Is beta modulation more or less potent than tune modulation?
Todd J. Satogata, Steve Peggs · 2002
It is shown that modulation of a single quadrupole with an amplitude of Delta (kL) causes beta and tune modulations of order Delta beta approximately= Delta (kL) and Delta Q approximately= Delta (kL)/4 pi . If the nearest significant resonance is Delta Q/sub res/ away, it is shown that parametric drive with tune modulation is about 1/(4 pi Delta Q/sub res/) times stronger than with beta modulation. In the nominal case this factor is about five, and it is unlikely to ever be less than one. The direct drive term is Delta Q/sub res// pi Q/sub I//sup 2/ times stronger with tune modulation. This factor is nominally almost 200, and only in pathological situations does it approach unity. Direct drive dominates parametric drive in normal tune modulation conditions. On all counts, beta modulation is much less potent than tune modulation.>