Dispersion with locally varying spread

[Aamna_Khan]

Hello Michael,

I have confusion about the dispersion definition in .twi and .sig file when local spread changes.

1) LSC kick changes the local spread (from my understanding it doesn't change central momentum): I am doing the simulation for first order so I would guess chromaticity is not an issue here. Could you please guide me how I get the non-zero dispersion at initial drifts and quadrupoles..

2) In the second example, I gave RF kicks (acceleration with no LSC) in a beamline without bends to check the dispersion. Still .sig file gives a non-zero dispersion.

Could you please check if the enclosed files are doing what I want to do correctly?

Thank you in advance.
Aamna

[michael_borland]

Aamna,

I don't see anything fundamentally wrong with your simulations. I think what is happening is that there are higher-order correlations developed in the beam in both cases. Since elegant doesn't look for anything other than linear correlations (e.g., s16, which is related to the dispersion), it can be fooled into reporting a non-zero linear correlation.

In the rf cavity simulation, for example, one can use &analyze_beam to find the effective transport matrix based on tracking. I shows strong third-order terms involving x, x', s, and delta. For example, from the first RFCA element I see large Q1551 and Q1552 terms. These will produce nonzero s16 correlations, which we then interpret (incorrectly) as linear dispersion.

I think the effect is similar for the LSC simulations. One reason these effects are so strong is presumably that your beam is not fully relativistic. For example, if I increase the starting momentum 10x and also increase the gradients 10x, the effects are still present, but much reduced.

--Michael

[Aamna_Khan]

Hi Michael,

Thanks for clearing that simulations are fine. I still wonder, is there any correct way to compute the first-order dispersion with LSC in the presence of bends? I am confused if we have variable s6 along the beamline, does it affect the linear <x*delta> . For example, Andrzej Wolski discussed how a linear map changes in transverse plane when there is a momentum spread variation on page no.: 114-115 in "beam dynamics in high energy particle accelerators" book (there he discussed it in the context of a RF cavity).

Second, I found that dispersion from twiss file is not matching with the R16/Dx from .mat/.sig (tried it for simple 2-3 cases).

Thanks,
Aamna

[michael_borland]

Aamna,

To compute the first-order dispersion in the presence of LSC, the best approach I can come up with is to fit (delta, x) using data from WATCH elements with mode="coordinate". You can use sddspfit to do the fitting, e.g.,

Code: Select all

sddsprocess test.w1 -pipe=out "-define=col,delta,p pCentral / 1 -" | sddspfit -pipe=in test.w1fit -col=delta,x -terms=5 -eval=test.w1eval,num=100
sddsplot -col=delta,x test.w1fit -graph=dot -title=@sddspfitLabel -col=delta,x test.w1eval -graph=line,type=1

As for you second question, the reason you don't get the same dispersion in those calculations is that &twiss_output by default computes the periodic solution. Set matched=0 to get the transport-line solution, which matches the R16 and D quantities.

--Michael

[Aamna_Khan]

Thank you Michael.

Aamna