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The quasi-isochronous linear non-scaling FFA (like EMMA) has a cell time-of-flight that varies like a parabola with energy.  So that means you could get both positive and negative R56 within a single doublet cell of just two magnets.  Perhaps not as large in magnitude as you want, though.

I think you are corect that it might not give enough of a range in R56. We'd also need more magnets to introduce and close the dispersion before and after the R56 adjustment.

Hi Kay, nice talk! Couple of questions:

1. why not use an RF cavity (probably a stupid question) to do longitudinal phase space manipulations?

One reason is that one of the attactions of using LWFA is that you replace the accelerating RF cavities; so introducing a cavity for chirp adjustment may seem counter productive. Another issue is the very high frequency that would be required as the bunches are only 1-10 fs long.

2. do you worry about what looks like quite a lot of longitudinal emittance growth?

For lengthening the bunch (promoting FEL radiation) I think it wouldn't be too much of a problem as the slice emittance will still reduce. However, I do think this lengthening will affect how well you can get the whole bunch to radiate coherently if you're going the other way and trying to shorten it (promoting CSR), so it could definitely be a problem for that scheme.

The longitudinal emittance growth looks to me like it's caused by a nonlinear coupling to the transverse plane. The initial beta function of the beam would lead to a large time of flight dependence on transverse amplitude over a relatively short space. I don't know how well you are matched to that beta function at the beginning of your line, but you then rapidly increase the beta function to something over the order of 100 m (4 orders of magnitude higher!) which will inevitably give even more chromaticity.

Yes, you're right. If we look at the bunch at the end and label each electron by its initial transverse momenta the ones with least (transverse momenta) end up at the front of the bunch and those with the most trail at the back because they have taken a longer path through the magnets.
The beta function at the start is quite challenging to control; we want strong focusing as close to the plasma exit as possible which is why I looked at PMQs because these can be inside the vacuum chamber next to the plasma source. The first magnet is only 5 cm away from the plasma exit (and may need some shielding to protect it from stray particles). With two adjustable PMQs with maximum fields of 100T/m this is the best I could achieve. Perhaps quadrupoles with higher fields could control the divergence more quickly? Although, I think to achieve higher fields would require a different design to the ZEPTO quads.

Nice talk! You may have mentioned somewhere, but can you measure the chirp and to what accuracy?

I don't think anyone has made this measurement yet! It would be very cool to be able to do it.
One way might be to compare the radiation produced from each R56 case to simulation. I think the challenge would be ensuring reproducibility of the electron bunches between runs.

@Dejan Trbojevic In the live session you mentioned a beamline I should look into that had a similar challenge of adjusting R56. Can you remind me which one? Thanks

I think he was referring to the CBETA splitter lines. In fact they were more challenging in the sense that we needed to get as much as 25 cm in a roughly 10 m long beamline, and that 25 cm was typically in the direction opposite to the "natural" direction for R56. Furthermore, the lines were also responsible for betatron matching, the geometry was not adjustable, and there was only one extra quadrupole degree of freedom. I can send you a lattice file (Bmad), but I'm not sure it would be particularly helpful for your task.