Trapping criterion for deuterium cluster ions in an accelerator using an accelerating potential wave

The behavior of cluster ions in an accelerating potential well is discussed in terms of a collective accelerator of cluster ions. By studying the time variation of the potential energy and the energy-like quantity of cluster ions, the trapping criterion in the accelerating potential well is obtained in an analytic form, which makes a simple calculation of acceleration efficiency possible for arbitrary distributions of the mass and initial injection phase of cluster ions. For a Gaussian mass distribution and continuous uniform injection, the efficiency amounts to 70%.