Theory of Collision-Broadened Ion Cyclotron Resonance Spectra

Abstract

A formalism for calculating collision-broadened ion cyclotron resonance spectra is developed in detail. The Boltzmann transport equation describing the time variation of the arbitrary function of ion velocity X (v) is extended to include resonant charge transfer. Then with X (v) =v and X (v) =v2, equations describing, respectively, the velocity and energy of an average particle are developed. The solution of these equations is used to obtain the power absorption of the ions from the observing radio-frequency electric field. The effects of collisions are treated in terms of specific ion—molecule interactions. The equations of motion for a mixture of ions, A and B, are coupled by the collision term which accounts for the charge-transfer process A++B⇄A+B+. As numerical examples the collision frequencies are evaluated for the rare gases and used to calculate absorption spectra for Ar+ in Ar and mixtures of He and Ne isotopes. The formalism permits the straightforward examination of the effects of electric-field strength, pressure, and temperature on the line shapes.