Fragment ion spectra are acquired in Kingdon ion traps that have a potential well for harmonic oscillations of the ions in the longitudinal direction and in which the ions can oscillate radially in a plane between two or more inner electrodes. Metastable ions, preferably produced by laser desorption, are introduced into the Kingdon ion trap close to the minimum of the longitudinal potential well and stored there locally for a predetermined time period. Excess internal energy in the metastable ions causes most of the ions to decompose ergodically to fragment ions. Then the fragment ions and any remaining analyte ions are excited to execute harmonic oscillations in the longitudinal potential well. The harmonic oscillations are measured as image currents, from which a high-resolution mass spectrum of the fragment ions can be calculated.