Effect of the ion distribution over longitudinal velocities on the efficiency and separating parameters of the ICR method of isotope separation

In the context of the ICR method of isotope separation, resonance RF heating of the ions in an electric field propagating along a constant magnetic field while simultaneously rotating in the direction perpendicular to it is calculated in a linear approximation. The analysis is carried out for two types of the initial ion distribution function over longitudinal velocities: a function proportional to the first power of the velocity in the range of low velocities and a shifted semi-Maxwellian distribution function. The distribution function of the ions over transverse velocities is calculated under the assumption that their initial distribution over transverse velocities is Maxwellian. The ion fluxes onto the collector plates are estimated by integrating the corresponding ion distribution functions over the allowed range of the longitudinal and transverse velocities and the transverse coordinates of the guiding centers of the ion trajectories in front of the extractor. In the first part of the paper, calculations are carried out for a model binary mixture of isotopes with mass numbers of 6 and 7. The effect of the shape of the ion distribution function over longitudinal velocities on the heating efficiency and on the concentration of the target isotope ions at the collector, as well as the effect of the longitudinal ion temperature on the width of resonance curves for the ion heating efficiency, is investigated. In the second part, a study is made of the selectivity of heating of isotope ions in a gadolinium plasma, in particular, the effect of the longitudinal magnetic field on the selectivity of heating of neighboring isotopes with atomic masses of 156, 157, and 158 is examined.