an electrostatic voltage difference between the inner spindle electrode and the outer electrodes (8a, 8b), wherein an established trapping field within the trapping region is such that ions of the introduced sample of ions are caused to exhibit radial motion with respect to the central longitudinal axis of the trapping region while undergoing harmonic motion in a dimension z defined by the central longitudinal axis, the frequency of harmonic motion of a particular ion being a function of its mass-to-charge ratio, wherein the population of ions is introduced into the trapping region through an injection aperture that is offset from a minimum of a z-axis harmonic potential; an inner spindle electrode having an outer surface that is axially symmetric about the central longitudinal axis and that is symmetric about a central equatorial plane that is perpendicular to the central longitudinal axis; and a pair of outer electrodes (8a, 8b) disposed at either side of the equatorial plane and having respective inner surfaces, wherein the outer surface of the inner spindle electrode and the inner surfaces of the outer electrodes (8a, 8b) are shaped such that a trapping potential corresponding to the trapping field is a quadro-logarithmic potential that is established by application of an electrostatic voltage difference between the inner spindle electrode and the outer electrodes (8a, 8b), wherein an established trapping field within the trapping region is such that ions of the introduced sample of ions are caused to exhibit radial motion with respect to the central longitudinal axis of the trapping region while undergoing harmonic motion in a dimension z defined by the central longitudinal axis, the frequency of harmonic motion of a particular ion being a function of its mass-to-charge ratio, wherein the population of ions is introduced into the trapping region through an injection aperture that is offset from a minimum of a z-axis harmonic potential; (b) superimposing a periodic modulation field onto the trapping field within the trapping region, the modulation field acting to either increase or reduce the harmonic motion amplitudes (34, 38) of the ions by an amount varying according to the frequency of harmonic motion; and (c) acquiring a mass spectrum of the ions in the trapping region by measuring a signal representative of an image current induced by the harmonic motion of the ions;