Sextupole magnet for correction of aberration with low energy spread

[Seong-Yeol Kim]

Dear Michael,

Hello, I am currently studying the correction of the aberration using the sextupole magnet.
For this study I used dog-leg achromat, and I did the optimization of the chromatic amplitude (Wx and Wy) and second-order dispersion (T166 and T266) using two pairs of the sextupole magnets.

In this case, what I found is that using the sextupole magnet gives me even worse emittance compared to the case without using them, if the beam energy spread is low enough (~0.1 %).
However, when I increased the energy spread to be 1 %, aberration seems to be corrected.

For the comparison, 1) if the energy spread is 0.1 % where the initial emittance is 1.936 mm mrad,
enx without sext: 1.942 mm mrad
enx with sext: 2.048 mm mrad

2) If the energy spread is 1.0%,
enx without sext: 126 mm mrad
enx with sext: 3.46 mm mrad

I am trying to understand why the emittance growth is even worse with the sextupole magnets, if the beam energy spread is low.
I was wondering if it is mainly due to the nonlinearity of the sextupole magnet (is the nonlinearity dominated in this case?).
Either that, I wonder this is due to some problems in the setting of the input script (matrix order, or mis-placed sextupole magnet).

In addition, is there a way to reduce the aberration using the sextupole with low energy spread and with extreme optics, like the maximum beta function along the transfer line is very large (i.e., > 200 m) ?

Please find attached file for the input script (in the case without sextupole magnets, I simply turned them off).
Thank you for your kind help!

Seong-Yeol

[michael_borland]

Seong-Yeol,

I don't see a huge difference between the cases with and without energy spread. When the sextupoles are on, I do see a noticeable increase in emittance. I guess this is from the T111 matrix element, which becomes very large when the sextupoles are on.

--Michael

[Seong-Yeol Kim]

Dear Michael,

Thank you for your kind help and suggestions for the analysis!

As a matter of fact, I checked with the energy spread of 0.1 % and 1 %, and there was significant reduction of the emittance increasing.

Anyhow, following your analysis, I think I will have to take a closer look at the second order matrix variation with energy spread // and large beta function to understand why the sextupole magnet does not work well with small beta function and low energy spread (if it is natural situation...).

Thank you for your suggestions again!
Best regards,

Seong-Yeol