Speaker: David Kelliher
Abstract: The RF program in FFAs, freed of the requirement to follow a ramping bending field, can be chosen with great flexibility. It is of interest to determine how rapidly the RF parameters can be varied without leading to an increase in longitudinal emittance. Here, making use of the KURNS 150 MeV FFA, we experimentally investigate adiabaticity by ramping the synchronous phase to zero at varying rates. From the resulting bunch monitor data, longitudinal tomography is used to calculate the emittance before and after the ramp and the results are compared with simulation.
7 replies on “Investigation of the adiabaticity of longitudinal dynamics in the KURNS FFA”
David, these are interesting experiments. I am trying to understand the slides. Slide #7, what is the colour scale? In particular are the darker areas, inside the intense red areas, voids? Likewise in slide #9 it looks like voids and tear-shapes are introduced into the phase space.
As I said, its an interesting question. The adiabatic theorem, as normally used, refers to a slow and continuous change of the focusing parameters with a fixed fixed-point of the focusing. (This covered at great length by Allan J. Lichtenberg in “Phase-space dynamics of particles” Wiley 1969). But you have a different situation. Does the bunch follow a moving fixed point (while focusing params held constant)? Did you try linearizing equation of motion, introducing a time-linear variation of synchronous phase, and transforming to action angle? I would guess the solution as a coherent oscillation with no emittance growth. You would need to add small cubic term sinx=x-x^3/6 to see the growth.
Shane, thanks for your comments and questions. Sorry, I should have included a colour scale. In terms of the bunch monitor signal, the colour ranges from dark blue (zero signal) to dark red (peak signal). I believe the regions you are referring to are dark red and so indicate regions where the bunch intensity is at its highest.
To understand the interesting features you describe on slide 9 it helps to look at the topographic reconstruction on slide 13. The features correspond to localised high density regions in phase space which oscillate around the stable fixed point.
In the experiment the synchronous phase was reduced from 20 degrees to zero as shown on slide 4. Ideally, the RF voltage would have been reduced in such a way that the bucket area is kept constant during this process (in fact it proved simpler to ramp the voltage of the RF amplifier linearly so the bucket are was not exactly conserved). The adiabaticity was calculated from the variation of the synchrotron tune during the ramp where the synchrotron tune was given by the usual expression from the linearised equations to motion. It would be interesting to look at the more involved analysis that you suggest!
Is the bucket area growing or shrinking from slide 12 to 13? By eye I would have said shrinking, but it appears close in any case.
In the tomography on slide 13, you see a clear structure for the 100 turn ramp. Do you see that same structure in the simulations?
If I understand correctly, there are really three phases:
1. Before transition, where the beam is accelerated at constant non-zero phase (20 deg from zero crossing, correct?)
2. Transition, where the beam phase changes from the nonzero phase to zero phase (=zero crossing)
3. Flattop, where the beam remains at zero phase
How do you ensure that the phase of the RF with respect to the beam is actually the desired phase?
Slide 7 indicates there is some synchrotron phase space structure before transition, possibly due to an injection mismatch into the bucket (could be time or energy? Was there any attempt to adjust frequency and timing to reduce that?
When you make the transition longer, does the pre-transition portion simply shorten so that the energies match up?
I’m wondering whether some of what I’m speculating on here is contributing to the emittance growth you see, and obscuring the underlying result from the simulations. On the flip side, maybe you could try to put some of the mismatches into the simulation.
Looks like some of the scatter in the data might be different machine initial conditions (injection parameters, timing) either from shot-to-shot or session-to-session.
I see some wobble in the beam on the waterfall plots even before your experiment starts, which may mess up the results. Ideally you’d somehow want to tune the injection timing or ramp until there is no wobble at that point. (Wobble could be centroid or shape mismatch, they’ll produce time-dependent waterfall features at omega_s and 2omega_s).
Looking at your formula for the adiabaticity parameter on slide 2, the value of 0.1 seems to pretty high to me: that’s a relative frequency change of 0.63 in one period! Should the expression be multiplied by 2*pi (i.e., using frequency in the formula rather than angular frequency)?