AbstractThe conventional static electric potential used to trap ions fro fourier‐transform ion cyclotron resonance (FTICR) mass spectrometry has been replaced by a low‐amplitude [as low as Vac≈︁0.5 V for N] alternating (17.5kHz) electric field applied to the end caps of an ICR ion trap. Ion z‐motion is then governed by a Mathieu equation, whose solution leads to a z‐stability diagram for which optimal results are obtained at z‐stability parameter, qz = 4qλV ac/(mω2)≈︁0.5, in which m/q is the ion mass‐to‐charge ratio, Ω is the RF frequency, and λ=2.7737/d2 for a cubic trap of edge length, d. A triangular waveform appears to be more effective than sinusoidal modulation. We demonstrate experimentally three major additional advantages of RF trapping for FTICR mass spectrometry: (a) both positive and negative ions may be trapped and detected simultaneously; (b) Magnetron motion is eliminated, along with the electrostatic radial field‐induced ICR frequency shift and sidebands; and (c) mass calibration follows a simpler law (m=a/v, in which a is a constant and v is the measured ICR orbital frequency) than for electrostatic trapping (m=a/v+b/v2, in which a and b are constants). All prior FTICR mass spectrometric capabilities are preserved, except that (as in an RF‐only quadrupole ion trap) optimal sensitivity is observed only for 0.4⩽qz⩽0.7, so that the mass‐to‐charge ratio range for a single FTICR mass spectrum is limited accordingly.