betax and betaxBeam

[Seong-Yeol Kim]

Hello,

I am confused with the fact that why the beta function in Twiss_output and betaxBeam in .sig file are different.
Also I noticed that, from Sx, Sy, beam size is calculated with betaxBeam, not the beta in Twiss parameters.

In the elegant file setup, first I extracted Twiss parameters and emittance using astra2elegant and sddsanalyzebeam from ASTRA output file.
Then, I put these Twiss parameters into the Twiss_output setup. In this case, default order=2. (Even though I set the
default order to be 1, beta values of Twiss_output and the one in .sig file is still different.)

for example,
s (m) betax (m) betay (m)
1.498676e+01 8.014801e-01 9.208712e-01
1.513676e+01 9.293887e-01 1.012960e+00 ,

and,
s (m) betaxBeam (m) betayBeam (m)
1.498676e+01 8.225385e-01 9.195021e-01
1.513676e+01 9.361804e-01 1.021141e+00

Indeed I am wondering why the Twiss parameters calculated from the beam distribution (on tracking) is different from the
Twiss parameters obtained by Twiss_output, and wondering what the difference comes from.
And also I am wondering if I could safely say that the beam size (Sx, Sy) is still valid even if the betaxBeam / betayBeam
value is still different from the one obtained by Twiss_output. Plus if possible, is there a way to make the betaxBeam
to be same as the beta function in Twiss_output?

Thank you!

Seongyeol

[michael_borland]

Seongyeol,

In a linear system, the results from tracking (e.g., betaxBeam) and analysis (e.g., betax) should be very close. However, if there are nonlinearities, e.g., chromatic effects, this may not be true. To give more advice, I would need to see your simulation files.

--Michael

[Seong-Yeol Kim]

Thank you Michael,

For the simulation file, I sent you an e-mail for the lattice and elegant files.
With another beam distribution, I've check that the beta function in Twiss_output and betax / betayBeam is almost similar.
In this case the beam is truncated Gaussian (cut by 2sigma) with some dispersion (I've obatined this distribution also from ASTRA).

However in the case where the beam distribution is almost flattop attached in the mail, the beta function is not same even on the first quadrupole.
I am wondering it is then due to the beam distribution, or to something another reason.


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Maybe I think that it is indeed due to the beam distribution. Since it is not uniform distribution, there should be emittance variation
when the beam is propagating through the beamline. Due to the variation, I think the beta function, beta = sigma^2 / emittance will not
hold the case for the real beam distribution. Therefore, I think it is the reason why the calculated beta function from the beam distribution
is also not same as the value obatined from Twiss_output.

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I understood why there is something different between betax and betaxBeam.
As you mentioned, due to the higher order Twiss parameter calculation and bending magent with CSR consideration,
beta calculated from the beam is different. I just checked with bunched_beam, and both Twiss parameters are perfectly same
if I set the default_order in &run_setup to be 1, and no higher order in bending magnets, and without CSR effects.

I am actually doing the optimization of the beta / dispersion functions of the lattice to get a target beam size.
In this case then I am wondering that I have to run the optimization for betaxBeam, not betax.

Thank you!

Seongyeol

[michael_borland]

Seongyeol,

I checked the files you sent me via email. The issue is that you have significant energy spread in the beam, while also having ORDER=2 on the dipole elements. This leads to chromatic effects in the tracking that affect the beam sizes, and thus the beam-derived lattice functions.

If I set ORDER=1 on the dipoles (and leave default_order=1 in &run_setup, as you have it), I get near perfect agreement, as shown in the figure.

--Michael

[Seong-Yeol Kim]

Dear Michael,

Thank you for your kind help! Now I understood why the beta function is different from the Twiss_output beta function.
According to your explanation, then in real tracking to check the beam size and emittance, I have to focus on the beta function calculated
from the tracking.

Thank you again for your help!
Best regards,

Seongyeol