How Does Elegant Calculate Dispersion {etax,etaxp}??

[Zamank]

Hi All,

I am wondering how Elegant goes about calculating the dispersion from a bedning magnet, namely CSRSBEN with or without some E1,E2?

When designing chicane/doglegs, the dispersion never fully quite cancels and I am thinking it has something to do with a discrepancy between my equations (s^2/(2rho)) and Elegant.

Thanks in advance!

[michael_borland]

elegant computes the dispersion from the transport matrix of the elements. The dispersion function in a transport line is the R16 value from the transport matrix from the start of the beamline to the observation point. This can include the effect the dipole edge angles, of course.

For a stand-alone dipole, you have three matrices to concatenate: Edge1*Body*Edge2. You can find the expressions for these individual matrices and work out the full expressions if interest. Wiedemann's book probably has all the relevant expressions. Using a simple equation only gives you an approximate idea of the dispersion and should not be used for detailed design.

--Michael

[jcytsai]

Dear Michael,
By continuing this topic, I have a question about ELEGANT-generated R16. How can I setup a simple chicane, e.g. 4-dipole chicane, with R16 vanishing at both the entrance and the exit, under CSRCSBEND element?

Thanks in advance!
Cheng-Ying

[michael_borland]

Cheng-Ying,

If you look in the elegant examples file, available here,
you'll find a subdirectory called bunchComp. The fourDipoleCSR.lte file in this directory is an example of a four-dipole chicane using CSRCSBEND. Basically, by making the system symmetric, you will guarantee R16=R26=0.

--Michael

[jcytsai]

Dear Michael,

Thank you for your quick reply. I looked at the example you mentioned; R16 vanishes at both entrance and exit. But, after checking the CSRCSBEND element description in the manual, I find it leaves edge effects turned on (in default setting). When turning off this effect, R16 does not vanish anymore. I originally thought edge effect off should be the simplest/ideal case that makes R16 vanishing at both ends. Not sure if I misunderstand something?

Thanks,
Cheng-Ying

[michael_borland]

Cheng-Ying,

That's because a four-dipole chicane made from sector dipoles (equivalent of turning off edge effects) is not achromatic. You have to use rectangular magnets, which have no horizontal focusing.

--Michael

[jcytsai]

Get it! Thanks!