Mixed ion beams near transition energy

A simple derivation has been developed which yields the synchronous particle parameters without the tacit assumption of an idealized RF frequency. Where they may be compared, the results obtained are entirely in agreement with those of more familiar derivations, except that a synchronous partner is revealed on the other side of transition. The predicted separation, both radially and longitudinally, of oxygen and sulphur ions as they approach transition are observed effects, and it is the latter which explains why the dominant species is more difficult to eliminate from the mixture.<>