Resonant excitation of relativistic-ion cyclotron orbital motion

A technique is proposed for the excitation of coherent cyclotron motion of ions undergoing a relativistic mass increase. The equations of relativistic-ion cyclotron motion excited by an rf electric dipolar field of fixed peak-to-peak amplitude and a phase that exactly matches the ion cyclotron orbital phase during the excitation process are solved analytically. The resonant cyclotron-motion excitation method is well-suited for bringing ions of low mass-to-charge ratio coherently to a large cyclotron orbital radius for detection or ejection. The method is demonstrated for the excitation of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}_{}^{3+}{}_{}{}^{}$ ions up to about 1% of the speed of light in the cubic ion trap of a Fourier-transform ion cyclotron-resonance mass spectrometer.