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.

Figure 1

Excitation amplitude of the ac dipole versus turn number.

Figure 2

Amplitude detunings used in the simulations.

Figure 3

Amplitude of the natural oscillation of the particle normalized to the amplitude of the forced oscillation in the flattop versus the number of turns used to ramp the excitation for negative, positive, and zero amplitude detuning.

Figure 4

Square root of twice the emittance blowup normalized to the amplitude of the driven oscillation with frequency $Q_D,A_0$ versus the turns of the ramp for negative, positive, and zero amplitude detuning.

Figure 5

Square root of twice the emittance blowup normalized to the amplitude of the driven oscillation with frequency $Q_D,A_0$ versus the turns of the ramp for three different values of the chromaticity.

Figure 6

Fourier spectrum of the simulated turn-by-turn particle position during the ramping process of an ac dipole. The natural and the ac dipole tunes are labeled with $Q_x$ and $Q_D$, respectively.