Adiabaticity of the ramping process of an ac dipole

ac dipoles in accelerators are used to excite coherent betatron oscillations at a drive frequency close to the tune. If the excitation amplitude is slowly increased to the desired value and slowly decreased back to zero there is no significant emittance growth. The aim of this article is to study the adiabaticity of the ramping process of an ac dipole as a function of the different parameters involved.