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### Coupling integral for sum resonance

Posted: **22 Mar 2011, 21:03**

by **twatanabe**

Dear Michael and others,

I found the elegant calculated "Coupling integral for difference resonance" in the .twi file.

It would be useful if elegant also calculates coupling integral for sum resonance.

Thank you,

Takahiro

### Re: Coupling integral for sum resonance

Posted: **04 Apr 2011, 11:57**

by **michael_borland**

Takahiro,

Thanks for the suggestion. We'll try to get it in the next release.

--Michael

### Re: Coupling integral for sum resonance

Posted: **24 Sep 2018, 01:30**

by **ChongChong**

Dear Michael and others,

I changed betatron tunes to realize the difference resonance (equal fractional betatron tunes)in order to obtain a round beam. I used "WATCH" to record the data of emittance x and emittance y for tracking particles in the elegant.

But the statistical results show that emittance x is not equal to emittance y, which is not consistent with the theory.

Could you help me solve my doubts?

Thank you,

Chongchong

### Re: Coupling integral for sum resonance

Posted: **24 Sep 2018, 08:34**

by **michael_borland**

Chongchong,

This is probably the result of correlations between the x and y coordinates. When there is strong coupling, the x and y planes are not the correct ones in which to analyze the beam distribution. See A. Wolski, PRSTAB 9, 024401 (2006). You can use the moments_output command in elegant to find the three actual emittances (parameters e1, e2, and e3). It will also give the projected emittances, which are not conserved (they vary around the ring).

You can also try putting in several watch elements at different locations and comparing the results. You should see that the emittances at the various locations vary.

If you continue to have problems, please post your input files.

--Michael