Matching a FODO cell with cavities inside

[dpe]

Dear all,

I know that "matched" option of twiss_output command produces strange results when a cavity is placed in a FODO cell. Then I'm matching my cell using a couple of markers (before and after) and equating their beta functions value. Do do this I'm varying the initial betas imposed by a TWISS object in front of the cell.
With no cavities the match is perfect.


With RFCA the match is good (if I match only betas, alphas are a little unmatched, but result is fine).


When I tried with a TWLA I got a totally unmatched cell.


I am wondering why this is happening and if there is a way to correct.

Thanks

[michael_borland]

There's a problem with the matrix that is generated for TWLA. It isn't symplectic. For now it should not be used. I'll try to figure it out for the next release.

--Michael

[michael_borland]

Actually, that's not the problem. Since the beam is accelerating the matrix looks odd, that's all.

I'm still not sure what the problem is.

--Michael

[michael_borland]

There are two setup issues: First, EZ is in MV/m, but you gave it a value of 69.2e6, the same as given for VOLT in the definition of the RFCA version. Use EZ="69.2e6 2.94 /". Second, PHASE Is in radians, but you gave 90, presumably meaning 90 degrees. GIve PHASE="pi 2 /" instead.

However, after fixing these problems, the transverse focusing properties of the TWLA seem to be quite different than those for RFCA, which I don't understand given that the beam is quite energetic. I think TWLA must be wrong, so I suggest not using it until I can figure out the problem.

--Michael

[dpe]

Thanks for the replies.

I actually do not need to use a TWLA for my tracks, I tried just to see the result and the first thing I noticed were the strange optics functions which can't be matched.

Also matching the structure with RFCA is not so straightforward, it took me weeks to figure out to use this method. There are a lots of publication where Linacs optics functions are perfectly periodic. I was wondering if they turned off the acceleration, if they can have a symplectic tracking (maybe with less dimensions), if there is a problem with elegant or what else...

[michael_borland]

I suspect that the publications where the linac optics are perfectly periodic are wrong, based on an incorrect matrix. The matrix for the linac structure changes with energy, so the quadrupoles must change too.

The way I test elegant is to track a beam with the same beta functions as the twiss calculation. The betaxBeam and betayBeam columns in the &run_setup sigma file agree very closely with the betax and betay columns from the &twiss_output output flle.


--Michael

[dpe]

The matrix for the linac structure changes with energy, so the quadrupoles must change too.

I used to fix K, the normalized gradient of the quadrupoles with respect magnetic rigidity of the beam. I should obtain the same focussing effect for each energy. If the cavities changes the optical functions in an odd way (as they seem to do, but why, and what do they do in reality?) I'm not able any more to keep them matched with just a couple of quadrupoles per period.

I've been studying accelerators Physics since few months, so please forgive me if I'm not very precise.

[michael_borland]

If you have a cavity that imparts a constant delta energy dE to the beam, the matrix of this cavity will be different depending on the incoming beam energy E0. For example, a zero-length cavity will have R22 = R44 = E0/E1, since the slopes are "adiabatically damped" by the increasing energy.

The end focusing also has an energy dependence, though it tends to zero as E0 goes to infinity.

--Michael

[dpe]

Adiabatic damping interest the emittance of the beam and so also the optical functions, as they are related by the Courant-Snyder invariants. Anyway the focussing effects of the cavities should be nice to me, helping to preserve low optical functions. I may have to vary the normalized gradient of my quadrupoles along the linac to compensate this, but this doesn't seem the case.

But now I wonder if the result that I obtained with RFCAs is correct, and why if I use the "match=1" option in twiss_output, I obtain totally different results with respect to a "manual" match of betas...

[michael_borland]

By default, elegant treats cavities as drifts if matched=1, if order to avoid annoying (small) effects in storage rings when the user includes an rf cavity in the lattice.

You can control this behavior with the cavities_are_drifts_if_matched parameter of &twiss_output.

--Michael